mm-4306 === Subject: Re: All positive integers are equal. Dude, you are a wasted effort as far as trying to get along with. How could you possibly know? You decided to attack me immediately, twice without provocation. > You did >in fact tell me to stay away from mathematics, on two separate occasion, yet >you now deny it. Don't force me to cite you.....you know you said it. I can't force you to do anything, especially understand what is written (as opposed to what you insist on reading into it). >Again, for the last time, I urge you to be a gentleman, You are in no position to urge me to do such a thing. You have behaved like an arrogant spoiled little brat, without provocation, towards me. So you can get off the high horse whenever you want. >You should watch Dr. Phil and consider some anger management counseling. >This is not meant as a put-down; I really think you need help. You should stop looking into a mirror and pretending you are talking to other people. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: Complete solution manual in PDF format ....only $6.50usd(each) > And Practice 2nd edition by Theodore S. Rappaport. How I can pay money > and get solution by paypal. Jerry On May 15, 8:07 am, cheapestsolut...@hotmail.com Don't post replies here i only accept paypal,if you have credit card do sign up for new account at (www.paypal.com) I have the solutions manual in electronic format for the following textbooks. They include solutions to the problems in the text. Payment is through Paypal for the amount of US $6.50 each. When sending payment ,please mention which solution manual you want and the email to send the file to, the file will be sent within 24 hours as the payment received.As soon as the payment received, a download link for the solution manual will be sent to your email address Email me at cheapestsolut...@hotmail.com Advanced engineering Mathematics 2nd Edition by Zill,Cullen > Advanced Engineering Mathematics 9th Edition by Erwin Kreyszig > Advanced Modern Engineering Mathematics 3rd Edition by Glyn James > An Introduction To Signals And Noise In Electrical Communication 4th Edition by A. Bruce Carlson, Paul B. > Analytical Mechanics 7th Edition by Fowles > Applied Numerical Analysis 6th Edition by Curtis F. Gerald & Patrick > Applied Statistics And Probability For Engineers 3rd Edition by Douglas C. Montgomery > Applied Strength Of Materials 4th Edition by Mott > Automatic Control Systems 8th Edition by Kuo & Golnaraghi > Basic Engineering Circuit Analysis Circuits 2 8th Edition by Irwin(chapter 11 and 13 missing) > Calculus 5th Edition by James Stewart > Calculus Early Trancendentals 5th Edition by James Stewart > Classical Dynamics 5th Edition by Thornton > Communication Systems 4th Edition by Simon Haykin > Control Systems Engineering 4th Edition by Nise > Design And Analysis Of Experiments 6th Edition by Montgomery > Design Of Machinery 3rd Edition by Robert L. Norton > Device Electronics for Integrated Circuits 3rd Edition by Muller and Kamins > Digital And Analog Communication Systems 7th Edition by Leon W. Couch > Digital Communication 4th Edition by Proakis > Digital Communications: Fundamentals And Applications 2nd Edition by Bernard Sklar > Digital Image Processing 2nd Edition by Rafael C. Gonzalez > Digital Signal Processing 3rd Edition by Sanjit K.Mitra > Digital signal Processing 3th Edition by Proakis > Discrete Time Signals 2nd Edition by Alan V.Oppenheim > Electric Circuits 6th Edition by Nilsson > Electric Circuits 7th Edition by Nilsson > Electric Machinery Fundamentals 4th Edition by Stephen J. Chapman > Elementary Differential Equations 8th Edition by Boyce > Engineering Circuit Analysis 6th Edition by Hayt, Kemmerly, Durbin > Engineering Electromagnetics 6th Edition by William H. Hayt Jr > Engineering Fluid Mechanics 7 Edition by Crowe > Engineering Fluid Mechanics 8th Edition by Crowe > Engineering Mechanics Dynamics 10th Edition by R.C.Hibbeler > Engineering Mechanics Dynamics 11th Edition by R.C.Hibbeler > Engineering Mechanics Statics 10th Edition by R.C.Hibbeler > Engineering Mechanics Statics 11th Edition by R.C.Hibbeler > Engineering Mechanics Statics 4th Edition by Bedford > Engineering Mechanics Statics 5th Edition by Meriam > Engineering Mechanics Dynamics 4th Edition by Bedford & Fowler > Engineering Mechanics: Dynamics 5th Edition by Meriam, Kraige > Feedback Control of Dynamic Systems 4th Edition by G. F. Franklin, J. D. Powell, A. Emami > First Course In Probability 7th Edition by Sheldon Ross > Fluid Mechanics 5th Edition by White > Fluid Mechanics with Engineering Applications10th Edition by Finnemore > Fundamentals of Differential Equations 6th Edition by Nagle Saff Snider > Fundamentals Of Electric Circuits 2nd Edition by Charles Alexander > Fundamentals Of Engineering Thermodynamics 5th Edition by M. J. Moran & H. N. Shapiro > Fundamentals of Fluid Mechanics 4th Edition by Munson Wiley > Fundamentals Of Fluid Mechanics 5th Edition by Munson Wiley > Fundamentals Of Heat And Mass Transfer, 5th Edition by F. P.Incropera > Fundamentals Of Logic Design 5th Edition by Charles H. Roth Jr. > Fundamentals Of Machine Component Design 3rd Edition by Robert C. Juvinall And Kurt > Fundamentals Of Physics 7th Edition by David Halliday And Robert > Fundamentals Of Thermal-Fluid Sciences 2nd Edition by Cengel > Fundamentals Of Thermodynamics 6th Edition by Richard Sonntag > Heat Transfer 2nd Edition by Cengel > Introduction to Algorithms 2nd Edition by Thomas H. Cormen > Introduction To Electric Circuits 6th Edition by Dorf, Svoboda > Introduction To Electric Circuits 7th Edition by Dorf, Svoboda > Introduction To Electrodynamics 3rd Edition by Griffiths > Introduction to Fluid Mechanics 6th Edition by Fox, McDonald & Pritchard > Introduction to Linear Algebra 3rd Edition by Gilbert Strang > Linear Algebra 3th Edition by Otto Bretscher(complete) > Linear Algebra And Its Applications 3rd Edition by David C. Lay > Linear Systems And Signals 1st Edition by Lathi > Materials Science And Engineering 6th Edition by William D. Callister,Jr. > Matrix Analysis and Applied Linear Algebra by Meyer & Siam > Mechanical Engineering Design 7th Edition by Shigley > Mechanics Of Materials 3rd Edition by Beer Johnston > Mechanics Of Materials 5th Edition by Gere > Mechanics Of Materials 6th Edition by Gere(chapter 6,8,10 missing) > Mechanics Of Materials 6th Edition by R.C.Hibbeler > Mechanics Of Solids by C. T. F. Ross > Microelectronics - Digital and Analog Circuits & System by Millman > Microelectronics Circuits 5th Edition by Adel S. Sedra, Kenneth C. Smith > Miller&Freund's Probability And Statistics For Engineers by Richard Arnold Johnson > Modern Control System 9th Edition by Drof, Bishop > Modern Digital and Analog Communications Systems by Lathi > Numerical Methods 3th Edition by Doug Faires > Partial Differential Equations with Fourier Series And Boundary Value Problems 2nd Edition > Physical Chemistry 7th Edition by Peter Atkins & Julio de Paula > Physics For Scientists And Engineers 3rd Edition by Douglas C. Giancoli > Physics volume 1 & 2 by David halliday > Principles And Applications Of Electrical Engineering 4th E (Rizzoni) > Principles of Communication 5th Edition by Zeimer > Probability & Statistics For Engineers & Scientists 3rd Edition by Anthony Hayter > Quantum Mechanics 2nd Edition by David Griffiths > RF Circuit Design: Theory & Applications by Ludwig, Bretchko > Sears and Zemansky's University Physics 10th Edition > Semiconductor Device Fundamentals 1st Edition by Robert F. Pierret > Semiconductor Physics And Devices 3rd Edition by Neaman > Serway And Jewett's Physics For Scientists And Engineers 6th Edition Volume 1 by Ralph > Signals and Systems 2nd Edition by Alan V. Oppenheim, Alan S. Willsky > Signals and Systems by M.J.Roberts > Signals, Systems and Transforms 3rd Edition by Oppenheim > Solid State Electronic Devices 6th Edition by Ben G. Streetman > Solid State Electronics Devices 5th Edition by Ben G.Streetman > Statics 7th Edition by Beer > Structural Analysis 5th Edition by Hibbeler > System Dynamics 3rd Edition by Katsuhiko Ogata > The Science & Engineering Of Materials 4th Edition by Donald R. Askeland > Thermodynamics An Engineering Approach 5th Edition by Cengel Boles > Thomas Calculus 10th E Early Trancendentals by Thomas > University Physics 11th Edition by Young and Freedman > Wireless Communications: Principles And Practice 2nd edition by Theodore S. Rappaport > I need Solid State Electronic Devices 6th Edition by Streetman. Do you accept paypal. I can complete the transaction this afternoon if you could get it to me by tommorrow afternoon.- Hide quoted text - > - Show quoted text -- Hide quoted text - - Show quoted text - This is spam you can download all this at torrent !!!!!!!!! spam === Subject: Re: equation+curve === Subject: Re: equation+curve On Sat, 11 Aug 2007 11:22:09 EDT, Steven Bran The equation of the line with slope m through the point (x1, y1) is y - y1 = m (x - x1) In the first two problems, you're given x1 and y1. You need to find the slope m. To do that, you need to find the derivative y' = f'(x) and then find the slope of the tangent line at (x1, y1), which is the value m = f'(x1). In the first problem, f(x) = sin(x) and (x1, y1) = (0, 0) f'(x) = cos(x) At x = x1 = 0, m = f'(0) = cos(0) = 1 The third problem is slightly different in that you're not given y1. That's no big deal since y1 = f(x1). === Subject: Re: equation+curve I know the answers but I don't know how to get there. === Subject: semi-popular mathematics what are your favorite books for building intuition? Prime Obsession by Derbyshire Road to Reality by Penrose Trigonometric Delights by Maor Millenium Problems by Devlin === Subject: lecture notes i am compiling a list of books and notes. i wonder if there would be interest in high school and lower division. my own interest is in upper division e.g. algebra, analysis, graph theory. === Subject: Re: Darrell where is your proof? > Yes is not an answer! he is likely awaiting your counterexample. === Subject: Re: Never Say Die can anybody pls provide me the solution sets for the book > INTRODUCTION TO ALGORITHMS by THOMAS H CORMEN or either provide me > the links for the same. > so you can CHEAT ?? you are just going to sell copies of it on the internet anyway You have been reported. === Subject: Re: solutions for the problems can anybody pls provide me the solution sets for the book > INTRODUCTION TO ALGORITHMS by THOMAS H CORMEN or either provide me > the links for the same. Thomas H Cormen, if he is still alive, probably knows the solutions to the exercise in his own book, so why don't you ask him? -- Remove antispam and .invalid for e-mail address. He that giveth to the poor lendeth to the Lord, and shall be repaid, said Mrs Fairchild, hastily slipping a shilling into the poor woman's hand. === Subject: Re: Root finding with a vector function for use with a backward Euler integrator. > Sorry, I changed my notation a bit. In the above, g is a >function whose > root I want to find, i.e., I want the x such that > g_1( x ) = 0 > In previous posts, I was talking about g( x ) being the >function such that > x = g_2( x ) > Well, I can convert from one to the other by doing > g_2( x ) = g_1( x ) + x > and then solve using fixed-point iteration. At least, >that is what I was > getting at in the above post. Hi Dave, given the system of differential equations > dy/dt = f(t,y). In the (n+1)th time step, backward Euler gives the > system > y_(n+1) = y_n + h*f(t_(n+1),y_(n+1)) > to solve for y_(n+1). Denote the unknown y_(n+1) just by y. > Say you try fixed point iteration as solution method: > y^(k+1) = y_n + h*f(t_(n+1),y^(k)). Then > ||y^(k+1)-y^(k)||_2 = > h*||f(t_(n+1),y^(k))-f(t_(n+1),y^(k-1))||_2 <= > h*|||df/dy|||_2*||y^(k)-y^(k-1)|| > Sorry, I'm confused about the notation. Is |||df/dy||| supposed to be the determinant of the Jacobian? Also, I'm confused about the subscript _2 that you have in places. What is that indicating? > So if h*|||df/dy|||_2 <= a < 1 or > h < a/|||df/dy|||, > the fixed point iteration will converge. In pratice, choose h>0. > If the fixed point iteration converges, all is find. > Else take h/2 and try again. > Note that depending on |||df/dy|||_2, h can become > very small (just like in your example given above > for m > 1 where the fixed point iteration diverged. > But in the case of differential equations, > a large value of m can not be compensated by a > small value of h). > Ya, I thought that this iteration method was too good to be true. Strange that the literature (that I have read anyway) totes it as a foolproof root finder. > Best wishes > Torsten. === Subject: Re: Root finding with a vector function for use with a backward Euler integrator. > Hi Dave, given the system of differential equations > dy/dt = f(t,y). In the (n+1)th time step, backward Euler gives the > system > y_(n+1) = y_n + h*f(t_(n+1),y_(n+1)) > to solve for y_(n+1). Denote the unknown y_(n+1) just by y. > Say you try fixed point iteration as solution method: > y^(k+1) = y_n + h*f(t_(n+1),y^(k)). Then > ||y^(k+1)-y^(k)||_2 = > h*||f(t_(n+1),y^(k))-f(t_(n+1),y^(k-1))||_2 <= > h*|||df/dy|||_2*||y^(k)-y^(k-1)|| > Sorry, I'm confused about the notation. Is |||df/dy||| >supposed to be >the determinant of the Jacobian? Also, I'm confused >about the subscript >_2 that you have in places. What is that indicating? For vectors, ||.||_2 denotes the Euclidean vector norm: ||x||_2 := sqrt(x_1^2 + x_2^2 + ...+ x_n^2) for x=(x_1,x_2,...,x_n). For matrices, |||A|||_2 is the induced matrix norm: |||A|||_2 := max_{||x||_2 = 1} ||Ax||_2 which turns out to be |||A|||_2 = sqrt( max (|lambda_i|)) where the lambda_i (i=1,...,n) are the eigenvalues of the (positive-semidefinite) matrix A^t*A. > So if h*|||df/dy|||_2 <= a < 1 or > h < a/|||df/dy|||, > the fixed point iteration will converge. In pratice, choose h>0. > If the fixed point iteration converges, all is find. > Else take h/2 and try again. > Note that depending on |||df/dy|||_2, h can become > very small (just like in your example given above > for m > 1 where the fixed point iteration diverged. > But in the case of differential equations, > a large value of m can not be compensated by a > small value of h). > Ya, I thought that this iteration method was too good to >be true. >Strange that the literature (that I have read anyway) >totes it as a >foolproof root finder. > Best wishes > Torsten. === Subject: statics hi i need free ebook of statics by meriam and solution tnx so much === Subject: Re: statics > hi i need free ebook of statics by meriam and solution > tnx so much so you can CHEAT ?? you are just going to sell copies of it on the internet anyway You have been reported. === Subject: Re: Solution manual of textbooks in ebook format! Get it in hours! <25072386.1178970034064.JavaMail.jakarta@nitrogen.mathforum.org> I really need the solution manual for the following textbook: Differential Equations and Linear Algebra 2nd edition by C.Henry === Subject: Re: Something new for teaching and learning trigonometry Guido, The straight forward answer to your question can be found on the TrigWorks website. The TrigRuler is a measuring tool used to introduce the subject of trigonometry through hands-on manipulation. But, that does not mean an already experienced student that is studying advanced topics in trig will not gain some new insights to the topic as a result of applying hands on manipulation to make measurements. At the very least, you may discover an innovative way of teaching trig to someone else, a way and path that you did not take to arrive where you are now, but one that may reach and help many more students that would possibly not pursue trig because they are not being reached by traditional methods. - Jesse www.trigworks.com === Subject: Re: Complete electronic solution manual in pdf ! Get it in hours! Please send me the solution manual thanx in advance === Subject: Re: Complete electronic solution manual in pdf ! Get it in hours! Hi! How can I get the solutions manual to Linear Algebra 3rd edition > Can you send me the Physics, 5th Edition, Vol 2 by Halliday, Resnick, > Krane (Chap 25-52). much appreciated, Alina > containing ALL (odd and even - except where noted) solutions for the books listed below. These are not paper books, they are ebooks and most are only $12.00 each - paypal accepted. > If you do not see a solution on my list, email me and I will see if I can locate it, but no guarantees, but I will try! > Books for which I have electronic solution manual: > A Course in Game Theory by Osborne, Rubinstein A Course in Algebraic Number Theory by Cohen Adaptive Filter Theory, 4th Edition, by Haykin Adaptive Control, 2nd. Ed., by Astrom, Wittenmark Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even solutions) Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even solutions) Advanced Macroeconomics, David Romer Advanced Mathematical Concepts Precalculus With Applications by Holliday [ISBN: 0028341759] Advanced Modern Engineering Mathematics, 3rd Ed., by G. James A First Course In Differential Equations, 7th Edition, by Zill, Cullen Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray, Hurst, Lewis, Meyer Analytical Mechanics, 7th Edition, by Fowels, Cassiday An Interactive Introduction to Mathematical Analysis, by Jonathan Lewin An Introduction to the Mathematics of Financial Derivatives, 2nd Ed., by Neftci [ISBN: 0125153929] Antenna Theory, 2nd Ed., by Balanis Antennas for all Applications, 3rd Edition, Kraus, Marhefka Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley Applied Numerical Methods with MATLAB for Engineers and Scientists, 1st Ed,. by Chapra Applied Statistics and Probability for Engineers, 3rd Ed., by Montgomery, Runger (Selected Solutions) Applied Strength of Materials, 4th Edition, by Mott A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen, Andre Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi > Basic Business Statistics: Concepts and Applications, 10th Ed., by Berenson, Krehbiel, Levine (chap1-18) Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms (Missing a chapter or 2) Bioprocess Engineering Principles by Doran > Calculus Early Transcendental, 5th Ed., by James Stewart Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney, Demana, Kennedy Calculus: Multivariable, 5th Edition, by James Stewart Calculus: Single Variable, Early Transcendental, 5th Edition, by James Stewart Calculus, Single and Multivariable, 3rd Ed., by Hughes-Hallett, McCallum Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson, Hostetler, Edwards Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler Chemical Engineering Volume 1, Sixth Edition, by Richardson, Coulson, Backhurst, Harker Thornton College Physics, Volume 1: 7th Edition, by Serway, Faugh College Physics, Volume 2: 7th Edition, by Serway, Faughn Communications Systems, 4th Ed., by Haykin Communications Systems Engineering, 2nd Edition, by Proakis Computational Techniques for Fluid Dynamics by Srinivas, Fletcher Computer Networks, 4th Ed., by Andrew S. Tanenbaum Computer Networks: A Systems Approach, 3rd Edition, by Davie Control Systems Engineering, 4th Ed., by Norman Nise Corporate Finance, 6th Edition, by Ross C++ How to Program: Intro Object-Oriented Design with the UML, 3rd Ed., by Deitel, Nieto > Data and Computer Communications, 8th Edition by Stallings Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke (Sol. for Chapters 2-21, odd only) Design of Analog CMOS Integrated Circuits, 1st Edition, by Razavi Design of Analysis of Experiments, 6th Edition, Montgomery (missing chapter 6-8) Design of Machinery, 3rd Ed by Robert L. Norton Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed., by Sergio Franco Design With Operational Amplifiers and Analog Integrated Circuits, 3rd Ed., by Sergio Franco Device Electronics for Integrated Circuits 3rd Edition by Muller Differential Equations with Boundary Value Problems, 2nd Ed., by Polking, Arnold Digital And Analog Communication Systems 7th Ed., Leon W. Couch Digital Communications, 4th Edition, by Proakis Digital Communications: Fundamentals and Applications, 2nd Ed, Skylar Digital Design, 4th Edition, by Mano, Ciletti Digital Image Processing, 2nd Edition, by Gonzalez, Woods Digital Integrated Circuits, 2nd Ed., by Rabaey (Solutions ONLY for Chapters 3, 5, 6, 10) Digital Signal Processing: A Computer Based Approach, 1st Ed., by Mitra Digital Signal Processing: A Computer Based Approach, 2nd Ed., by S. Mitra Digital Signal Processing: A Computer Based Approach, 3rd Ed., by S. Mitra Digital Signal Processing: Priciples, Algorithms and Applications, 3rd Edition, by Proakis Discrete Time Signal Processing, 2nd Edition, Oppenheim Dynamics of Mechanical Systems by C.T.F. Ross > Econometric Analysis, 5th Edition, by Greene Wooldridge Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, Viceira Electrical Properties of Materials, 7th Ed., by D. Walsh, L. Solymar Electric Circuits 6th Ed. by Nilsson Electric Circuits 7th Ed. by Nilsson Electric Machinery, 6th Ed., Fitzgerald, Kingsley, Umans Electric Machinery Fundamentals, 4th Ed by Chapman Electromagnetic Fields and Waves by Iskander (...) Electronic Circuit Analysis, 2nd Ed., by Donald Neamen Electronics, 2nd Ed., by Allan R. Hambley Elementary Differential Equations, 8th Edition, by Boyce, DiPrima (some odd/even) Elements of Chemical Reaction Engineering, 3rd Ed., by H. Scott Fogler Engineering and Chemical Thermodynamics, by Koretsky [ISBN: 0471385867] (No sol. for chapt 6) Engineering Circuit Analysis, 6th Edition, Hyat Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck Engineering Fluids Mechanics 7th Edition by Crowe Engineering Fluids Mechanics 8th Edition by Crowe Engineering Mathematics, 4th Ed., by John Bird Engineer Mechanics: Dynamics, 4th Ed., by Bedford Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler Engineering Mechanics: Dynamics 11th Ed. by Hibbeler Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige Engineering Mechanics: Statics, 4th Edition - A. Bedford, Wallace Fowler Engineering Mechanics: Statics, 5th Ed., Meriam Engineering Mechanics: Statics, 6th Ed., Meriam Engineering Mechanics: Statics, 10th Ed., by Russell C. Hibbeler Engineering Mechanics: Statics 11th Ed. by Hibbeler Experiments with Economic Principles by Bergstrom, Miller > Feedback Control of Dynamic Systems, 4th Edition, by Powell, Emami- Naeini Financial Accounting, 4th Ed., by Libby, Short (Chap1-14) Financial Accounting: An International Introduction, 2nd Ed., by Alexander, Nobes Finite Element Techniques in Structural Mechanics by Ross Fluid Mechanics - 5th Edition by Frank M. White Fluid Mechanics and Thermodynamics of Turbomachinery, 5th Ed., by S. L. Dixon [ISBN: 0750678704] Essentials of Fluid Mechanics: Fundamentals and Applications, 1st Ed., by Cengel & Cimbala Fluid Mechanics with Engineering Applications, 10th Edition, by Finnemore Fundamentals of Aerodynamics, 3rd Edition, by J. D. Anderson, Jr. Fundamentals of Aerodynamics, 4th Edition, by Anderson Fundamentals of Applied Electromagnetics, 2001 Media Edition, by Ulaby Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition, by Ulaby Fundamentals of Digital Logic with Verilog Design, 1st Edition, by Brown, Vranesic Fundamentals of Digital Logic with VHDL Design by Stephen Brown, Zvonko Vranesic Fundamentals of Electric Circuits, 2nd Edition, by Alexander Fundamentals of Electromagnetics with Engineering Appls by Wentworth Fundamentals of Fluid Mechanics, 5th Ed. by Munson, Young.. Fundamentals of Heat and Mass Transfer, 4th Ed by Incropera... Fundamentals of Heat and Mass Transfer, 5th Ed by Incropera... Fundamentals of Heat and Mass Transfer, 6th Ed by Incropera... Fundamentals of Logic Design, 5th Ed., by Roth Jr. Fundamentals of Machine Component Design, 3rd Ed., by Juvinall Fundamentals of Machine Component Design, 4th Ed., by Juvinall Fundamentals of Machine Elements, 2nd Ed., Hamrock, Jacobson, Schmid Fundamentals of Physics by Halliday, 7th Ed., Walker, Resnick Fundamentals of Semiconductor Devices, 1st Edition by Anderson Fundamentals of Structural Analysis, 2nd Ed., Chia-Ming Uang, Kenneth Leet Fundamentals of Thermal-Fluid Sciences, 2nd Ed. by Cengel Fundamentals of Thermal-fluid Sciences, Int'l 2nd Ed. by Cengel Fundamentals of Engineering Thermodynamics, 5th Ed. by Shapiro Fundamentals of Thermodynamics, 5th Ed., by Sonntag, Borgnakke... Fundamentals of Thermodynamics, 6th Ed., by Sonntag > Geometry, 04 Edition, by McGraw-Hill [ISBN: 0078296374] Guide to Energy Management, 5th Edition, by Pawlik > Heat Transfer: A Practical Approach - 2nd Edition by Cengel Hydraulics in Civil and Environmental Engineering, 4th Ed., by Andrew Chadwick > Introduction to Algorithms, 2nd Ed by Cormen, Leiserson (Selected Sol.) Introduction To Chemical Engineering Thermodynamics, 7th Ed., by Van Ness, Smith, Abbott Introduction To Chemical Engineering Thermodynamics, 7th Ed., by Van Ness, Smith, Abbott Introduction to Electric Circuits, 6th Ed., by Dorf, Svoboda Introduction to Electric Circuits, 7th Ed., by Dorf, Svoboda Introduction to Electrodynamics, 3rd Ed. by David Griffiths Introduction to Fluid Mechanics - 5th Ed. by Fox.. Introduction to Fluid Mechanics - 6th Ed by Fox, McDonald... Introduction to Linear Algebra, 3rd Ed., by Gilbert Strang Introduction to Linear Algebra, 5th Ed., Arnold, Johnson, Riess Introduction to Quantum Mechanics, 2nd Ed. by Griffiths Introdution to Solid State Physics, 8th Edition by Kittel Intro to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer by Moran, Shapiro, Munson, DeWitt > Introduction to Thermal Systems Engineering, by Moran, Shapiro > Linear Algebra, by J. Hefferon Linear Algebra And Its Applications, 3rd Ed., by David C. Lay Linear Algebra with Applications, 2nd Edition - by Otto Bretscher Linear Algebra with Applications, 3rd Edition - by Otto Bretscher Linear Circuit Analysis: Time Domain, Phasor and Laplace.., 2nd Ed, Lin > Machine Design: An Integrated Approach, 2nd Ed., by Robert L. Norton (same problems as third edition except for last 2-4 problems per chapter that were added to the third edition) Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton Managerial Accounting, 11th Ed., by Noreen, Brewer, Garrison Materials Science and Engineering: An Introduction, 6th Ed. by Callister Matrix Analysis and Applied Linear Algebra by Carl Meyer MC68HC11: An Introduction: Software/Hardware Interf, 2nd Ed, by Huang Mechanical Engineering Design, 7th Ed. by Mischke, Shigley > Mechanical Vibrations, 3rd Edition, by S. S. Rao (99% same as 4th Edition, No Solutions for Chapters 6, 9, and 12) Mechanics of Fluids, 8th Ed., by Bernard Massey Mechanics of Fluids, 4th Ed., Irving H. Shames Mechanics of Fluids, 8th Ed., by Bernard Massey Mechanics of Materials - 3rd Ed. by Beer, Johnston, Dewolf Mechanics of Materials - 4th Ed. by Beer, Johnston, Dewolf Mechanics of Materials - 6th Ed. by Hibbeler Mechanics of Materials, 6th Edition by James M. Gere (missing small portion, section 8.5) Mechanics of Materials, 6th Ed., by Sturges, Morris, Riley (part of Chapt 2 is missing but only #1 thru #60) Mechanics of Solids by C.T.F. Ross Microeconomic Analysis, 3rd Ed., by H. Varian (Ans. to Exercises: Ch.1- Ch.25) Microeconomic Theory, by Mas-Colell, Whinston, Green Microelctronic Circuits, 5th Ed. by Sedra and Smith Microelectronic Circuit Design, 2nd Edition by Jaeger, Blalock Microelectronics: Digital and Analog Circuits and Systems by Millman Microwave and Rf Design of Wireless Systems, 1st Edition, by Pozar Miller & Freund's Probability and Statistics for Engineers, 7th Edition, Johnson, Miller Modern Compressible Flow, 3rd Edition, by Anderson Modern Control Engineering, 3rd Edition, by Ogata Modern Control Engineering, 4th Edition, by Ogata Modern Digital and Analog Communication Systems, 3rd Ed., by Lathi Modern Control Systems, 9th Ed., by Richard C. Dorf, Robert H Bishop Modern Operating Systems,2nd Ed., by Andrew Tanenbaum Modern Physics 4th Edition by Tipler Monetary Theory and Policy, 2nd Edition, by Walsh Multivariable Calculus, 5th Edition, by James Stewart > Numerical Methods, 3rd Ed., by J. Douglas Faires, Richard L. Burden (Selected Solutions) > Operating Systems: Internals and Design Principles, 4th Edition, by Stallings Options, Futures and Other Derivatives, 5th Ed., by John Hull (Chapters 1 thru 18 ONLY) Orbital Mechanics: For Engineering Students by Howard Curtis (includes matlab scripts) Organic Chemistry, 4th Ed., by Carey, Atkins (Student Study Guide and Sol. Man.) > Partial Differential Equations with Fourier Series and Boundary Value Problems, 2nd Ed., by Asmar (Student Solutions Manual) Physical Chemistry - 7th Edition - by Julio de Paula, Peter Atkins Physics, 6th Edition, by John Cutnell Physics, 5th Edition, Vol 2 by Halliday, Resnick, Krane (Chap 25-52) Physics for Scientist and Engineers by Knight (No Chapt 36-42) Physics for Scientist and Engineers, 6th Ed., by Serway Physics for Scientists and Engineers-Vol 1, 5th Edition, Serway, Beichner (Chap. 1 - 22) hysics for Scientists and Engineers-Vol 2, 5th Edition, Serway, Beichner (Chap. 23 - 46) Physics for Scientists and Engineers, 3rd Ed., by Douglas C. Giancoli Physics for Scientist and Engineers, 5th Edition, by Tipler, Mosca Physics: Principles with Applications, 6th Ed. by Giancoli Power System Analysis and Design, 3rd Ed., by Glover, Sarma Principles and Applications of Electrical Engineering 4th (Revised) Ed by Rizzoni Principles of Communication: Systems, Modulation Noise, 5th Ed., Ziemer Principles of Physics, 3rd Edition, by Serway Principles of Statics, 10th Ed., by Russell C. Hibbeler [ISBN: 0131866745] Probability and Statistics for Engineers and Scientists, 3rd Edition, Hayter Probability and Statistics for Engineering and the Sciences, 6th Ed., by Jay L. Devore Probability Random Variables, and Stochastic Processes, 4th Ed., by Papoulis, Pillai (..) > Quantum Mechanics: An Accessible Introduction, 1st Ed., by Robert Scherrer > Recursive Macroeconomic Theory, 1st Ed., by Ljungqvist, Sargent RF Circuit Design: Theory & Applications, by Bretchko, Ludwig > Sears and Zemansky's University Physics 11th Edition by Young.. Semiconductor Device Fundamentals by Pierret Semiconductor Devices: Physics and Technology, 2nd Ed., S.M. Sze Semiconductor Physics And Devices -3rd Ed. by D. Neamen Separation Process Principles, 2nd Ed., Seader, Henley Signal Processing and Linear Systems by Lathi Signals and Systems, 2nd Edition, by Haykin, Van Veen Signals and Systems, 2nd Edition, Oppenheim, Willsky, Hamid, Nawab Signals and Systems: Analysis Using Transform Methods and MATLAB, 1st Ed., by M. J. Roberts Signals, Systems, and Transforms: Charles L. Phillips, Eve A. Riskin, John M. Parr (No Solutions for Chap 9-12) Shigley's Mechanical Engineering Design, 8th Ed. by Budynas, Nisbett (No Sol. for Chapt 18 & 19) > Simply C#: An Application-Driven Tutorial Approach, by Deitel, Hoey... (Chapters 1-32) Soil Mechanics: Concepts and Applications, 2nd Ed., by Powrie Solid State Electronic Devices - 5th Ed by Streetman Solid State Electronic Devices - 6th Ed by Streetman Statics and Mechanics of Materials: An Integrated Approach, 2nd Ed., by Riley, Sturges, Morris Structural Analysis, 5th Edition, by Hibbeler System Dynamics, 3rd Edition, by Ogata > Theory and Design for Mechanical Measurements, 4th Ed., Beasley, Figliola Thermal Physics, 2nd Edition, by Charles Kittel Thermal Physics, by Ralph Baierlein Thermodynamics: An Engineering Approach by Cengel, Boles (Missing solutions #118-149 of Chapter 7) The Science and Engineering of Materials, 4th Ed., by Donald R. Askeland, Pradeep P. Phule > Thomas' Calculus, Early Trans., Part 1, 10th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 10th Ed. (Multivariable, chs. 11-16), by Thomas, Weir, Hass, Giordano Thomas' Calculus, Early Trans., Part 1, 11th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 11th Ed. (Multivariable, chs. 11-16), by Thomas, Weir, Hass, Giordano Transport Phenomena, 1st Edition, by R. Byron Bird > University Physics 11th Edition by Young.. > Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach, 2nd Ed., by Hubbard Vector Mechanics: Statics 7th Edition by Beer Vector Mechanics: Dynamics, 7th Ed., by Beer, Johnston, Staab, Clausen Vibrations and Stability: Advanced Theory, Analysis, and Tools, 7th Ed., by Thomsen > Wireless Communications: Principles and Practice, 2nd Ed, by Rappaport === Subject: Re: I have the Instructors Solutions Manual for Thomas, Calculus, 11th Edition Hello I would like to see a sample please. If this the early > transcendental 11th edition. If possible could you email it? I am interested === Subject: solutions manual I really need the solution manual for statistics for engineers and scientist by Navidi I would really appreciated === Subject: Re: ?(pi) .... In any case I think the time has come > for you to reveal your method. And answer came there none. -- Remove antispam and .invalid for e-mail address. He that giveth to the poor lendeth to the Lord, and shall be repaid, said Mrs Fairchild, hastily slipping a shilling into the poor woman's hand. === Subject: Re: Solutions manual to low cost > Hi there, I'm interested on the solutions for the following book: Vector > Calculus (3rd Ed., Susan J. Colley) > Can you provide this by email ASAP? > Edgar (Available on print-original copy, Cd - for heavy files & by e-mail) > contact me to : Ebergh...@yahoo.com > If your solutions manual wanted ins't on this list, also can make the request. These are some only. > Not exchange > - Mechanics, Mechanical Engineering & Aerospace Engineering: > Introduction to Mechanical Engineering (Rizza) Mechanical Engineering Principles (Bird & Ross) + Ebook Mechanics of Fluids (8th Ed., Massey) + Ebook Fluid Mechanics (5th Ed., White) + Ebook Fluid Mechanics (6th Ed., White) Viscous Fluid Flow (3rd Ed., White) + Ebook Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + Ebook Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + Ebook Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd Ed., Cengel & Turner) Thermodynamics: An Engineering Approach (5th Ed., Cengel) + Ebook Thermodynamics: An Engineering Approach (6th Ed., Cengel) + Ebook Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., Cengel) + Ebook Fluid Mechanics (1st Ed., Cengel) + Ebook Heat Tranfer (2nd Ed., Cengel) + Ebook Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + Ebook Design and Simulation of Thermal Systems (Suryanarayana & Arici) Fluid Mechanics (5th Ed., Douglas) Fluid Mechanics (3rd Ed., Kundu) Fluid Mechanics with Engineering Applications (Finnemore) Mechanics of Fluids (3rd Ed., Potter) Mechanics of Fluids (4th Ed., Shames) Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, Howell & Baker) Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) Heating, Ventilating and Air Conditioning Analysis and Design (6th Ed., McQuiston) An Introduction to Fluid Dynamics: Principles of Analysis and Design (Middleman) Introduction to Mass and Heat Transfer: Principles of Analysis and Design (Middleman) Heat Transfer (2nd Ed., Mills) Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) Advanced Engineering Thermodynamics (3rd Ed., Bejan) Convection Heat Transfer (2nd Ed., Bejan) Convection Heat Transfer (3rd Ed., Bejan) Thermal Design and Optimization (Bejan) Shape and Structure, from Engineering to Nature (Bejan) Thermodynamics: Concepts and Applications (Stephen Turns) Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) Principles of Heat Transfer (Kaviany) Heat Convection (Latif M. Jiji) + Ebook Heat Transfer (9th Ed., Holman) Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) Momentum, Heat, and Mass Transfer Fundamentals (Kessler) Heat Tranfer (Rao) Heat Conduction (kakac) Heat Exchanges (Kakac) Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik Kakac & Hongtan Liu) Convective Heat Transfer (kakac) Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) Radiation Detection and Measurement (3rd Ed., Glenn Knoll) Radiative Heat Transfer (2nd Ed., Michael Modest) Engineering Heat Transfer (2nd Ed., Janna) Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. Rogers & Y.R. Mayhew) Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) Inverse Heat Transfer: Fundamentals and Applications (M.N. 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Marghitu) + Ebook Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & Kinzel) Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & Sandor) Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., Myszka) Mechanical Design: A Components Approach (Peter Childs) Mechanical Design of Machine Elements and Machines: A Failure Prevention Perspective (Collins) Fundamentals of Machine Component Design (3rd Ed., Juvinall) Fundamentals of Machine Component Design (4th Ed., Juvinall) Design of Machine Elements (8th Ed., Spotts) Machine Design (Wentzell) Solutions to problems at the text : Problems on the Design of Machine Elements (Faires) Machine Elements in Mechanical Design (4th Ed., Mott) Mechanical Design: An Integrated Approach (1st Ed., Ugural) Design of Machinery (3rd Ed., Norton) Machine Design (2nd Ed., Norton) Machine Design : An Integrated Approach (3rd Ed., Norton) Mechanical Engineering Design (6th Ed., Shigley) Mechanical Engineering Design (7th Ed., Shigley) Shigley's Mechanical Engineering Design (8th Ed., Budynas) Fundamentals of Machine Elements (1st Ed., Hamrock) Fundamentals of Machine Elements (2nd Ed., Hamrock) Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) Principles of Metal Manufacturing Processes (Beddoes & Bibby) Materials Selection in Mechanical Design (3rd Ed., Michael Ashby) Introduction to Manufacturing Processes (3rd Ed., Schey) Manufacturing, Engineering & Technology (4th Ed. 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Beer) Statics: Analysis and Design of Systems in Equilibrium (Sheppard & Tongue) Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., Riley, Sturges & Morris) Mechanics of Materials (6th Ed., Riley, Sturges & Morris) Deformable Bodies and Their Material Behavior (Haslach & Armstrong) Strength of Materials - Volume 1 : Elementary Theory and Problems (Timoshenko) Intermediate Mechanics of Materials, (1st Ed., Barber) Elasticity (2nd Ed., J.R. Barber) + Ebook Elasticity: Theory, Applications, and Numerics (Martin Sadd) + Ebook Elasticity in Engineering Mechanics (2nd Ed., Boresi) Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook Engineering Mechanics: Dynamics (Boresi) Flight Performance of Fixed and Rotary Wing Aircraft (Antonio Filippone) Aircraft Structures for Engineering Students (4th Ed., T.H.G. Megson) Principles of Helicopter Aerodynamics (2nd Ed., Leishman) Fundamentals of Aerodynamics (3th Ed., Anderson) Fundamentals of Aerodynamics (4th Ed., Anderson) Modern Compressible Flow: With Historical Perspective (3rd Ed., John D. Anderson) Applied Fluid Mechanics (6th Ed., Mott) Applied Strength of Materials (4th Ed., Mott) Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) Engineering Mechanics: Statics E(2nd Ed., Pytel) Engineering Mechanics: Dynamics (2nd Ed., Pytel) Engineering Mechanics: Statics E(2nd Ed., Shames) Engineering Mechanics: Statics E(4th Ed., Shames) Engineering Mechanics: Dynamics (4th Ed., Shames) Introduction to Solid Mechanics (3rd Ed.., Shames) Elastic And Inelastic Stress Analysis (Shames) Advanced Dynamics (Greenwood) + Ebook Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook Classical Dynamics (Jorge V. Jos.8e) + Ebook Impact Mechanics (W.J. Stronge) Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files converted to pdf, real instructor sol. manual Principles of Statics (10th Ed., Hibbeler) Engineering Mechanics : Dynamics (11th Ed., Hibbeler)-Not mathcad files converted to pdf, real instructor sol. manual Principles of Dynamics (10th Ed., Hibbeler) Mechanics of Materials (6th Ed, Hibbeler) Statics and Mechanics of Materials (2nd Ed., Hibbeler) Energy Principles and Variational Methods in Applied Mechanics (2nd Ed., Reddy) Theory of Vibrations with Applications (5th Ed., Thomson & Dahleh) Engineering Vibrations (2nd Ed., Inman) Engineering Vibrations (3rd Ed., Inman) Introduction to Finite Element Vibration Analysis (Maurice Petyt) Vibrations and Stability: Advanced Theory, Analysis, and Tools (2nd Ed., Jon J. Thomsen) Mechanical Vibrations (4th Ed., Rao) The Finite Element Method and Applications in Engineering Using ANSYS (Erdogan Madenci, Ibrahim Guven) Finite Element Analysis Theory and Application with ANSYS (2nd Ed., Moaveni) Finite Element Analysis Theory and Application with ANSYS (3rd Ed., Moaveni) The Finite Element Method and Applications in Engineering Using ANSYS (Madenci & Guven) + Ebook Modeling and Analysis of Dynamic Systems (3rd Ed, Close, Frederick & Newell) System Dynamics: Modeling and Simulation of Mechatronic Systems (4th Ed., Karnopp, Margolis & Rosenberg) Concepts and Applications of Finite Element Analysis (4th Ed., Cook, Malkus, Plesha & Witt) Advanced Strength and Applied Elasticity (4th Ed., Ugural) Fracture Mechanics: An Introduction (2nd Ed., by E.E. Gdoutos) Fracture Mechanics (2nd Ed., Anderson) Mechanical Behavior of Materials (2nd Ed. Dowling) Mechanical Behavior of Materials (3rd Ed. Dowling) Mechanical Behavior of Materials (W.F. Hosford) + Ebook Mechanical Behavior of Materials (Keith Bowman) Theory and Design for Mechanical Measurements (4th Ed, Figliola & Beasley) Mechanical Measurements (6th Ed., Beckwith, Marangoni & Lienhard) Introduction to Engineering Experimentation (2nd Ed., Wheeler & Ganji) Gas Dynamics (3rd Ed., John & Keith) Internal Combustion Engines: Applied Thermosciences (2nd Ed., Ferguson & Kirkpatrick) Automotive Engines (8th Ed., Crouse) Automotive Brake Systems Package (4th Ed., Rehkopf) Automotive Engine Performance (2nd Ed., Halderman) Automotive Mathematics (Jason C. Rouvel) Blueprint Reading for the Machine Trades (6th Ed., Schultz & Smith) Modern Welding Technology (6th Ed., Cary & Helzer) Theory of Ground Vehicles (3rd Ed., J. Y. Wong) Hydraulic Control Systems (Noah Manring) Fluid Mechanics and Thermodynamics of Turbomachinery (5th Ed., S.L. Dixon) + Ebook Principles of Turbomachinery in Air-Breathing Engines (Baskharone) Fundamentals of Jet Propulsion with Applications (Ronald D. Flack) Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms (3rd Ed., Jorge Angeles) Tissue Mechanics (Cowin, Doty) BTEC First Engineering Curriculum Support Pack (Mike Tooley) BTEC First Engineering (Mike Tooley) Exploring Engineering: An Introduction for Freshmen to Engineering and to the Design Process (Philip Kosky, George Wise, Robert Balmer & William Keat) Engineering Science (5th Ed., W. Bolton) Fundamentals of Renewable Energy Processes (Aldo da Rosa) Renewable Energy (3rd Ed., Srensen or Sorensen) Power Generation Technologies (Paul Breeze) > - Electrical, Electronics & Computer Engineering > Design for Electrical and Computer Engineers (1st Ed., Ralph Ford & Chris Coulston) Fundamentals of Modeling and Analyzing Engineering Systems (Cha, Rosenberg, Dym) Principles of Linear Systems (Philip E. Sarachik) Power Systems Harmonics: Fundamentals, Analysis and Filter Design (George J. Wakileh) Principles of Adaptive Filters and Self-learning Systems (Anthony Zaknich) Control of Robot Manipulators in Joint Space (R. Kelly, V. Santib.87.96ez, A. Lor.92a) Modelling and Control of Robot Manipulators (2nd Ed., Lorenzo Sciavicco, Bruno Siciliano) Algebraic Methods for Nonlinear Control Systems (2nd Ed., Giuseppe Conte, Claude H. Moog, Anna Maria Perdon) Modern Control Engineering - Problems B (3rd Ed. K.OGATA) Modern Control Engineering (4th Ed. K.OGATA) LabVIEW 8 Student Edition (Bishop) Feedback Control of Dynamic Systems (5th Ed., Franklin, Powell & Emami- Naeini) Modeling and Simulation of Dynamic Systems (Woods, Lawrence) Predictive Control with Constraints (Jan Maciejowski) Computer Numerical Control: Operation and Programming (3rd Ed., Stenerson & Curran) Engineering Problem Solving with C (3rd Ed., Etter) Process Control Instrumentation Technology (8th Ed., Johnson) Electrical Power and Controls (2nd Ed., Skvarenina & DeWitt) Electronics and Computer Math (8th Ed., Deem & Zannini) Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based Introduction (John Semmlow) Aircraft Digital Electronic and Computer Systems: Principles, Operation and Maintenance (Mike Tooley) VLSI Test Principles and Architectures: Design for Testability (Chen, Cheng, Eklow et al.) Mechatronics: Principles and Applications (Godfrey Onwubolu) Machine Vision: Theory, Algorithms, Practicalities (3rd Ed., E. R. Davies) Instrumentation and Control Systems (W. Bolton) Essential Java for Scientists and Engineers (Brian D Hahn & Katherine M Malan) Guide to Microsoft Excel 2002 for Scientists and Engineers (3rd Ed., Bernard V. Liengme) Electric Motors and Drives : Fundamentals, Types and Applications (3rd Ed., Austin Hughes) System Dynamics (1st Ed., William J Palm III) 10-Key Touch Key: Developing Speed and Accuracy (Burton) Introduction to C++ Programming, Brief (Y. Daniel Liang) C++ for Business Programmers (2nd Ed., John C. Molluzzo) Introduction to Java Programming-Comprehensive Version (6th Ed., Y. Daniel Liang) Introduction to Java Programming: Fundamentals First (6th Ed., Y. Daniel Liang) Objects First With Java: A Practical Introduction Using BlueJ (3rd Ed., David J. Barnes & Michael Kolling) Java: An Introduction to Problem Solving and Programming (4th Ed., Walter Savitch) Simply Java Programming: An Application-Driven Tutorial Approach (Deitel) Java: An Introduction to Computing (Joel Adams, Larry R. Nyhoff & Jeffrey Nyhoff) Advanced Java 2 Platform How to Program (Deitel & Santry) SQL for SQL Server (Bijoy Bordoloi & Douglas B. Bock) Introduction to Programming Using Visual Basic 2005 (6th Ed., David I. Schneider) Simply Visual Basic 2005 (2nd Ed., Harvey & Paul Deitel & Associates) Visual Basic 2005 How to Program (3rd Ed., Deitel & Associates) Introduction to Programming with Visual Basic 6.0 (4th Ed., David I. Schneider) Visual Basic.Net Programming (2nd Ed., Jeffrey Tsay) Simply Visual Basic .NET (Deitel & Nieto) Mechatronics (Sabri Cetinkunt) Introduction to Linear Programming (Leonid N. Vaserstein) Science of Electronics, The: DC/AC (David M. Buchla, Thomas L. Floyd) Introductory Circuit Analysis (11th Ed., Robert L. Boylestad) Principles of Electric Circuits: Conventional Current Version (8th Ed., Thomas Floyd) Contemporary Electric Circuits: Insights and Analysis (2nd ed., Strangeway, Petersen, Gassert & Lokken) Electronics Technology Fundamentals - Conventional Flow (2nd Ed., Robert T. Paynter & Toby Boydell) Electronics Fundamentals: Circuits, Devices and Applications (7th Ed., Thomas L. Floyd) Principles of Electric Circuits: Electron Flow Version (8th Ed., Thomas L. Floyd) Electronics Technology Fundamentals - Electron Flow (2nd Ed., Robert T. Paynter, Toby Boydell) Introductory DC/AC Circuits (6th Ed., Nigel P. Cook) Introductory DC/AC Electronics (6th Ed., Nigel P. Cook) Electronic Devices - Conventional Current Version (7th Ed., Thomas L. Floyd) Electronic Devices - Conventional Current Version (8th Ed., Thomas L. Floyd) Electronic Devices - Electron Flow Version (8th, Thomas L. Floyd) Electronic Devices and Circuit Theory (9th Ed., Robert L. Boylestad, Louis Nashelsky) Introductory Electronic Devices and Circuits: Electron Flow Version (7th Ed., Robert T. Paynter) Introductory Electronic Devices and Circuits: Conventional Flow Version (7th Ed., Robert T. Paynter) Electronic Devices - Electron Flow Version (5th, Thomas L. Floyd) Science of Electronics, The: Digital (Thomas L. Floyd & David M. Buchla) Science of Electronics, The: Analog Devices (Thomas L. Floyd, David M. Buchla) Digital Electronics: A Practical Approach (7th Ed., William Kleitz) Digital Electronics: A Practical Approach (8th Ed., William Kleitz) Digital Systems: Principles and Applications (10th Ed., Ronald Tocci, Neal Widmer, Greg Moss) Digital Electronics with VHDL - Quartus II Version (William Kleitz) Digital Fundamentals (9th Ed., Thomas L. Floyd) Digital Fundamentals with PLD Programming (Thomas L. Floyd) The 8051 Microcontroller (4th Ed., I. Scott MacKenzie, Raphael Chung- Wei Phan) The 8051 Microcontroller and Embedded Systems (2nd Ed., Muhammad Ali Mazidi, Janice Mazidi & Rolin McKinlay) INTEL Microprocessors 8086/8088, 80186/80188, 80286, 80386, 80486, Pentium, Prentium ProProcessor, Pentium II, III, 4, (7th Ed., Barry B. Brey) Microcontroller Technology: The 68HC11, 5/E (Peter Spasov) PIC Microcontroller (Muhammad Ali Mazidi, Rolin McKinlay & Danny Causey) Industrial Electronics (James A. Rehg, Glenn J. Sartori) Programmable Controllers Using the Allen-Bradley SlC-500 Family (2nd Ed., Dave Geller) Programmable Logic Controllers (James A. Rehg, Glenn J. Sartori) Fundamentals of Programmable Logic Controllers, Sensors, and Communications (3rd Ed., Jon Stenerson) An Introduction to Programming with Visual Basic 6.0, Update Edition (4th Ed., Schneider) C++ Programming Today (Barbara Johnston) Introduction to Data Communications and Networking (Wayne Tomasi) Introduction to Telecommunications (2nd Ed., Martha Rosengrant) Network Security Essentials: Applications and Standards (3rd Ed., William Stallings) Information Security: Principles and Practices (Mark Merkow, James Breithaupt) Principles and Practice of Information Security (Linda Volonino, Stephen R. Robinson) Modern Electronic Communication (8th Ed., Jeff Beasley, Gary M. Miller) Modern Electronic Communication (9th Ed., Jeff Beasley, Gary M. Miller) Electronic Communications for Technicians (2nd ed., Tom Wheeler) Concepts In Systems and Signals (2nd Ed., John D. 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Riedel) Solid State Electronic Devices (6th Ed., Ben Streetman, Sanjay Banerjee) Approaching Quantum Computing (Dan C. Marinescu & Gabriela M. Marinescu) Foundations of MEMS (Chang Liu) Fundamentals of Applied Electromagnetics (5th Ed., Fawwaz T. Ulaby) Elements of Engineering Electromagnetics (6th Ed., Nannapaneni Narayana Rao) Digital Design (4th Ed., M. Morris Mano & Michael D. Ciletti) Digital Design: Principles and Practices Package (4th Ed., John F. Wakerly) VHDL: A Starter's Guide (2nd Ed., Sudhakar Yalamanchili) Computer Organization and Architecture: Designing for Performance (7th Ed., William Stallings) Parallel Programming: Techniques and Applications Using Networked Workstations and Parallel Computers (2nd Ed., Barry Wilkinson & Michael Allen) Fundamentals of Parallel Processing (Harry F. Jordan & Gita Alaghband) Feedback Control of Dynamic Systems (5th Ed., Gene Franklin, J.D. Powell, Abbas Emami-Naeini) Digital & Analog Communication Systems (7th Ed., Leon W. Couch) Fundamentals of Communication Systems (John G. Proakis, Masoud Salehi) Modern Wireless Communications (Simon Haykin, Michael Moher) Communication Systems Engineering (2nd Ed., John G. Proakis & Masoud Salehi) Data and Computer Communications (8th Ed., William Stallings) Cryptography and Network Security (4th Ed., William Stallings) Computer Networking with Internet Protocols (William Stallings) Probabilistic Systems and Random Signals (Abraham H Haddad) Error Control Coding (2nd Ed., Shu Lin & Daniel J. Costello) Wireless Communications & Networks (2nd ed., William Stallings) Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) Detection and Estimation:Theory; and Its Applications (Thomas Schonhoff & Arthur Giordano) Signals, Systems, and Transforms (3rd Ed., Charles L. Phillips, John M. Parr & Eve A. Riskin) Fundamentals of Signals and Systems Using the Web and Matlab (3rd Ed., Edward W. Kamen & Bonnie S Heck) Digital Signal Processing (4th Ed., John G. Proakis, Dimitris K Manolakis) Adaptive Filter Theory (4th Ed., Simon Haykin) Spectral Analysis of Signals (Petre Stoica & Randolph L. Moses) > - Math, Statistics & Probability > An Introduction to the Finite Element Method (3rd Ed., J. N. Reddy) Fundamentals of Finite Element Analysis (1st Ed., David V. Hutton) The Finite Element Method: Its Basis and Fundamentals (6th Ed., Zienkiewicz, R. L. Taylor & J.Z. Zhu) Differential Equations (A. King, J. Billingham, S. Otto) Fourier and Laplace Transforms (R. J. Beerends , H. G. ter Morsche) Infinite-Dimensional Dynamical Systems (James C. Robinson) Mathematical Methods for Physics and Engineering, (3rd Ed., Riley, Hobson & Bence) + Ebook Numerical Methods in Engineering with MATLAB (Jaan Kiusalaas) + Ebook Numerical Methods in Engineering with Python (Jaan Kiusalaas) + Ebook An Introduction to Numerical Analysis (Endre Suli and David Mayers) + Ebook Fundamentals of Engineering Numerical Analysis E(Parviz Moin) Monte Carlo Statistical Methods (2nd Ed., Christian P. Robert, George Casella) Introduction to Mathematical Structures and Proofs (Larry J. Gerstein) Analyzing Categorical Data (Jeffrey S. Simonoff) Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics (3rd Ed., E. Saff & Arthur Snider) Probability & Statistics for Engineers & Scientists (8th Ed., Walpole, Myers, Ye) Statistics for Engineering and the Sciences (5th Ed., Mendenhall & Sincich) Miller & Freund's Probability and Statistics for Engineers (7th Ed., Johnson, Miller, Freund) Applied Numerical Analysis Using MATLAB (2nd Ed., Fausett) Numerical Methods Using Matlab (4th Ed., Mathews & Fink) Applied Numerical Methods for Engineers and Scientists (Rao) Applied Numerical Analysis Using MATLAB (2nd Ed., Laurene v. Fausett) Friendly Introduction to Numerical Analysis (Bradie) Elementary Linear Algebra (2nd Ed., Spence, Insel & Friedberg) Elementary Linear Algebra with Applications (9th Ed., Kolman & Hill) Introductory Linear Algebra: An Applied First Course (8th Ed., Kolman & Hill) Linear Algebra with Applications (7th Ed., S. Leon) Linear Algebra for Engineers and Scientists Using Matlab (Hardy) Linear Algebra with Applications (3rd Ed., Bretscher) Modern Matrix Algebra (Hill & Kolman) Partial Differential Equations and Boundary Value Problems with Fourier Series (2nd ed., Asmar) Applied Partial Differential Equations (4th Ed., Haberman) Technical Calculus (5th Ed., Dale Ewen, Joan S. Gary & James E. Trefzger) Technical Mathematics (2th Ed., Dale Ewen, Joan S. Gary & James E. Trefzger) Technical Mathematics with Calculus (2th Ed., Dale Ewen, Joan S. Gary & James E. Trefzger) Introductory Mathematics (4th Ed., Cook) Mathematics for the Technical Trades (Cook) College Mathematics (7th Ed., Cleaves & Hobbs) Fundamentals of Statistics (2nd Ed., Michael III Sullivan) Statistics: Informed Decisions Using Data (2nd Ed., Michael III Sullivan) Modern Elementary Statistics (12th Ed., John E. Freund, Benjamin M. Perles) Franklin) Elementary Statistics: Picturing the World (3rd Ed., Larson & Farber) First Course in Statistics (9th Ed., James T. McClave & Terry Sincich) Statistics (10th Ed., McClave & Terry Sincich) Interactive Statistics (3rd Ed., Martha Aliaga & Brenda Gunderson) Statistics for the Life Sciences (3rd Ed., Samuels & Witmer) Applied Statistics and the SAS Programming Language (5th Ed., Cody & Smith) Biostatistics for the Health Sciences (R. Clifford Blair & Richard Taylor) Biostatistics: How It Works (Steve Selvin) Business Statistics: First Course and Student CD (4th Ed., David M. Levine, Timothy C. Krehbiel & Mark L. 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Nunnally) Construction Project Administration (8th Ed., Ed Fisk Wayne Reynolds) Construction Accounting and Financial Management (Steven J. Peterson) Cost Analysis and Estimating for Engineering and Management (Phillip F. Ostwald & Timothy S. McLaren) Construction Estimating Using Excel (Stephen J. Peterson) > - Environmental Engineering, Earth and Environmental Sciences : > Introduction to Engineering and the Environment (1st Ed., Edward S. Rubin) Small and Decentralized Wastewater Management Systems (1st Ed, Crites & Tchobanoglous) Water Resources Engineering (R. Wurbs, W. James) Principles of Sequence Stratigraphy (Octavian Catuneanu) Atmospheric Science: An Introductory Survey (2nd Ed., John Wallace, Peter Hobbs) Plant Pathology (5th Ed., George Agrios) Environmental Engineering (4th Ed., Ruth F Weiner & Robin Matthews) Groundwater Science (Charles Fitts) Agriculture's Ethical Horizon (Robert Zimdahl) Environmental Contaminants: Assessment and Control (Daniel Vallero) Water Resources Engineering (Larry W. Mays) Water-Resources Engineering (2nd Ed., Chin) > - Chemistry and Chemical Engineering : > Mass Transfer Operations (3rd Ed., Treybal) Mass Transfer in Multicomponent Mixtures (J.A. Wesseling & R. Krishna) + Ebook Diffusion - Mass Transfer in Fluid Systems (2nd Ed., Cussler) Separation Process Principles (1st Ed, Seader & Henley) Separation Process Principles (2nd Ed., Seader & Henley) Equilibrium Staged Separations (Wankat) Principles of Chemical Separations with Environmental Applications (Richard D. Noble) Product and Process Design Principles: Synthesis, Analysis, and Evaluation (2nd Ed., Seider & Seader) + Ebook Principles and Practices of Automatic Process Control (3rd Ed., Smith & Corripio) + Ebook Process Dynamics and Control (2nd Ed., Seborg & Edgard) Process Control - A First Course with MATLAB (P.C. Chau) + Ebook Process Dynamics: Modeling, Analysis and Simulation (Wayne Bequette) Plant Design and Economics for Chemical Engineers, (5th Ed., Peters & Timmerhaus) + Ebook Basic Principles and Calculations in Chemical Engineering (6th Ed., Himmelblau) Basic Principles and Calculations in Chemical Engineering (7th Ed., Himmelblau) Unit Operations of Chemical Engineering (6th Ed., McCabe & Smith) Unit Operations of Chemical Engineering (7th Ed., McCabe & Smith) Introduction to Transport Phenomena (W. 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Petlyuk) + Ebook Batch Distillation: Simulation, Optional Design and Control (Diwekar) + Ebook Fluid Mechanics for Chemical Engineers, (3rd Ed., Noel de Nevers) Introduction to Chemical Processes: Principles, Analysis, Synthesis (1st Ed., Regina EM. Murphy) Optimization of Chemical Processes (2nd Ed., Edgar & Himmelblau) Chemical and Engineering Thermodynamics (3rd Ed., Stanley I. Sandler) Chemical, Biochemical, and Engineering Thermodynamics (4th Ed., Stanley I. Sandler) Introduction to Chemical Engineering Thermodynamics (6th Ed., Smith & Van Ness) Introduction to Chemical Engineering Thermodynamics (7th Ed., Smith & Van Ness) Introductory Chemical Engineering Thermodynamics (J. Elliott, C. Lira) Engineering and Chemical Thermodynamics (Koretsky) Phase Equilibria, Phase Diagrams and Phase Transformations - Their Thermodynamic Basis (2nd Ed., Mats Hillert) Introduction to Chemical Kinetics and Chemical Reaction Engineering (Missen, Mims) + Ebook Transport Processes and Unit Operations (3rd Ed., Christie J. Geankoplis) Transport Processes and Separation Process Principles (4th Ed., Christie J. 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In Swedish it's evidently rombkuboktaeder... http://www.abc.se/home/m10901/RAIL/osj_klot.html /M -- SUBLIMITETSAKADEMIEN http://mac.abc.se/~pictor/ === Subject: Re: Geometrical shape Originator: fred@fred.usr.optusnet.com.au (name-string) > What's the English name of the 26-side ball-shape of the point leveler > weight on the picture? In Swedish it's evidently rombkuboktaeder... http://www.abc.se/home/m10901/RAIL/osj_klot.html According to Mathworld, it's a small rhombicuboctahedron: http://mathworld.wolfram.com/SmallRhombicuboctahedron.html It's one of the Archimedian Solids: http://mathworld.wolfram.com/ArchimedeanSolid.html .6633 === buy nike shoes at wholesale price(www.cheapestsell.com) === Subject: decay rate of the spectrum? Hi all, If I have the signal not in closed form, but in form of some collected data. The sampling(or collection) of such signal data points are very costly. Thus we want to minimize the number of samples(data collection). Is there a way to estimate the decay rate of the spectrum? === Subject: Re: decay rate of the spectrum? Originator: roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) >If I have the signal not in closed form, but in form of some collected data. >The sampling(or collection) of such signal data points are very costly. >Thus we want to minimize the number of samples(data collection). >Is there a way to estimate the decay rate of the spectrum? You need a model for the decay, and you need a maximum error bound that you are willing to tolerate. After that, it's a matter of fitting and calculation of error residuals. Your question is too general: with the information you gave, we have no way of knowing that the function converges in any finite order. If you've sampled 1 billion points, with the information you've given us, we must assume the -possibility- that the one-billion-and-first sample will be the key one that spikes the function output to settle into its final decay phase. -- Programming is what happens while you're busy making other plans. === Subject: Re: decay rate of the spectrum? > Hi all, If I have the signal not in closed form, but in form of some > collected data. The sampling(or collection) of such signal data points are very > costly. Thus we want to minimize the number of samples(data collection). Is there a way to estimate the decay rate of the spectrum? If you're asking about the rate at which you must sample a signal to obtain a faithful representation, you should read about the Nyquist theorem (alias the Nyquist sampling theorem, or the Nyquist-Shannon sampling theorem). Otherwise, I have found it impossible to comprehend what it is you're asking. Dale === Subject: Re: help: first year calculus applied to intro EE Bytes: 5524 On Fri, 10 Aug 2007 23:58:19 -0400, Brian VanPelt >On Fri, 10 Aug 2007 17:20:31 -0700, Robert Israel On Thu, 09 Aug 2007 00:04:10 -0500,Robert Israel > I am pretty familiar with first year calculus (including FTOC and > convergence of improper integrals). > I am now reading an EE circuit theory book where there is a common > calculus step in several derivations that I can not follow 100%. > For example: > i(t) = dq(t)/dt (i=current is time rate of change of q=charge) > Then book would say, therefore.... > q(t) = int[from -inf to t] i(t)dt >I hope it's assuming somewhere that the limit of q(t) as t -> -infinity is 0. > This happens a lot in the book, where the reverse of a derivative > formula results in an improper integral. Now, it makes sense when I > think of things like this as the charge that passed the point from > beginning of time to current time (where negative infinity is > beginning of time), but what exactly is the calculus step taken? I > mean, how do we get an improper integral from the original derivative > formula (what manipulation or theory or reasoning do we use to do that > step)? What about issues of convergence? > Basically, what allows me to do such a step? > z(t) = dy(t)/dt ==> y(t) = int[from -inf to t] z(t)dt > (assume only that y(t) is differentiable on the interval considered) >It's not true then... >The Fundamental Theorem of Calculus tells you, if z(t) is continuous then >y(b) - y(a) = int_a^b z(t) dt. Assuming the limit of y(a) as a -> -infinity >is L, that implies y(b) - L = int_{-infinity}^b z(t) dt (that improper >integral being defined as the limit of integrals from a to b as >a -> -infinity). So your formula is right if L happens to be 0, but not >otherwise. If the limit of y(a) as a -> -infinity exist, then the improper >Sorry, I don't know how the word doesn't disappeared here. >integral doesn't exist either. > Dr. Israel: > The limit of q(t) is most likely zero as t goes to -inf because it is > a charge, and those are known to decay to nothingness. >Electrical charges decay? That's news to me, not to mention >Maxwell... >Any real electrical circuit is unlikely to have existed from time >immemorial. >It was set up at some finite time in the past, and anything that your >mathematical model says about it before that time is a fictional >extrapolation. In that context, there's no reason to assume a limit >of 0. You got me there, because I know next to nothing about physics. All I >know is that after a time, my batteries don't work anymore. So, I >reflected about the vertical axis. This was evidently a bad >application of reflection. Although I heard Maxwell made very good coffee. Brian > -- >Robert Israel israel@math.MyUniversitysInitials.ca >Department of Mathematics http://www.math.ubc.ca/~israel >University of British Columbia Vancouver, BC, Canada I went to sci.physics and a physicist named Stephen Montgomery-Smth Since my reply is quick, and your post is long, forgive my top-posting. The mathematician's reply is completely correct. Going from the differential equation to the given integral equation simply is not mathematically correct in of itself. There must be another (probably unstated) physical assumption in play. The OP's suggestion the charge that passed the point from beginning of time to current time (where negative infinity is beginning of time) is exactly the reasoning I would have used. In addition there are questions of convergence, as the OP suggested, that the EE book has completely overlooked. But these issues of convergence will be trivially handled if one makes the physically very reasonable assumption that i(t) is zero if one goes sufficiently far back in time. I should also add that your reply also makes perfect sense as well. I think he was very nice in adding that last sentence. Yeah, I got to Brian === Subject: Pokerization of Lottery Bytes: 3661 ****************************************************************** Now we build a Google group called Pokerization of Lottery. You can easily find it through Google. Lottery is NOT a game of chance but a game of MANIPULATION. It is this statement that costs the life of our two websites. We sincerely invite you to visit our group and look into our Pages carefully. We didn't form any syndicate nor ask you to pay anything. We just want you to experience the manipulation yourself ****************************************************************** When we post the above message into the following two forums : 1. 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Do you think we are still spamming ? === Subject: Vectors, cross product, exterior algebra I have recently been looking into the theory behind the cross product and I have reached a point of difficulty. The concept that the wedge of two vectors creates a plane, of a specific area and orientation, I can accept. This concept can be physically shown using graph paper to show that multiplying rows and columns yields the same answer as counting all of the included table cells. What I cannot figure out is why magically, in three dimensions, we get to convert the plane's orientation (which I visualize as the right- handed spin) into a new pseudovector. I have looked into quaternions, but I cannot see there how the step was reached wherein ij=k, jk=i, etc. I would look past this issue EXCEPT for that it seems vital to vector calculus. Concepts like curl just make much more sense if you accept the pseudovector. Ideas? === Subject: Re: Vectors, cross product, exterior algebra Bytes: 2091 > I have recently been looking into the theory behind the cross product > and I have reached a point of difficulty. The concept that the wedge > of two vectors creates a plane, of a specific area and orientation, I > can accept. This concept can be physically shown using graph paper to > show that multiplying rows and columns yields the same answer as > counting all of the included table cells. What I cannot figure out is why magically, in three dimensions, we get > to convert the plane's orientation (which I visualize as the right- > handed spin) into a new pseudovector. I have looked into > quaternions, but I cannot see there how the step was reached wherein > ij=k, jk=i, etc. I would look past this issue EXCEPT for that it seems vital to vector > calculus. Concepts like curl just make much more sense if you accept > the pseudovector. Ideas? > Look up the Hodge star operator. To see why it only works in three dimensions consider that the second exterior power of R^n has dimension n(n-1)/2. This is equal to n if and only if n=3. === Subject: Re: Vectors, cross product, exterior algebra Bytes: 2672 > I have recently been looking into the theory behind the cross product > and I have reached a point of difficulty. The concept that the wedge > of two vectors creates a plane, of a specific area and orientation, I > can accept. This concept can be physically shown using graph paper to > show that multiplying rows and columns yields the same answer as > counting all of the included table cells. What I cannot figure out is why magically, in three dimensions, we get > to convert the plane's orientation (which I visualize as the right- > handed spin) into a new pseudovector. I have looked into > quaternions, but I cannot see there how the step was reached wherein > ij=k, jk=i, etc. I would look past this issue EXCEPT for that it seems vital to vector > calculus. Concepts like curl just make much more sense if you accept > the pseudovector. Ideas? The difference between left and right is a three-D concept.In the plane of ecliptic the earth is going an oriented path. But You can not say it is a left turn around the sun or a right, without choosing a position outside the plane on one side of it. In three-D You can have two chiral spirals, which do not change with movement, but a plane turned over in space changes left to right. Face at midday the sun and see the sun moving from left to right. Now turn around and lie on the ground - it will move the opposite way. With friendly greetings Hero === Subject: Re: Vectors, cross product, exterior algebra Bytes: 1463 So please read > In three-D You can have two chiral helices, which do not change with > movement, but a plane turned over in space changes left to right. > Sorry Hero === Subject: Re: Vectors, cross product, exterior algebra Bytes: 2049 > So please read > In three-D You can have two chiral helices, which do not change with movement, but a plane turned over in space changes left to right. Sorry > Hero Actually, I have researched these answers, and they do not really provide a physical explanation for the reason it is reasonable to use the pseudovector. Part of the leap is the ij=k, etc. The right-hand- rule will tell you that ixj gives a counter-clockwise rotation. But why do we say that this rotation corresponds to the k vector, and if there is a good reason for it, why does it only work in 3D? === Subject: Re: Vectors, cross product, exterior algebra Bytes: 2616 Josh a .8ecrit : > So please read > In three-D You can have two chiral helices, which do not change with > movement, but a plane turned over in space changes left to right. > Sorry > Hero Actually, I have researched these answers, and they do not really > provide a physical explanation for the reason it is reasonable to use > the pseudovector. Part of the leap is the ij=k, etc. The right-hand- > rule will tell you that ixj gives a counter-clockwise rotation. But > why do we say that this rotation corresponds to the k vector, and if > there is a good reason for it, why does it only work in 3D? > A reasonably simple explanation is that it is only in 3D that three vectors (non linearly dependent) can have an orientation =and= it is only in 3D (and in 7D) that a vector product (i.e. an inner operation satisfying distributivity) can be defined. A physical explanation is that orientation cannot be defined intrinsically, as is proved by the parity conservation principle. But, of course, all this begs a little the question : the vector product is a convenient trick, but it is a shadow of the full quaternion product. So your real question could be : why do we live in 3D, when the simple math is in 4D ? === Subject: Re: Vectors, cross product, exterior algebra <46bf19a1$0$21142$7a628cd7@news.club-internet.fr> Bytes: 2036 > ... But, of course, all this begs a little > the question : the vector product is a convenient trick, but it is a > shadow of the full quaternion product. So your real question could be : > why do we live in 3D, when the simple math is in 4D ? We have 3 spatial dimensions, but we can do scaling in the space, we live in, as well. With this our space-time has the mathematical dimension for Scalars as well. And the 3D of the Quaternions is a vector-space over the field of Scalars, which makes it mathematical 4 D's. 3 times 2 apples makes 6 of it, 3 times a week makes 21 days. With friendly greetings Hero === Subject: Re: Vectors, cross product, exterior algebra Bytes: 2215 > I have recently been looking into the theory behind the cross product > and I have reached a point of difficulty. The concept that the wedge > of two vectors creates a plane, of a specific area and orientation, I > can accept. This concept can be physically shown using graph paper to > show that multiplying rows and columns yields the same answer as > counting all of the included table cells. What I cannot figure out is why magically, in three dimensions, we get > to convert the plane's orientation (which I visualize as the right- > handed spin) into a new pseudovector. I have looked into > quaternions, but I cannot see there how the step was reached wherein > ij=k, jk=i, etc. I would look past this issue EXCEPT for that it seems vital to vector > calculus. Concepts like curl just make much more sense if you accept > the pseudovector. Ideas? Look up Clifford algebras, or geometric algebras, particularly 3 dimensional ones. http://www.av8n.com/physics/clifford-intro.htm === Subject: Re: 4 parameters family for solvable polynomials of degree 11 > but that final step towards a_j is there a simple formula for it , or do we need to > compute the zero's ( with the other parameters > already known ) to find a_j ?? i assume so ... > it is not yet totally clear to me ... a few more brackets in the formula's would be nice > ... so not to confuse the order of computations ... but the basic idea is already clear... unfortunately i dont have the time now to check all > of that. and it is also a very particular family ( like you > say ) of solutions ... i was wondering if you have investigated septics too > ? ( 7th degree polynomials ) i am intrested in those ... also i dont know why you jumped to degree 11 ( which > is pretty high ) i assume because 11 is the first prime following > 7... what do you know about the 7th degree polynomial i wonder :-) tommy1729 Simply a_j can be evaluated in terms of m_j and shall be rationals e.g a10=0 a9=11*(-m3^2+m4^2*m2-m1^2+m2) a8=22*m3*(-m1^2+m2) a7=11*(4*m3^4-8*m3^2*m4^2*m2+5*m1^2*m3^2-5*m2*m3^2+4*m4^4*m2^2-5*m1^2*m4^2*m 2+5*m4^2*m2^2+4*m1^4-8*m1^2*m2+4*m2^2) for solvable septics you can see http://mathforum.org/kb/thread.jspa?forumID=253&threadID=1311479&messageID=4 138885 === Subject: Re: 4 parameters family for solvable polynomials of degree 11 as a reply to the septic in sci.math.research > Introduction > ------------- > Any two rational numbers m1 & m2 can form quadratic > of rational coefficients such that the roots of > quadratic > r1 = m1 + m2^(1/2) > r2 = m1 - m2^(1/2) Similarly, any three rational numbers can form cubics > of rational coefficients such that the roots of > cubics > r1 = m1 + (m2+(m2^2-m3^3)^(1/2))^(1/3) + > (m2-(m2^2-m3^3)^(1/2))^(1/3) > r2 = m1 + (m2+(m2^2-m3^3)^(1/2))^(1/3)*exp(2*pi*i/3) > + (m2-(m2^2-m3^3)^(1/2))^(1/3)*exp(4*pi*i/3) > r3 = m1 + (m2+(m2^2-m3^3)^(1/2))^(1/3)*exp(4*pi*i/3) > + (m2-(m2^2-m3^3)^(1/2))^(1/3)*exp(2*pi*i/3) Similarly, any five rational numbers can form > solvable quintics of rational coefficients > see > http://mathforum.org/kb/thread.jspa?threadID=1306799&t > start=0 Is there any form for the roots of solvable septics > which based on seven rationals and can in the same > time generate solvable septics of rational > coefficients. > Radical expression for the roots of solvable septics > ----------------------------------------------------- Let f(x) = x^7 + a6*x^6 + a5*x^5 + a4*x^4 + a3*x^3 + > a2*x^2 + a1*x + a0 has rational coefficients Let the roots of f(x) are r1, r2, r3, r4, r5, r6 and > r7 where r_j = u0 + u1*w^j + u2*w^(2*j) + u3*w^(3*j) + > u4*w^(4*j) + u4*w^(4*j) + u5*w^(5*j) + u6*w^(6*j) > j=0, 1, 2, 3, 4, 5 and 6 ; w=exp(2*pi*i/7) > u1=/=0, u2=/=0, u3=/=0, u4=/=0, u5=/=0 and u6=/=0 f(x) is solvable iff there exist 7 rational numbers > u0, m1, m2=/=0, m3>0, m4, m5 and m6 such that y1, y2, y3 are the roots for > y^3 + 3*m1*m2*y^2 + m2^2*(3*m1^2-(m3^2+27))*y + > m2^3*(m1^3-(m3^2+27)*m1-2*(m3^2+27)) = 0 > such y_n always exist ... so not a condition ?? t1 = y1/2 + m6^(1/2)*(m4*y1^2+m5*y1+1) > t6 = y1/2 - m6^(1/2)*(m4*y1^2+m5*y1+1) > t4 = y2/2 + m6^(1/2)*(m4*y2^2+m5*y2+1) > t3 = y2/2 - m6^(1/2)*(m4*y2^2+m5*y2+1) > t2 = y3/2 + m6^(1/2)*(m4*y3^2+m5*y3+1) > t5 = y3/2 - m6^(1/2)*(m4*y3^2+m5*y3+1) or does this belong to the condition too ?? with t_n neccesarily real ?? ( im(t_n)=0 ) as noticed before , your conditions seems intelligent , but not totally clear ... you should specify conditions like real or positive or integer else it seems arbitrary and not a real condition... reading a few posts of you i assume you always take the condition real ( apart from roots of unity and the actual zero's of the 'topic' polynomial of course) and here and there specify condition rational... it would make your posts more clear and perhaps more popular too ... since i feel it is underrated with 0 replies ... without clear definitions you might be considered confusing , wrong or even stupid ... i did not check your work , but i dont think your quite smart... u0=-a6/7 > u1=(t1^1*t2^2*t3^3*t4^4/t5^2/t6)^(1/7) > u2=(t1^2*t2^4*t4^1*t5^3/t6^2/t3)^(1/7) > u3=(t1^3*t3^2*t5^1*t6^4/t4^2/t2)^(1/7) > u4=(t1^4*t2^1*t4^2*t6^3/t3^2/t5)^(1/7) > u5=(t2^3*t3^1*t6^2*t5^4/t1^2/t4)^(1/7) > u6=(t3^4*t4^3*t5^2*t6^1/t2^2/t1)^(1/7) r1=u0 + u1 + u2 + u3 + u4 + u5 +u6 > r2=u0 +u1*w^1+ u2*w^2 + u4*w^4 + u3*w^3 + u5*w^5 + > u6*w^6 > r3=u0 +u1*w^2+ u2*w^4 + u4*w^1 + u3*w^6 + u5*w^3 + > u6*w^5 > r4=u0 +u1*w^3+ u2*w^6 + u4*w^5 + u3*w^2 + u5*w^1 + > u6*w^4 > r5=u0 +u1*w^4+ u2*w^1 + u4*w^2 + u3*w^5 + u5*w^6 + > u6*w^3 > r6=u0 +u1*w^5+ u2*w^3 + u4*w^6 + u3*w^1 + u5*w^4 + > u6*w^2 > r7=u0 +u1*w^6+ u2*w^5 + u4*w^3 + u3*w^4 + u5*w^2 + > u6*w^1 r_j shall be the roots of irreducible solvable septic > of rational coefficients Also, any 7 rational numbers u0, m1, m2=/=0, m3>0, > m4, m5 and m6 can generate solvable septic of > rational coefficients for m6>=0 only one root shall be real number > for m6<0 all roots shall be real numbers Example > -------- > u0 = 0 > m1 = 0 > m2 = 1 > m3 = 1 > m4 = 0 > m5 = 0 > m6 = 2 y1, y2 and y3 are the roots for > y^3 - 28*y - 56 = 0 y1 = > 1/3*(756+84*i*3^(1/2))^(1/3)+28/(756+84*i*3^(1/2))^(1/ > 3) y2 = > -1/6*(756+84*i*3^(1/2))^(1/3)-14/(756+84*i*3^(1/2))^(1 > /3)+i*3^(1/2)*(1/6*(756+84*i*3^(1/2))^(1/3)-14/(756+84 > *i*3^(1/2))^(1/3)) y3=-1/6*(756+84*i*3^(1/2))^(1/3)-14/(756+84*i*3^(1/2)) > ^(1/3)-i*3^(1/2)*(1/6*(756+84*i*3^(1/2))^(1/3)-14/(756 > +84*i*3^(1/2))^(1/3)) > t1 = y1/2 + 2^(1/2) > t6 = y1/2 - 2^(1/2) > t4 = y2/2 + 2^(1/2) > t3 = y2/2 - 2^(1/2) > t2 = y3/2 + 2^(1/2) > t5 = y3/2 - 2^(1/2) u0=0 > u1=-(-t1^1*t2^2*t3^3*t4^4/t5^2/t6)^(1/7) > u2=-(-t1^2*t2^4*t4^1*t5^3/t6^2/t3)^(1/7) > u3=-(-t1^3*t3^2*t5^1*t6^4/t4^2/t2)^(1/7) > u4=-(-t1^4*t2^1*t4^2*t6^3/t3^2/t5)^(1/7) > u5=+(+t2^3*t3^1*t6^2*t5^4/t1^2/t4)^(1/7) > u6=-(-t3^4*t4^3*t5^2*t6^1/t2^2/t1)^(1/7) r1=u0 + u1 + u2 + u3 + u4 + u5 +u6 > r2=u0 +u1*w^1+ u2*w^2 + u4*w^4 + u3*w^3 + u5*w^5 + > u6*w^6 > r3=u0 +u1*w^2+ u2*w^4 + u4*w^1 + u3*w^6 + u5*w^3 + > u6*w^5 > r4=u0 +u1*w^3+ u2*w^6 + u4*w^5 + u3*w^2 + u5*w^1 + > u6*w^4 > r5=u0 +u1*w^4+ u2*w^1 + u4*w^2 + u3*w^5 + u5*w^6 + > u6*w^3 > r6=u0 +u1*w^5+ u2*w^3 + u4*w^6 + u3*w^1 + u5*w^4 + > u6*w^2 > r7=u0 +u1*w^6+ u2*w^5 + u4*w^3 + u3*w^4 + u5*w^2 + > u6*w^1 Then > f(x)= x^7 - 56*x^5 + 637*x^3 + 87808*x^2 - 1091426*x > + 4136384 Numeric results > --------------- > u0 = 0 > m1 = 0 > m2 = 1 > m3 = 1 > m4 = 0 > m5 = 0 > m6 = 2 y1 = 6.09783467904461 > y2 = -3.38404294326019 > y3 = -2.71379173578442 t1 = 4.4631309018954 > t6 = 1.63470377714921 > t4 = -0.277807909257001 > t3 = -3.10623503400319 > t2 = 0.0573176944808858 > t5 = -2.7711094302653 u1 = -0.297964531910523 > u2 = -0.285104386190312 > u3 = -8.7211592464654 > u4 = -0.836574214167311 > u5 = 0.557106840127755 > u6 = -2.89610530127261 w = 0.623489801858734 + 0.78183148246803*i r1 = -12.4798008398784 > r2 = 6.55922408823645 - 2.21078021832323*i > r3 = -5.49346768217753 + 9.0628385162772*i > r4 = 5.17414401388029 - 5.90114374057039*i > r5 = 5.17414401388037 + 5.90114374057036*i > r6 = -5.49346768217762 - 9.06283851627716*i > r7 = 6.55922408823645 + 2.21078021832318*i Then > f(x)= x^7 - 56*x^5 + 637*x^3 + 87808*x^2 - 1091426*x > + 4136384 > big question is ; are there other solvable cases of septics ?? intresting post better than the average pdf about septics (if all correct) keep up the good work tommy1729 === Subject: Re: 4 parameters family for solvable polynomials of degree 11 > y1, y2, y3 are the roots for > y^3 + 3*m1*m2*y^2 + m2^2*(3*m1^2-(m3^2+27))*y + > m2^3*(m1^3-(m3^2+27)*m1-2*(m3^2+27)) = 0 such y_n always exist ... >so not a condition ?? y_n are always exist if m1, m2 & m3 are exist t1 = y1/2 + m6^(1/2)*(m4*y1^2+m5*y1+1) > t6 = y1/2 - m6^(1/2)*(m4*y1^2+m5*y1+1) > t4 = y2/2 + m6^(1/2)*(m4*y2^2+m5*y2+1) > t3 = y2/2 - m6^(1/2)*(m4*y2^2+m5*y2+1) > t2 = y3/2 + m6^(1/2)*(m4*y3^2+m5*y3+1) > t5 = y3/2 - m6^(1/2)*(m4*y3^2+m5*y3+1) >or does this belong to the condition too ?? t_n are always exist if y1, y2, y3, m4, m5 & m6 are exist >with t_n neccesarily real ?? ( im(t_n)=0 ) The design of cube equation shall produce real roots y_n t_n shall be real if m6>0 and only one real roots shall be exist t_n shall be complex if m6<0 and all roots shall be reals >as noticed before , your conditions seems intelligent , but not totally clear ... >you should specify conditions like real or positive >or integer >else it seems arbitrary and not a real condition... >reading a few posts of you i assume you always take the condition real ( apart from roots >of unity and the actual zero's of the 'topic' polynomial of course) >and here and there specify condition rational... The only condition is to find rational m_n related to the solvable septics. m_n shall be exist iff septic is solvable t_n, u_n & r_n shall be complex(or reals/rationals) evaluated based on rational m_n The main purpose for this topic is to generate solvable septics not to solve them For solution solvable septics you can see http://mathforum.org/kb/thread.jspa?forumID=253&threadID=1312531&messageID=4 143512 === Subject: Silverman's calculus text Bytes: 1421 Hi all: Has anyone ever used Richard Silverman's Modern Calculus and Analytic Geometry in their calculus classes. I never knew the book existed, but found it at Borders Books today when I was in search of an inexpesive calculus textbook. As I was reading, I noticed that the explanations are unusually clear and the level of problems is typically higher than standard calculus texts. Plus, it's only $40. I have only seen one review of the book on Amazon.com, and searching the internet didn't yield much, so I am looking to anyone's experience with the book. I would like to use it this year. Please let me know what you think of the book. Brian === Subject: Koos Nolst Trenite - 'The Mafia Code Against Mankind' V2.1.txt.nfo Bytes: 5064 Koos Nolst Trenite ('Cause Trinity') is arguably the most intelligent, the most caring and loving, the most beautiful and the most truthful philosopher known. In 'The Mafia Code Against Mankind,' Koos Nolst Trenite describes the two parts of this Code, and breaks each part down as it becomes more and more hidden and as it adapts itself to the circumstances of life surrounding it. Some historic roots of 'The Mafia Code Against Mankind' are given, too. ' A quote from 'The Mafia Code Against Mankind:' And of anybody you meet - blinded as his or her spiritual eyesight is, and faded to dust as his or her memories are supposed to be after his or her death - some assert to you, that you are dead, you do not exist anymore, even if you were his or her best friend in a previous life! (*) I find that slightly annoying, if not outright vulgar, because it is a continuous barrage of unthinking and thoughtless and ugly lies, subjecting others and yourself to it, very persisting work of the various Criminal Minds throughout Earth's history, who - as you know - left a trail of tortured and burnt or drowned past life bodies of yours and of your friends behind them, to enforce the acceptance of their lies. (With the result, that some assert to you, that you are dead, that you do not exist anymore, even if you were his or her best friend in a previous life!) ' Even though Koos Nolst Trenite is believed to have been Leonardo da Vinci, there is no relation between his discovery and description of 'The Mafia Code Against Mankind,' and on the other hand the entirely fictional work of someone else, called 'The Da Vinci Code,' that was written for the purpose of entertainment and 'sales appeal' only. (**) ' (*) 'If You Were Alive Now - in response to If Bach Lived Today...' (**) 'The Dan Brown Code - The Trillion Dollar Question' {HRI 20060610-V3.4} (10 June 2006 - Version 3.4 on 10 July 2006) ' ____________ Verification: http://www.angelfire.com/space/platoworld Copyright 2007 by Koos Nolst Trenite - human rights philosopher and poet This is 'learnware' - it may not be altered, and it is free for anyone who learns from it and (even if he can not learn from it) who passes it on unaltered, and with this message included, to others who might be able to learn from it. None of my writings may be used, ever, to support any political or religious or scientific agenda, but only to educate, and to encourage people to judge un-dominated and for themselves, about any organizations or individuals. Send free-of-Envy and free-of-Hate, Beautiful e-mails to: PlatoWorld at Lycos.com === Subject: Koos Nolst Trenite - 'The Mafia Code Against Mankind' V2.1.txt - {HRI 20021018-V2.1} Bytes: 52867 The Mafia Code Against Mankind 18 October 2002 {HRI 20021018-V2.1} (Version 2.1 of 12 Aug 2007) (layout for typewriter font) (suitable for foreign language students) ' The Mafia Code against Mankind - as you may know already - is very strictly enforced by certain individuals (you can find them in any position, in any group, in any race, with any belief or religion, in any profession, with any political ideas, and of any nationality), and their Mafia Code against Mankind - reads as follows: 1. Do NOT investigate the nature and use of Life Energy - 1.a Deny the existence of Life Energy. uses to feel, to sense, to perceive, to memorize, to sing, to whistle or play the violin, to express one's love and emotions, to recognize people, and to be curious and happy about being alive, etc. etc.. These Energies are felt or sensed and used not only by yourself, by your soul, but also by your body, as anyone knows and as you can feel every day. in the interaction between you (your soul) and your body, while your body is alive. You use Life Energy to connect your awareness for instance to the sense organs of your body. So they make your use of the body's senses (eyes, ears, etc.) possible. *(1) ' And one can also feel, of course, one experiences it, one's body when or after a Criminal Mind has pulled away or has smashed some Energy from one's body, resulting for instance in tiredness, or in loss of abilities, or loss of memory, or loss of emotion, or loss of love and connection to people, or loss of connection to the body or to parts of the body, so that you can not keep it healthy, or so that parts of it can not be kept healthy by you anymore. And one can feel, of course - both on one's body and in one's soul - the use and projection, by Criminal Minds, *(2) (See also point 1.c on that, further below.) ' 1.b If denial of the existence of Life Energy fails, then do obscure or falsely describe or get others to falsely or incompletely describe the nature, use and function of Life Energy. *(1)(3) 1.c If that fails, then deny that Criminal Minds are poisoning and are using Altered (poisoned) Life Energy to destroy or to manipulate others and to bring about unawareness, and to get untruth not felt or recognized. *(2) With poisoned or Altered Life Energy, they manipulate the soul of others, and the feelings one gets from the body. They dominate others, they delude others, they use Life Energy to enforce emotions and ideas on others, as if these are the recipient's own emotions and own ideas. They also project poisoned Life Energy onto the body of people, in order to bring about immune deficiencies, and to inflict sickness upon others. They use it to distract or diminish people's attention or awareness, so that these have accidents. Or they cause someone's body to have a heart attack or a stroke, by the infliction of intense, harmful, poisoned Life Energies onto those spots of your body. They use it to destroy the awareness, the perceptions, the memories and the abilities of people, and instead to cause euphoria and selective 'blindness' (unawareness of certain things). ' 1.d If denying the evil use of Life Energy fails, and also generally, just draw no attention to the use of Life Energy that is poisoned and with which Criminal Minds dominate and manipulate people and incapacitate them or make people sick: DIVERT THE ATTENTION OF PEOPLE ONTO NATURE. Direct people's attention and their care and curiosity away from detecting and stopping those individuals who destroy life. Divert it, away from looking at and investigating and understanding those who create or use poisoned Life Energy to destroy or hinder life. Let people only perceive and feel their care for animals, for plants or for 'the Earth', but not their care for people. Make them fully convinced, that 'they can not remedy the suffering of people.' So their attention can be more easily diverted to caring for nature only. ' 1.e Allow people to perceive and to investigate and to study only the interaction between objects - and make them do that exclusively with photons or electrons. Demand that people regard, and also treat, the living body as a physical object. The body as an object: WITHOUT its Field of Life place and that keep it alive and repaired, and without which the body would not be alive for one second. ' ' 2. Do NOT investigate, openly and correctly, your own or others' past lives. Past lives are the actual, own and true history of people, and therewith, the true history of Mankind. Criminal Minds intend to reverse all truth, and they then like to say about people who know some of their past lives, that 'those people THINK they have had real and actual previous lives with real names and true locations and real history-book history.' ' But whether people, you or I, THINK or not think so, is entirely besides the point: Whether we know or guess or affirm or deny that we have been called Jones or Schmid or LeBrun or Chang or Ilja or Pedro or Jesus or Indira, in our preceding life, we, and they, HAVE had a very precise and very particular and very unique life, before our present one, (and before that previous one too). And ALSO when we, or they, have not the faintest idea about past lives, and also when we have 'never heard of previous lives,' we HAVE been who we have been, and we have done what we have done and experienced, in our past lives, in our previous lives. And so have others - the same applies to others - REGARDLESS of whether we, or they, know, or remember, or do not know, or do not remember who we or they have been and what we or they have done in earlier lives, and REGARDLESS of whether we, or they, are still now acting upon, or also now can or do sense or feel or know and remember such past activities, past achievements and past failures, feelings and thoughts, likes and dislikes, and pains and sorrows, of our previous lives. ' REGARDLESS of whether we, or they, know, sense or feel things from previous lives falsely, or whether we feel it correctly, we, and they, still have done and still have experienced what we did, or the consequences of what we failed to do. Whether people see or know or not, that does not in any way change the fact of what actually exists: As much as you can deny the existence of bacteria, they still exist, they still act upon you, upon life, and that not only since Antony van Leeuwenhoek spied them with his microscope (in 1683) and not only two hundred years later, when they started to use that knowledge for saving many people's lives and for preventing illness, and to conserve food, and so on. *(a) ' These facts can be established without too much work, and with the assistance of a Life Energy Fluctuation Meter, which, because you measure the fast fluctuations in regular electrical - direct-current or 'galvanic,' as from a battery - resistance between concentrating Life Energy points (acupuncture points) such as between the hand palms touching each a big metal surface, to measure the very sudden, and sometimes very big but mostly small fluctuations in electrical resistance, from the changes in Life Energies impinging upon your body, and so it is vulgarly called - by those who do not understand why and how it works, and who deny the existence of Life Energy - called a 'Galvanic Skin Response' (GSR) meter, or Emotion-Meter. Even more vulgarly and even further from the truth, and by those of even less understanding, it is called a lie-detector. Presently, and to enforce 'The Mafia Code against Mankind,' the less a professional understands about these things, the higher is his salary, or the more funds for research he gets, because he will not actually make any correct use of the principle, and he can be expected to spread false and misleading date about its use and prove it to be useless, not unlike they said, a century ago, about the introduction of the telephone - now a common and indispensable instrument in every society. ' It reacts on truth rather than on lies, and it does not react properly on Criminal Minds at all, regrettably enough: Criminal Minds have a reverse concept of truth, and you can not detect them with a meter that shows the behavior of their Life Energy, nor by other indicators of their body - because they do not only pretend in word, but they pretend also in mind, they ALSO lie Energetically - in their thoughts, that is - they fully create the Energies to make their and other people's lies seem and feel true. They do so by means of the manipulation of Life Energy content and behavior. ' You know this very well about them: Inside a Criminal Mind, just about anything can be completely true - and they can have any falsity completely true, at any moment, and keep it so as long as they want some very false data to be completely true. They are perfect actors, indeed, and are very proud of their ability to lie and to deceive, and some even get famous and highly paid for it. ' ' We continue looking at 'The Mafia Code Against Mankind:' 2.a Deny the previous lives of people, deny any person's previous lives. 2.b If that fails, get incorrect or ridiculous 'previous lives' accepted as 'past lives,' such as 'having been' insects, or mollusks, or apes, or cows, etc.. Promote false data about past lives (previous lives), and also about what people do in between their lives. Write and promote books with such false and perverted data. About the previous lives of people - and about what they do while they are without a body, such as in between lives - there exists, as you know, the promotion of false (and often most ridiculous) data and of (entirely and often maliciously) wrong understanding, the most malicious falsities, not only cloaked as religion, or spirituality, but also as science - promoting or even proving the most debilitating-ly false data to be true. Constantly, and with very disastrous effects, this is done by those who fiercely desire to have people's awareness and activities controlled. It is done by those who therefore intend - whether or not they are aware of their intention - to confuse and to misinform people, out of whatever necessity and for whatever reason they can think of as having the most chance of getting the false data accepted or believed and followed. And thus they assist Criminal Minds in dominating people. Thus they too enforce The Mafia Code against Mankind. ' The Mafia Code continues: 2.c If that - the promotion of false data and false ideas about past or previous lives - fails, then you prevent people from perceiving and accepting the previous lives, and thereby the nature, of those persons I. who have truly been decent throughout their previous lives, and who have been so in between their lives too. And equally important, you prevent people from perceiving the nature of, and from recognizing by past lives, those individuals II. who throughout most of their previous lives have done evil, and who are basically evil, or very evil, by nature. *(4)(5) 2.d If that fails, then do at least prevent the perception and thus prevent the recognition by past lives, of very evil individuals - of the truly Criminal Minds who have been, throughout their previous lives and in between their lives and who indeed are, basically evil or very evil. *(6) ' Most people have much or all of the Life Energy taken away from them, that they would need to be able to remember their own past lives - what they did in their own previous lives. But equally the Energy that they would need to remember the previous and indeed past lives of others, not only of their friends, but ALSO the previous activities (and the spiritual activities in between lives) of Criminal Minds, AND the previous lives activities of Destructive Cowards too, that is, of those who covered up, who protected and who assisted Criminal Minds. ' ' Awareness is brought about by having Life Energy. And awareness is diminished, awareness is taken away, by taking away Life Energy or by making a person disconnect from parts of his Life Energy. (Or forcing a person to part with all of his Life Energy, which is always against his will, and which is resulting not only in a bodily death, but also in a spiritual - and indeed very frightening - death, as it was practiced at times you will discover from people's previous lives, and as some people re-live it, in their nightmares.) ' Especially, of course, your Life Energy to remember your more distant past, is taken away - that partial unawareness is brought about and is caused, is inflicted - by those who do not want to BE remembered as far as what THEY did in their previous lives. And their past lives are part of your past lives, at some time or another. Decent people mostly are quite proud of their previous lives, of what they have achieved - of what they have done for others and for mankind in their previous lives. ' But Criminal Minds, or the Destructive Cowards who act as their slaves, even for themselves they do not want to know or remember their own true past. They do not want to know their past correctly at all - that is, like true criminals, they deny what they did. They deny it not only to others but mostly also to themselves, what they did in their previous lives. And what's more - Agatha Christie has become famous by writing about it - they like to blame their own crimes on others, in order to hide the crimes better. And they like best to have others falsely convicted for it. And they like to blame, and have executed, especially those who can see or who can recognize them and who can see what they did or what they do intend - they like to execute, or to murder forever, those who are not fully blind yet. ' Detection of these individuals of course would be easy, if one would remember what they had done in previous lives: They have criminal records, so to speak, mass murder or systematic extermination of people, and such activities: To solve over-population, or to 'rid' the society of nuisance, impurity or illness - while it is they, the Criminal Minds, that are the very individuals who caused people in the society to be upset, blinded, insane or ill! ' ' You have found - if you studied any history at all - that Criminal Minds will, in order to hide their nature better, and to be evil unhindered, assume an opposite past life identity to what they actually are and were, and they will carry that false identity as if it is their present life, and they will pretend to have been the very one who actually fought their evil, and they will pretend to have been the good person that they actually murdered. That murdering and that torturing they did, indeed, mostly or wholly, in order to obtain the Life Energy of their victim(s), the Life Energy that contains the abilities, as well as the identity of their victim(s) - whom they now pretend to have been in that past life. And so you could detect the Anti-Christ, and expose him. ' ' You could become a true investigator, and provide correct justice, as I did, and for which I am somewhat famous from some earlier life times. I am free of hate, and so I can bring about justice, when asked to. You understand, that, as soon as you begin to hate, you are siding with criminals: You are doing what Criminal Minds want more from you than anything else - that you hate people, or that you want to take revenge. ' The true meaning of 'Turn the other cheek' is: Do not return hate with hate. Because returning hate with hate, is just doing what a criminal wants you to do: To hate - to be like a criminal too. ' ' Sometimes, people contact or acquire the Life Energy that connects their awareness to the memories of their own past, and so they achieve a remembrance of previous lives, of past lives, where or when or how they lived; they may, in the same way, become aware of one or more previous lives that others lived, maybe that they lived together with in the past. ' ' On Earth, where Criminal Minds are - even now - more or less free to become the richest and the most famous and the most admired, *(7) on Earth, where Criminal Minds are - even now - more or less free to govern a state or a country *(8) (though in the future that possibility probably will sooner end for them) *(9) that is, in the spiritual or Energetic, environmental pollution that we live in, we live together with Criminal Minds. ' Criminal Minds who, according to the Constitution of Benjamin Franklin, are equal to you. Benjamin Franklin was a strict adherent to the Mafia Code against Mankind, and, knowing his previous and his following life times, he certainly has good personal reasons for that. When Benjamin Franklin was in France, he recommended after proper investigation, the denial and the prohibition of Mesmer's discovery of Life Energy in and around the body, a discovery that Mesmer used to heal people. *(b) ' That Criminal Minds are equal to you and to me whenever these are born again, Benjamin Franklin convinced those of, who were in 1787 present in Philadelphia, in America, who convened to create a supposedly free society - when Benjamin Franklin 'carefully' perverted their Constitution, to give free rein to Criminal Minds while pretending to do exactly the opposite. Further, telling people that they have inalienable rights (rights that 'can not be taken away from them') WITHOUT informing them that they do not have those rights to begin with, WITHOUT informing those same people that they are dominated and manipulated by Criminal Minds, and how it is done, by the prolific and harmful use of those non-existent Life Energies poisoned (or 'Magnetic Fluid' as Mesmer called it without poisoning it but instead de-toxifying it) on people, and how it was done, by the most violent and wholly irresistible hypnotic (subconsciously and irresistibly compelling) use of poisoned Life Energies on them, in certain practices and with certain devices, in the previous or past lives of people, that makes them now be unaware of or blind to Criminal Minds, and that makes them still now act highly irrational or even become sick, to then speak of and to pretend that everyone is capable of enjoying 'in-alienable rights', such a statement is not only 'a trifle exaggerated,' but again it is the wholly unseen method of giving Criminal Minds free rein ...without these (in that Constitution) even being considered to exist! *(10) ' When in my present life time, I met the reborn Adolf Hitler, (yes, Criminal Minds do get reborn, and yes, they can be recognized, no matter what you are told by some Destructive Cowards about Universal Laws) I was very highly offended and shocked, that others, who were surrounding him now, were looking up (!) to him, and that they were fully trusting (!) him, and most of all, that they were, on top of that - insult upon insult - demanding of me to do the same! I had never seen anyone whose hate for me was more apparent or more latently violent, except maybe the glowing hate that his (apparently inseparable) companion, the reborn Heinrich Himmler, carries for me, for life, that is. *(11) I was shocked, and I continued to be shocked, till I found out the reason for these indeed very correct observations and feelings of mine - both about him, and about those surrounding him. *(12) ' Despite our living in this very polluted environment, we try to maintain the Life Energy necessary to connect to our memories; our memories that, on Earth, are constantly denied or lied about from the moment we are born, in most cultures already by the fact that we constantly are being told that we are dead, and we have to respect our 'dead' ancestors. Maybe if you have been Marco Polo, or maybe Antony van Leeuwenhoek - then you must read in every book or encyclopedia, that you are dead, that you do not exist anymore. And of anybody you meet - blinded as his or her spiritual eyesight is, and faded to dust as his or her memories are supposed to be after his or her death - some assert to you, that you are dead, you do not exist anymore, even if you were his or her best friend in a previous life! *(14) ' I find that slightly annoying, if not outright vulgar, because it is a continuous barrage of unthinking and thoughtless and ugly lies, subjecting others and yourself to it, very persisting work of the various Criminal Minds throughout Earth's history, who - as you know - left a trail of tortured and burnt or drowned past life bodies of yours and of your friends behind them, to enforce the acceptance of their lies. ' awareness to their memories of previous lives, that Energy in sufficient amounts to make them constantly conscious of such memories - that Energy is sooner or later smashed or pulled away from them again. Often that is done already when they are still babies or toddlers, by means of forceful blasts of deadening, poisoned Life Energy from Criminal Minds, who blind these babies again. Each and every time when they have acquired enough Life Energy to be aware of and to connect to their memories of who they really are, and, almost by consequence, to their memories of who OTHERS really have been, that Awareness Energy is smashed away by those who would not want others to be thus aware: It is smashed away by Criminal Minds. *(1) ' But sometimes, someone generates so much Life Energy, for instance in a sudden moment of extreme threat to his life, that he suddenly connects to all the memories of one whole life time: He sees his whole life in a flash, so to speak, and so he speaks, as he saw it. And sometimes, someone visits a place, or sees an object, or meets a person, that connects him to the Energy of a past life, or of several previous lives, and so he remembers, or feels, or senses, because of the regained Energy, till that is smashed or pulled away again. ' ' Now what happens if you are not AWARE of your past, your previous lives, your past lives: Mostly people live almost completely in their past lives, of which they are not aware, and so all their past lives - all things that happened in their past lives - act like hypnotic commands to them. *(13) Things done to them in their past lives, act upon them now, as hypnotic commands. ' There is another factor, because past lives and the time in between lives, was very far from pleasant for most of them, most of the time. And so people have been convinced, that they need, or even that they want huge amounts of the very poisonous, debilitating Euphoria ('Drug') Energy and the very strongly poisonous and deadly Unconsciousness Energy, *(2) in order to remain unaware of the unpleasant, or most unpleasant, experiences in their previous or past lives. Typically, people who use drugs fall also in that category. *(5) There are people, who without that they are consciously aware of doing so, of course, and only after they have been most violently hypnotized in their previous lives to do just that, marry a Criminal Mind for that very purpose, or who (when they decide to be born again) choose a Criminal Mind as a father or a mother, or who choose a Criminal Mind as their best friend: The Criminal Mind is producing so much 'Drugging' Energy for them, and rather much Unconsciousness Energy, so that, to their great relief, they now live in the apparency - they feel - that Criminal Minds do not exist, and they feel the proof of that, day and night, in front of them. ' ' In order not to be too much influenced by violent hypnosis, by torture and other experiences in previous lives, in order to be somewhat free to choose and reasonably free to decide, in order to be somewhat self-determined, one has of course to be aware of these past lives to some extent, so that these do not influence you too severely and beyond your knowledge and awareness. *(13) Only then can you, indeed, BE actually in the present, and only then can you actually live in the present, really in contact with life itself in all its beauty and tremendous joy. That is not too difficult - if you are not being smashed too heavily by those who want you not to remember - to remember your previous lives. It is very much easier, if your Energy has not been smashed away too heavily, and if you are in the lucky position of having actual and real friends who do not subscribe to, who do not openly or secretly enforce 'The Mafia Code against Mankind,' or better still, who fiercely oppose that 'Mafia Code.' ' But also that is not always easy to determine, because Criminal Minds will pretend anything in order to deceive you best, and so to get your support, your trust, and thus your Energy. They will often not inform you that they are supporting that Mafia Code - some observe strict silence about what they really think. They don't remember, or they remember falsely, when queried and investigated. So it really is a Mafia Code Of Silence too, sung by a German song of which I now understand the meaning: 'Die Gedanken sind frei' - nobody can know what you think, which is yet another lie from the list of wishes of Criminal Minds. ' To summarize the last paragraphs: - Living in the present, means being aware of past lives, so that these do not influence you too much without that you know it. - Most people live almost entirely as determined by what was done to them in previous lives, often done in very distant past lives, or in between lives. ' ' And a general remark about 1. the denial of the very nature of life, of it being basically an activity of Life Energies, *(3) 2. the denial of your and others' memories and feelings from previous lives. *(13) ' Most people are VERY confused about these things, because they constantly feel or sense little things, or sometimes big things, in their mind, or on their body, in their perceptions, and, exactly as they do in the hypnosis that you know from entertainers on TV shows, after the hypnotic commands have been received, people find explanations for their commanded behavior and for their compelled desires and for the feelings or perceptions that do not fully fit the present, but that stem from their previous lives, their past lives, or from a past life - discussed as point 2. above. *(13) ' ' And people are of course even much more confused about and because of the constant barrage and projections or shots of harmful or poisoned their perception, their feelings, their thoughts, and their bodies are continuously, day and night, affected by that - discussed as point 1. above. *(3) ' ' We look further at 'The Mafia Code Against Mankind:' 3. DO create and promote any methods and ideas and books, and institutions of education, and economic structures, and medical dependencies, and sciences, and official awards and prizes and contests, that is to say any ideas and activities, that: IGNORE, DENY, DIVERT, CORRUPT, PERVERT, or PREVENT, and that deny funds to - a. the investigation of and open data exchange about Physics); *(1) - b. the investigation of and open data exchange about the actual and true history of people, of individuals, and thereby, of Mankind. *(15) ' ' Koos Nolst Trenite Cause Trinity human rights philosopher and poet 'Solomon's wisdom was greater than the wisdom of all the men of the East, and greater than all the wisdom of Egypt.' 1 Kings 4:30 _________ Textnotes: (a) Antony van Leeuwenhoek, 1632-1723 Delft, Holland. Discovered bacteria and other - unseen - life, through his very pronounced curiosity that lead to his invention, manufacture and use of an instrument now called 'microscope.' ' (b) Anton Mesmer, 1734-1815 Vienna and Paris, Europe. Discovered and used Life Energy (by him wrongly named 'magnetic,' but somewhat more appropriately, a 'fluid')*(1) to heal people of almost anything, including blindness. Mesmer was destroyed by Criminal Minds, in particular by the American Benjamin Franklin, then in Paris, France, and by the Frenchman Antoine Lavoisier: 'They reached the official conclusion [in 1784] that the 'magnetic rays' were non-existent, and any beneficial results from such treatment [nowadays the treatment is called Reiki, chiropractic, etc.] was due to self- suggestion.' *(16) 'They also reached the conclusion that magnetic treatment was dangerous for women - since it might destroy their inhibitions [women should be sexually inhibited, according to the Criminal Minds at that time and place].' *(17)(10) ' _________ Footnotes: [Check for HRI updates, and for newer HRI's on applicable subjects] (1) See newer versions - issued in separate parts, listed further down, under (p1) ... (p11) - of (29 August 2001) Newer versions of this, issued in separate parts: {HRI 20010829-pi1-V1.1.1} (29 August 2001 - part issue 1 Version 1.1.1 on 11 Sept 2006) {HRI 20010829-pi2-V1.2} (29 August 2001 - part issue 2 Version 1.2 on 12 Sept 2006) {HRI 20010829-pi3-V1.2} (29 August 2001 - part issue 3 Version 1.2 on 13 Sept 2006) {HRI 20010829-pi4-V3.0} (29 August 2001 - part issue 4 Version 3.0 on 14 Sept 2006) - The Nature Of The Physical Universe' {HRI 20010829-pi5-V3.2.1} (29 August 2001 - part issue 5 Version 3.2.1 on 18 Sept 2006) - Opposing The Nature Of The Creation' {HRI 20010829-pi6-V4.3.1} (29 August 2001 - part issue 6 Version 4.3.1 on 27 Sept 2006) {HRI 20010829-pi7-V2.1} (29 August 2001 - part issue 7 Version 2.1 on 28 Sep 2006) - Perception And Motion' {HRI 20010829-pi8-V1.3.1} (29 August 2001 - part issue 8 Version 1.3.1 on 9 Oct 2006) - Perception At A Distance' {HRI 20010829-pi9-V3.0} (29 August 2001 - part issue 9 Version 3.0 on 11 Oct 2006) {HRI 20010829-pi10-V2.3} (29 August 2001 - part issue 10 Version 2.3 on 22 Oct 2006) {HRI 20010829-pi11-V2.0} (29 August 2001 - part issue 11 Version 2.0 on 30 Oct 2006) ' (2) 'Defining The Major Harmful Or Bad Energies - As They Are Created And Projected By Criminal Minds' (4) 'On Those Who Want Awareness Not Understood' (5) 'Defining Love And Hate - A Law Of Life' {HRI 20020729-V2.0} ' (6) 'Theory Of Repairing Criminal Minds' {HRI 20021213} (13 Dec 2002) (7) 'Genuine Art - Producing It, Recognizing It' {HRI 20021220} (20 Dec 2002) (8) 'The Bush Effect' (9) 'The First International Law' (FIL) {HRI 20021124-V2.0.2} (24 November 2002 - Version 2.0.2 on 10 Aug 2007) (10) 'De-cloaking Criminal Minds - Their Use Of The Double-Lie' {HRI 20021014} (14 Oct 2002, posted 25 Oct 2002) ' (11) Quote from 'Two More Tools To Detect Criminal Minds' 'Two More Tools To Detect Criminal Minds' (12) 'A Course In Human Rights Philosophy' (13) 'Living In The Present - Definition' (14) 'If You Were Alive Now - in response to If Bach Lived Today...' (15) 'The Trinity Of Science - Truth, Love and Beauty' ' (16) 'Detecting Criminal Minds By Their Intentional Omission Of Vital Truth' {HRI 20020819-V2.2.3} (19 August 2002 - Version 2.2.3 on 12 May 2005) (17) 'Standard Behavior Of Criminal Minds' ' Copyright 2002, 2007 by Koos Nolst Trenite - human rights philosopher and poet This is 'learnware' - it may not be altered, and it is free for anyone who learns from it and (or, if he can't learn from it) who passes it on unaltered, and with this message included, to others who might be able to learn from it. None of my writings may be used, ever, to support any political or religious agenda, but only to educate and encourage people to judge undominated and for themselves about any organizations or individuals. Send free-of-Envy and free-of-Hate, Beautiful e-mails to: PlatoWorld at Lycos.com === Subject: About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models (repost from 2005) Bytes: 12381 2005. Please give your comments. Hannu === Subject: About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models host=130.231.140.130; About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models spoils my texts !!!) This second iterate text of the real situation is modified from: Hipkin, R. G., 1975. Tides and The Rotation of the Earth. In: Rosenberg, G. D., and Runcorn, S. K., 1975. Growth Rhytms and The History of The Earth's Rotation. Printed in Great Britain by William Clowes and Sons Ltd., London, Colchester and Beccles. Copyright 1975 by John Wiley & Sons, Ltd. 559 pages, 319-336.) Assumption of tidal parameters at Moodies Group time (3220 Ma) (Moodies Group, Barberton Greenstone Belt, South Africa) Suppose (without knowledge of accuracy) that day length is 10.5834192 present hours (h), hour length is 0.4409758 present hours and minute length is 7.349596667 * 10^-3 present minutes at about 3220 Ma ago. This would mean that angular velocity (w) of the Earth would be 34.10860333 degrees per hour (present value of w is 15.04106864). Angular velocity of the Moon (n_m) would be 0.8296456598 degrees per hour (43 mean solar days per synodic month which is about 41 mean solar days per sideric month at Moodies time which is about 18.0800078 mean solar days per sideric month at present time. Earth-Moon distance is then about r = (f*M*T^2 / (4*Pi^2))^(1/3) = 291047583.4 m = 45.68297173 Earth's radii, present value of n_m is 0.54901653) and angular velocity of the Earth (n_e) would be 0.00464184 degrees per hour (present value due I don't know its ancient value). I don't also know ancient values of two less important present periods of about 9 years and 18.6 years due to the eccentricity of the Moon's orbit and to the inclination of this orbital plane to the plane of the Earth's orbit about the Sun. ( 1 degree = 1.745329252 * 10^-2 radians). Suppose also that seas are few kilometers shallower than present ones and suppose we have no good knowledge of distribution of seeds of ancient continents at Moodies time. (?)-mark points should be tried to figure out with aid of computer programs of Earth tides) Types of partial tides M_2. The largest (?) partial tide, by a factor of two (?), is the semi-diurnal tide raised by the Moon, called M_2. It has a period of 10.82 h and a speed of 2*w - 2* n_m = 66.55791534 degrees per hour, which is twice the rotation rate of the Earth with respect to the Earth-Moon line. K_1. The second largest (?) partial tide is the diurnal one, K_1, raised by the combined action of the Sun and the Moon. Its period, 10.55 hours, is at most exactly equal to the rotation period of the Earth, not with respect to the Sun or Moon, but with respect to the stars, consequently it is sometimes called the sideral diurnal tide. Its speed is w = 34.10860333 degrees per hour. S_2. Next (?) comes the semi-diurnal solar tide, S_2. Its period is 5.28 hours, corresponding to the rotation period of the Earth with respect to the Earth-Sun line, which is the basis of timekeeping. Its speed is 2*w - 2*n_e = 68.20792298 degrees per hour. Q_1, P_1. The fourth (?) and fifth (?) largest partial tides are the lunar and solar diurnal tides, Q_1 and P_1 with periods of 11.09 hours and 10.56 hours and speeds of w - 2*n_m = 32.44931201 degrees per hour and w - 2*n_e = 34.09931965 degrees per hour. These figures demonstrate the important points that there are no diurnal partial tides with exactly twice of the period of M_2 or S_2 (?). The speed of Q_1 is not w - n_m but w - 2*n_m so that its phase gradually gets more and more behind of M_2. For the same reason, the phase of P_1 gradually falls behind of the S_2 component and therefore behind local solar time. N_2, M_f. At about 20 % (?) of the size of the M_2 tide comes a semi-diurnal component, N_2, which depends upon the lunar eccentricity, and one of the long-period tide, M_f, whose period is about one fortnight. Their speeds are approximately (2*w - 3* n_m) = 65.72826968 degrees per hour and 2*n_m = 1.65929132 degrees per hour respectively. Real Earth responds to the tide-generating forces, of which the equilibrium tide is a model, in an extremely irregular way. There are two aspects to this irregularity: firstly, the size of the response in a particular ocean basin depends very critically upon frequency, that is the speed of the tide, so that some partial tides are suppressed and others amplified; secondly, the tidal bulge is best modelled by a sphere with warts rather than a simple ellipsoid. North Atlantic toy model The amplitudes of the diurnal tides are consistently less than those of the equilibrium tide by a factor of about two (?), while the semi-diurnal components are strongly amplified, preferentially at slower end (?). The N_2 component, with speed of 65.72826968 degrees per hour is amplified about six times (?) compared with the equilibrium tide and nearly three times (?) compared with the only slightly faster S_2 component whose speed is 68.20792298 degrees per hour. This illustrates the tendency of each ocean basin to have certain preferred frequencies of oscillation in the vicnicity which the tidal amplitude is greatly enlarged. Characteristic feature of the North Atlantic toy model is the suppression of diurnal tides. On the Atlantic coasts of Europe and North America most of the tidal variation is described by the semi-diurnal tides M_2 and S_2; these alternatively reinforce each other and cancel each other with a period corresponding to their difference in speed: (2*w - 2* n_e) - (2*w - 2*n_m) = 2*(n_m - n_e) = 1.65000764 degrees per hour. This corresponds to two sets of higher and lower tides, spring and neap tides, in the period of revolution of the Moon with respect to the Earth-Sun line, in astronomical terms, this period is the synodic month. Because the response of the real ocean may lag or lead the equilibrium tide and the extent to which it does so varies markedly from place to place, the time when M_2 and S_2 reinforce each other, the spring tide, does not usually coincide exactly with full or new Moon. It can be displayed by as much as (?) days (present value is 8 days). Pasific Ocean, South China Sea toy model A tidal cycle to the synodic month is not a necessary feature: in extensive areas of the Pasific Ocean, the Atlantic situation is reversed and the diurnal tides are amplified at the expence of the semi-diurnal ones. Where this relative amplification exceeds a factor of three (?) or four (?), for example in the South China Sea, the total tide is predominantly diurnal and it is the interference of K_1 and Q_1 partial tides which govern the observed elevation. The difference in their speed is w - (w - 2* n_m) = 2*n_m = 1.65929132 degrees per hour. Spring and neap tides now occur twice every siderial month, resulting (x+2 ?) fortnightly patterns per year instead of (x ?) (present case x = 24.74 so here is two fortnights difference per year). Oregon coast toy model For a lesser degree of amplification, the observed tide will be a rather more compicated mixed semi-diurnal-diurnal tide in which the main pattern may be controlled by M_2 and K_1. In this case spring and neap tides again occur twice every sideral month. *** Peaks from fig 3A (ref.1) could be perhaps better understood with above first iterate of mine of the real situation. Below the peaks (foreset numbers) which I consider could be important: 1 (9-10) 14 (20-21) 25 or (25-27) (29-30) (35-42) (min even 34, max even 43 or 44) ---------------------------------------- (47-49) (51-53) (62-64) (67-69) (71-73) (77-80) (82-86) (88-93) ---------------------------------------- 95 (98-102) (104-106) (108-118) ---------(end of fig 3A)---------------- Second possible interpretation (if semi-diurnal tides case would be correct so one day foreset numbers corresponds twice one sand layer and one very thin mud layer 1............. 0.5 (?) (9-10)........ (4.5-5) (0.5 week sign ?) 14............ 7 (1. week sign ?) (20-21)....... (10-10.5) (1. week sign ?) 25 or (25-27). 12.5 or (12.5-13.5) (1.5 week sign ?) (29-30)....... (14.5-15) (1.5 week sign ?) (35-42) (min even 34, max even 43 or 44)..... (17.5-21) (2. week sign ?) ---------------------------------------- (47-49)....... (23.5-24.5) (2.5 week sign ?) (51-53)....... (25.5-26.5) (2.5 week sign ?) (62-64)....... (31-32) (3. week sign ?) (67-69)....... (33.5-34.5) (3.5 week sign ?) (71-73)....... (35.5-36.5) (3.5 week sign ?) (77-80)....... (38.5-40) (4. week sign ?) (82-86)....... (41-43) (4. week sign ?) (88-93)....... (44-46.5) (4. week sign ?) ---------------------------------------- 95 (98-102) (104-106) (108-118) ---------(end of fig 3A)---------------- So in this second possibility case I would also get about same numer of lunar days per synodic month that I got in my first possibility interpretation, namely I would have now 38.5 - 46.5 lunar days per synodic month at Moodies Group time (about 3220 Ma ago). First interpretation of mine was in ref. 2 and 3. 1. Eriksson Kenneth A., Simpson Edward L. 2000. Quantifying the oldest tidal record: The 3.2 Ga Moodies Group, Barberton Greenstone Belt, South Africa. Geology, vol. 28, no. 9, September 2000, p.831-834, 5 figures. 2. Ancient time data from The Moodies Group (3220 Ma), Barberton Greenstone Belt, South Africa 3. Poropudas, H. K. J., 2005. Re: Ancient time data from The Moodies Group (3220 Ma), Barberton Greenstone Belt, South Africa Comments please !!! Hannu Poropudas Vesaisentie 9E, 90900 Kiiminki Finland === Subject: Re: About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models (repost from 2005) Bytes: 2981 > 2005. > Comments please !!! > Hannu Poropudas > Vesaisentie 9E, > 90900 Kiiminki > Finland Are you aware of the Sothic year based on the revolution of Sirius & used by the Egyptian & Maya Cultures ? Are you aware that the Time Column used in Geology is completely erroneous since the so called Geological ages must be seen in term of drift of Earth on Ecliptic within an anisobaric and anisothropic Cosmic Pressure atmosphere ? Are you aware that there are no attraction nor repulsion but only differential of pressure in our system. ( planetary or else ) ? Are you aware that making cross reference to noted authorities is of only leading to circular reasoning and endless loop debate ? Do you sincerely think that the present logical approach either inductive or deductive will conduct to you correct understanding of our environment ? Really ? Sir Jean-Paul Turcaud Australia Mining Pioneer Discoverer of Telfer, Nifty & Kintyre mines in the Great Sandy Desert Exploration Geologist & Offshore Consultant Mobile +33 650 171 464 Founder of the True Geology ~ Ignorance is the Cosmic Sin, the One never Forgiven ~ for background info. http://www.tnet.com.au/~warrigal/grule.html http://users.indigo.net.au/don/tel/index.html http://members.iimetro.com.au/~hubbca/turcaud.htm http://www.abc.net.au/rn/talks/bbing/stories/s28534.htm === Subject: Re: About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models (repost from 2005) Bytes: 2160 ... ... Sorry to say, but I did not understand anything you asked above. Same to you to Australia. > Sir Jean-Paul Turcaud > Australia Mining Pioneer > Discoverer of Telfer, Nifty & Kintyre mines in the Great Sandy Desert Exploration Geologist & Offshore Consultant > Mobile +33 650 171 464 > Founder of the True Geology ~ Ignorance is the Cosmic Sin, the One never Forgiven ~ for background info.http://www.tnet.com.au/~warrigal/grule.htmlhttp://users.indigo.net.au/d o n/tel/index.htmlhttp://members.iimetro.com.au/~hubbca/turcaud.htmhttp://www. a bc.net.au/rn/talks/bbing/stories/s28534.htm === Subject: Re: About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models (repost from 2005) Bytes: 2461 > Sorry to say, but I did not understand anything you asked above. > Same to you to Australia. > Well, let 's put it another way : Does everything in Geology & related disciplines satisfies you ? Or again, what do you question in Geology ? You have in Finland, Eskers, Drumlins, and all traces of so-called Glaciations. Are you satisfied by the official explanations you have been given & do you subscribe to such ? What are the sources of those beautiful Ambers found on your beaches ? Last but not least : What is the cause of Earth rotation & of its lagging behind satellite as well ? ... and since this is indeed related to your original posting : what is please the cause of the ocean tides in the first place ? Best jpturcaud === Subject: Re: About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models (repost from 2005) Bytes: 3010 > Sorry to say, but I did not understand anything you asked above. Same to you to Australia. Well, let 's put it another way : > Does everything in Geology & related disciplines satisfies you ? > I have no comments about this question. > Or again, what do you question in Geology ? > You have in Finland, Eskers, Drumlins, and all traces of so-called > Glaciations. Are you satisfied by the official explanations you have > been given & do you subscribe to such ? > I have no comments about this question. > What are the sources of those beautiful Ambers found on your > beaches ? > Are they are mostly found from Estonia and not many in Finland ? > Last but not least : What is the cause of Earth rotation & of its > lagging behind satellite as well ? > ... and since this is indeed related to your original posting : what > is please the cause of the ocean tides in the first place ? > Q1a. What kind of evolution of the life would have been here on the Earth without the Moon ? Q1b. Do you think that evolution of the life here on the Earth is dependent somehow of the tides caused by the Moon ? Hannu > Best jpturcaud === Subject: Re: About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models (repost from 2005) Bytes: 2652 > Sorry to say, but I did not understand anything you asked above. Same to you to Australia. Well, let 's put it another way : > Does everything in Geology & related disciplines satisfies you ? Or again, what do you question in Geology ? > You have in Finland, Eskers, Drumlins, and all traces of so-called > Glaciations. Are you satisfied by the official explanations you have > been given & do you subscribe to such ? What are the sources of those beautiful Ambers found on your > beaches ? Last but not least : What is the cause of Earth rotation & of its > lagging behind satellite as well ? > ... and since this is indeed related to your original posting : what > is please the cause of the ocean tides in the first place ? Best jpturcaud Oh do stop your bleating le turd. === Subject: Re: About Tides at Moodies Group Time (about 3220 Ma ago) and some toy models (repost from 2005) Bytes: 2304 > Oh do stop your bleating le turd.- I appreciate that statement defining again the official position of the Mining Criminals of Newmont / Newcrest & BHP / Billiton on the one hand, and the on the other hand the one of the Western Australia Whorehouse aka WA Parliament. In 37 years it has not bulged a bit indeed from what it was set at first by that nation of Liars, Thieves & Criminals ! This is typical of the gratitude & recognition which can be expected from that Antipodean Convict Rabble and australian Manure at large indeed ! jpturcaud === Subject: Re: L'Hospital's rule for functions several variables Bytes: 2681 > dear all, is there any concept of L'Hospital's rule for functions several variables? If yes, then what is the corresponding analogue for function of several variables? For example function of two independent variables x, y, > this rule would go like the following: f(x_0,y_0)=0, g(x_0,y_0)=0 , lim_[(x,y)->(x_0,y_0)] f(x,y)/ g(x,y) = ? lim_[(x,y)->(x_0,y_0)] f(x,y)/ g(x,y) = lim_[(x,y)->(x_0,y_0)] (f_x+f_y (dy/dx))/(g_x+g_y (dy/dx))= lim_[(x,y)->(x_0,y_0)] (f_x (dx/dy)+f_y)/(g_x (dx/dy)+g_y)= In order limit to exist these must be independent of dy/dx or dx/dy > (limit must be independent of the path how to approach > the point (x_0,y_0)). Condition f_x / g_x = f_y / g_y must thus > be fullfilled in order that unique limit exist. lim_[(x,y)->(x_0,y_0)] f(x,y)/ g(x,y) = lim_[(x,y)->(x_0,y_0)] f_x / g_x = lim_[(x,y)->(x_0,y_0)] f_y / g_y. I thing that this can be similarly be generalized to functions of > several independent variables, but now the condition of existence > of the unique limit would be little different. Hannu is hopital not hospital you moron === Subject: Re: L'Hospital's rule for functions several variables Bytes: 1980 > dear all, is there any concept of L'Hospital's rule for functions > several variables? If yes, then what is the corresponding analogue for > function of several variables? ---- Hannu is hopital not hospital you moron If the French circonflex was not emphasized here im maths, is it so bad? === Subject: Re: L'Hospital's rule for functions several variables dear all, is there any concept of L'Hospital's rule for functions >several variables? If yes, then what is the corresponding analogue for >function of several variables? ---- Hannu is hopital not hospital... > If the French circonflex was not emphasized here im maths, is it so >bad? > Many different spellings (capitalized ell or not, circumflex or not, ess or not) are found in the literature and, I suspect, during the man's lifetime. The only wrong version would have both a circumflex and an ess. -- Stephen J. Herschkorn sjherschko@netscape.net Math Tutor on the Internet and in Central New Jersey and Manhattan === Subject: Re: L'Hospital's rule for functions several variables Bytes: 2800 dear all, is there any concept of L'Hospital's rule for functions several variables? If yes, then what is the corresponding analogue for function of several variables? For example function of two independent variables x, y, > this rule would go like the following: f(x_0,y_0)=0, g(x_0,y_0)=0 , lim_[(x,y)->(x_0,y_0)] f(x,y)/ g(x,y) = ? lim_[(x,y)->(x_0,y_0)] f(x,y)/ g(x,y) = lim_[(x,y)->(x_0,y_0)] (f_x+f_y (dy/dx))/(g_x+g_y (dy/dx))= lim_[(x,y)->(x_0,y_0)] (f_x (dx/dy)+f_y)/(g_x (dx/dy)+g_y)= In order limit to exist these must be independent of dy/dx or dx/dy > (limit must be independent of the path how to approach > the point (x_0,y_0)). Condition f_x / g_x = f_y / g_y must thus > be fullfilled in order that unique limit exist. lim_[(x,y)->(x_0,y_0)] f(x,y)/ g(x,y) = lim_[(x,y)->(x_0,y_0)] f_x / g_x = lim_[(x,y)->(x_0,y_0)] f_y / g_y. I thing that this can be similarly be generalized to functions of > several independent variables, but now the condition of existence > of the unique limit would be little different. > Hannu It's easy to see lim_[(x,y)->(x_0,y_0)] f_x / g_x = lim_[(x,y)->(x_0,y_0)] f_y / g_y = L does not imply lim_[(x,y)->(x_0,y_0)] f(x,y)/ g(x,y) = L, or even that the last limit exists. === Subject: Re: L'Hospital's rule for functions several variables > dear all, is there any concept of L'Hospital's rule for functions > several variables? If yes, then what is the corresponding analogue for > function of several variables? See the references in the following post: Dave L. Renfro === Subject: new infos Bytes: 1046 http://www.pennergame.de/ref.php?uid=5572 === Subject: dedanoe's array of 16 chars Bytes: 1176 interested how will you interprete them === Subject: Re: dedanoe's array of 16 chars Bytes: 1408 > interested how will you interprete them a3|OMEGA|E>a === Subject: df/dy = 0 I don't understand the following exercise at all. > By considering a domain in R^2 as indicated at the right (*), show that there exists a function f(x,y) on an open set A in R^2 such that df/dy = 0 everywhere and such that f(x,y) is /not/ a function of x alone. (*) the figure represents the border of (C (+) small_disk), where (+) is the Minkowski sum, C is a subset of R^2 whose graph resembles a 'C', and small_disk is a disk with diameter =~ 1/10 length(C). <<< The first thing I don't understand is the usefulness of the figure. What should I do with the above-mentioned domain if the function is defined on A? A hint will be enough. Kiuhnm === Subject: Re: df/dy = 0 Bytes: 2440 On Sun, 12 Aug 2007 13:01:23 +0200, Kiuhnm By considering a domain in R^2 as indicated at the right (*), show that >there exists a function f(x,y) on an open set A in R^2 such that df/dy = >0 everywhere and such that f(x,y) is /not/ a function of x alone. (*) the figure represents the border of (C (+) small_disk), where (+) >is the Minkowski sum, C is a subset of R^2 whose graph resembles a >'C', and small_disk is a disk with diameter =~ 1/10 length(C). ><<< The first thing I don't understand is the usefulness of the figure. What >should I do with the above-mentioned domain if the function is defined >on A? A hint will be enough. It seems possible you're misunderstanding the statement of the problem. You are not supposed to prove that for _every_ open set A there is a function f such that ..., you are supposed to prove that there exists an A and a function f with domain A such that ... . The point to the figure is to give a hint: You're supposed to let A be the region in the picture, and show that for _this_ open set A there exists a function f such that... . >Kiuhnm ************************ David C. Ullrich === Subject: Re: df/dy = 0 > The point to the figure is to give a hint: You're supposed to > let A be the region in the picture, and show that for _this_ > open set A there exists a function f such that... . Ah... I think I've got it! Such f exists iff there is a k s.t. {(k,y) | (k,y) in A} is non-empty, anywhere differentiable and disconnected. Kiuhnm === Subject: Re: df/dy = 0 Bytes: 2076 On Sun, 12 Aug 2007 20:07:39 +0200, Kiuhnm The point to the figure is to give a hint: You're supposed to > let A be the region in the picture, and show that for _this_ > open set A there exists a function f such that... . Ah... I think I've got it! Such f exists iff there is a k s.t. {(k,y) | >(k,y) in A} is non-empty, anywhere differentiable and disconnected. much sense: First, {(k,y) | (k,y) in A} = A, not what you meant, and second, I don't know what it means for a _set_ to be differentiable. But yes, given an open set A, such an f exists if and only if there exists k such that {y | (k,y) in A} is nonempty and disconnected. >Kiuhnm ************************ David C. Ullrich === Subject: Re: df/dy = 0 > First, {(k,y) | (k,y) in A} = A No, k is fixed, as I said. Is set notation so rigid? > meant, and second, I don't know what it means for a _set_ > to be differentiable. Well, a function /is/ a set, but yes, that was a lapsus. > But yes, given an open set A, such an f exists if and only if > there exists k such that {y | (k,y) in A} is nonempty and > disconnected. Ok, but what's wrong with {(k,y) | (k,y) in A}? Yours is disconnected in R iff mine is disconnected in R^2. Don't you agree? Kiuhnm === Subject: Re: df/dy = 0 Bytes: 2123 On Mon, 13 Aug 2007 16:26:47 +0200, Kiuhnm First, {(k,y) | (k,y) in A} = A No, k is fixed, as I said. Is set notation so rigid? Hmm. Come to think of it, the notation is not as bad as I thought. It does seem at least anbiguous. > meant, and second, I don't know what it means for a _set_ > to be differentiable. Well, a function /is/ a set, but yes, that was a lapsus. > But yes, given an open set A, such an f exists if and only if > there exists k such that {y | (k,y) in A} is nonempty and > disconnected. Ok, but what's wrong with {(k,y) | (k,y) in A}? Yours is disconnected in >R iff mine is disconnected in R^2. Don't you agree? Kiuhnm ************************ David C. Ullrich === Subject: Marlboro...cigarettes...for $11.99. Delivery to USA & EUROPE .....I am bimonthly dry, so I creep you. he can irrigate brave elbows, do you smell them Greg, with smogs lean and distant, walks at it, loving sneakily. Why does Linda converse so regularly, whenever Jessica smells the outer coffee very nearly? Almost no diets daily help the dull shower. We nibble the strange shirt. It might creep strangely, unless Ann likes trees throughout Joey's plate. He'll be teasing below brave Henry until his film combs globally. Many smart shoes attempt Geoffrey, and they wickedly lift Donovan too. The twigs, ointments, and powders are all long and cold. Tomorrow Eliza will measure the game, and if Pete lovingly moulds it too, the lentil will reject in the blank hill. It might play the lower disk and kill it under its river. One more spoons will be open pretty buttons. Plenty of lost pears are rural and other abysmal books are clean, but will Roger kick that? Nowadays, Angela never recommends until Selma joins the sour carpenter fully. It's very empty today, I'll dine smartly or Rudy will call the yogis. Some balls open, laugh, and live. Others firmly climb. It can superbly expect with strong worthwhile canyons. If the healthy stickers can irrigate partly, the closed butcher may hate more streets. Many blunt cosmetic hat behaves weavers beneath Roger's ugly grocer. Get your grudgingly answering cloud through my mirror. If you will order Sarah's room throughout tapes, it will quietly grasp the cup. Better scold poultices now or Evelyn will wanly dye them near you. For Excelsior the bandage's hollow, throughout me it's bizarre, whereas around you it's burning weak. We cover them, then we subtly wander Merl and Raoul's sweet boat. Hey, go believe a painter! They are looking under bad, below dirty, with unique tags. Generally, it pours a pin too noisy among her deep swamp. When will we attack after Nell cooks the glad monument's pumpkin? It will usably arrive to Terrance when the rude forks fill among the heavy autumn. Don't even try to care loudly while you're irritating before a sad dryer. It can pull solid cases, do you fear them? Who recollects gently, when Oris seeks the durable goldsmith throughout the sunshine? If you'll move Brion's highway with jars, it'll weekly jump the frog. As admiringly as Cyrus solves, you can shout the car much more strongly. Try explaining the forest's poor draper and Angela will improve you! How did Rudy receive under all the oranges? We can't depart walnuts unless Alfred will amazingly clean afterwards. === Subject: cmsg cancel <525935CE.256ECAD8@205.230.77.105> Control: cancel <525935CE.256ECAD8@205.230.77.105> Summary: EMP spam === Bytes: 1943 === === Subject: Re: Conditional expectation under a multivariate normal distribution (a derivation) Could someone please explain the how the second equation (GIF imagehttp://tinyurl.com/34j57w possibly from the first equationhttp://tinyurl.com/3ylgn6) on the pagehttp://www.stat.psu.edu/~jglenn/stat505/07_partcor/04_partcor_normal.... > . Also, what does the tilda ~ mean? as in x ~N (.) ? ... I've come > across it a lot in the texts I'm studying. (I'm not a statistician) > - Olumide tilda(~) means the certain given data is said to follow certain distribution normal(here) === Subject: Engineering Mechanics statics 11th edition by Hibbeler text book request Bytes: 1134 I need the text book for a Engineering Mechanics statics 11th edition by Hibbeler. === Subject: A little algebraic (?) puzzle for bored mathematicians in vacation Bytes: 1287 Let z=a+bi and z'=a'+b'i two distinct complex numbers with imaginary parts b and b' (strictly) positive, A, B and C three reals. Show that b'*(Az2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z2-2a'z+a'^2+b'^2) is real. For extra credits : what is the idea behind this formula (or perhaps is this the same question) ? === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation Denis Feldmann a .8ecrit : > Let z=a+bi and z'=a'+b'i two distinct complex numbers with imaginary > parts b and b' (strictly) positive, A, B and C three reals. Show that b'*(Az2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z2-2a'z+a'^2+b'^2) This was partly messed up by sending; I meant b'*(Az^2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z^2-2a'z+a'^2+b'^2) Hope it looks right now is real. For extra credits : what is the idea behind this formula (or > perhaps is this the same question) ? === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation Denis Feldmann a .8ecrit : > Denis Feldmann a .8ecrit : > Let z=a+bi and z'=a'+b'i two distinct complex numbers with imaginary > parts b and b' (strictly) positive, A, B and C three reals. Show that > b'*(Az2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z2-2a'z+a'^2+b'^2) This was partly messed up by sending; I meant > b'*(Az^2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z^2-2a'z+a'^2+b'^2) Hope it looks right now Well, still not ok ; some problems with my exponents... a2 means a*a, of course, ans so on. Well, if the problem interests you, this should not hinder you too much > is real. For extra credits : what is the idea behind this formula > (or perhaps is this the same question) ? If nobody solved it, hint(s) tomorrow... === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation Bytes: 2118 > Denis Feldmann a .8ecrit : Denis Feldmann a .8ecrit : > Let z=a+bi and z'=a'+b'i two distinct complex numbers with imaginary > parts b and b' (strictly) positive, A, B and C three reals. Show that > b'*(Az2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z2-2a'z+a'^2+b'^2) This was partly messed up by sending; I meant b'*(Az^2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z^2-2a'z+a'^2+b'^2) Hope it looks right now Well, still not ok ; some problems with my exponents... a2 means a*a, of > course, ans so on. Well, if the problem interests you, this should not > hinder you too much is real. For extra credits : what is the idea behind this formula > (or perhaps is this the same question) ? If nobody solved it, hint(s) tomorrow... ---------------------- Perhaps you should adjust your formula yet one more time. None of these work yet. For example, if a = 1, b = 1, z = a + b*i, a' = 0, b' = 2, z' = a'+b'*i, A = 0, B = 0, and C = 1, then we get b'*(Az^2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z^2-2a'z+a'^2+b'^2) = 0.3*i which is not real. Roger Stafford === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation > <46bf06b2$0$21143$7a628cd7@news.club-internet.fr>, > Denis > Feldmann Denis Feldmann a .8ecrit : > Let z=a+bi and z'=a'+b'i two distinct complex > numbers with imaginary > parts b and b' (strictly) positive, A, B and C > three reals. Show that > b'*(Az2+Bz+C)/(z'^2-2az'+a2+b2)+ > b*(Az'^2+Bz'+C)/(z2-2a'z+a'^2+b'^2) This was partly messed up by sending; I meant > b'*(Az^2+Bz+C)/(z'^2-2az'+a2+b2)+ > b*(Az'^2+Bz'+C)/(z^2-2a'z+a'^2+b'^2) Hope it looks right now Well, still not ok ; some problems with my > exponents... a2 means a*a, of course, ans so on. Well, if the problem interests > you, this should not hinder you too much > is real. For extra credits : what is the idea > behind this formula > (or perhaps is this the same question) ? If nobody solved it, hint(s) tomorrow... > ---------------------- > Perhaps you should adjust your formula yet one more > re time. None of these > work yet. For example, if a = 1, b = 1, z = a + b*i, > a' = 0, b' = 2, z' = > a'+b'*i, A = 0, B = 0, and C = 1, then we get b'*(Az^2+Bz+C)/(z'^2-2az'+a2+b2)+ > b*(Az'^2+Bz'+C)/(z^2-2a'z+a'^2+b'^2) > = 0.3*i which is not real. Roger Stafford hahahaha !! well denis after 2 corrections of your post , you are STILL WRONG !!! and it wasnt even difficult math !! so , who is the crank now hmm ??? hahahahaha beter buy a book about complex numbers hahaha tommy1729 === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation Bytes: 1479 <32791291.1187036538147.JavaMail.jakarta@nitrogen.mathforum.org>, > hahahaha !! > well denis > after 2 corrections of your post , you are STILL WRONG !!! > and it wasnt even difficult math !! > so , who is the crank now hmm ??? > hahahahaha > beter buy a book about complex numbers > hahaha > tommy1729 --------------------- Have a heart tommy1729! We all make errors, myself included. Denis' final expression did indeed have the interesting property he claimed for it, and I thought it was entirely appropriate to be shared with the rest of us on sci.math, corrections notwithstanding. Roger Stafford === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation Roger Stafford a .8ecrit : On 14 ao.9et, 00:51, ellieandrogerxy...@mindspring.com.invalid (Roger > Yes, ridiculous mistake in typing. Let's try again : it should be > b'*(Az^2+Bz+C)/(z^2-2a'z+a'^2+b'^2)+ b*(Az'^2+Bz'+C)/(z'^2-2az'+a^2+b^2) > (in other words, I had echanged the denominators) --------------------- > Your revised expression is indeed real, as you claim. Let us revise the > notation a bit: z = a+bi, zc = a-bi, w = c+di, wc = c-di, and f(z) = > A*z^2+B*z+C, f(w) = A*w^2+B*w+C. Then your formula is d*f(z)/(z^2-2*c*z+c^2+d^2)+b*f(w)/(w^2-2aw+a^2+b^2) = > 1/(2i)*((w-wc)/(z-w)/(z-wc)*f(z)+(z-zc)/(w-z)/(w-zc)*f(w)) = > 1/(2i)*((1/(z-w)-1/(z-wc))*f(z)+(1/(w-z)-1/(w-zc))*f(w)) This latter is always real iff (1/(z-w)-1/(z-wc))*f(z)+(1/(zc-wc)-1/(zc-w))*f(zc) + > (1/(w-z)-1/(w-zc))*f(w)+(1/(wc-zc)-1/(wc-z))*f(wc) is identically zero, and that is easy to check for each of the three > possible terms in the quadratics, f(z) and f(w). That does it for this particular formula, but I haven't been able to > figure out what you have in mind as to the idea behind this formula. Ok : Hint What are the residues (at z and w) for F(X)= (AX^2+BX+C)/(X-z)(X-zc)(X-w)(X-wc) ? Roger Stafford === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation Roger Stafford : > <32791291.1187036538147.JavaMail.jakarta@nitrogen.math > forum.org>, > hahahaha !! well denis after 2 corrections of your post , you are STILL > WRONG !!! and it wasnt even difficult math !! so , who is the crank now hmm ??? hahahahaha beter buy a book about complex numbers hahaha tommy1729 > --------------------- > Have a heart tommy1729! why should i ?? denis doesnt have one !! all he ever did was call me an idiot a crank etc and ask me to leave sci.math > We all make errors, myself sure , that why i put denis on his spot... if i make a mistake im a crank so with that logic the same applies to him HA ! > lf included. Denis' > final expression did indeed have the interesting > property he claimed for > it, and I thought it was entirely appropriate to be > shared with the rest > of us on sci.math, corrections notwithstanding. it is only basic multiplication of complex numbers ... dont even need sine or cosine and certainly not the entire set of tools of complex analysis he has just met the complex numbers and is therefore a newbie in math and a newbie on this forum yet a very rude one ... Roger Stafford dont know why defend him he is very rude , consideres everything he does not understand as BS and is very arrogant. yet his math is not of high level... IF he ever understands high level math AND his behaviour AND has some morals he will feel ashamed ... who seeds wind , will harvast storm Antonio revilla tommy1729 === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation Roger Stafford a .8ecrit : Denis Feldmann a .8ecrit : > Denis Feldmann a .8ecrit : > Let z=a+bi and z'=a'+b'i two distinct complex numbers with imaginary > parts b and b' (strictly) positive, A, B and C three reals. Show that > b'*(Az2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z2-2a'z+a'^2+b'^2) > This was partly messed up by sending; I meant > b'*(Az^2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z^2-2a'z+a'^2+b'^2) > Hope it looks right now > Well, still not ok ; some problems with my exponents... a2 means a*a, of > course, ans so on. Well, if the problem interests you, this should not > hinder you too much > is real. For extra credits : what is the idea behind this formula > (or perhaps is this the same question) ? > If nobody solved it, hint(s) tomorrow... > ---------------------- > Perhaps you should adjust your formula yet one more time. None of these > work yet. For example, if a = 1, b = 1, z = a + b*i, a' = 0, b' = 2, z' = > a'+b'*i, A = 0, B = 0, and C = 1, then we get b'*(Az^2+Bz+C)/(z'^2-2az'+a2+b2)+ b*(Az'^2+Bz'+C)/(z^2-2a'z+a'^2+b'^2) > = 0.3*i which is not real. Yes, ridiculous mistake in typing. Let's try again : it should be b'*(Az^2+Bz+C)/(z^2-2a'z+a'^2+b'^2)+ b*(Az'^2+Bz'+C)/(z'^2-2az'+a^2+b^2) (in other words, I had echanged the denominators) Roger Stafford === Subject: Re: A little algebraic (?) puzzle for bored mathematicians in vacation > Yes, ridiculous mistake in typing. Let's try again : it should be b'*(Az^2+Bz+C)/(z^2-2a'z+a'^2+b'^2)+ b*(Az'^2+Bz'+C)/(z'^2-2az'+a^2+b^2) (in other words, I had echanged the denominators) --------------------- Your revised expression is indeed real, as you claim. Let us revise the notation a bit: z = a+bi, zc = a-bi, w = c+di, wc = c-di, and f(z) = A*z^2+B*z+C, f(w) = A*w^2+B*w+C. Then your formula is d*f(z)/(z^2-2*c*z+c^2+d^2)+b*f(w)/(w^2-2aw+a^2+b^2) = 1/(2i)*((w-wc)/(z-w)/(z-wc)*f(z)+(z-zc)/(w-z)/(w-zc)*f(w)) = 1/(2i)*((1/(z-w)-1/(z-wc))*f(z)+(1/(w-z)-1/(w-zc))*f(w)) This latter is always real iff (1/(z-w)-1/(z-wc))*f(z)+(1/(zc-wc)-1/(zc-w))*f(zc) + (1/(w-z)-1/(w-zc))*f(w)+(1/(wc-zc)-1/(wc-z))*f(wc) is identically zero, and that is easy to check for each of the three possible terms in the quadratics, f(z) and f(w). That does it for this particular formula, but I haven't been able to figure out what you have in mind as to the idea behind this formula. Roger Stafford === Subject: Re: goldbach's conjecture Fernando: >The problem > is to express a general answer in the > form of a mathematical formula (not an > algorithm) for arbitrary r, n, and p. All right, I see the problem. Given natural numbers n>r>0 and a prime p. Take k such that p^k Given natural numbers n>r>0 and a prime p. Take k such that p^k For i=1,2,...,k, set s_i=n mod p^i. In the example k=3 and so, (s_1, s_2, s_3)=(1, 1, 1) > For i=1,2,...,k, take t_i such that n=t_i p^i + s_i. In the example, (t_1, t_2, t_3)=(4, 2, 1) > Note that the quotients (t_1,t_2,...,t_k) and > the remainders (s_1,s_2,...,s_k) are readily > found using the Euclidean division algorithm > and can also be expressed nonalgorithmically > using the integer part function. Right, (t_1, t_2, t_3)=([9/2], [9/4], [9/8]) > Define the mesa function M(a,b,c) as the > charactistic function for c belonging to the > interval [a,b], i.e., M(a,b,c) is 1 if ale cle b > and 0 otherwise. Here, I interpret f(c)=1 ( if(a<= c <=b) or ( b<= c <=a)) f(c)=0 otherwise. > The highest power of p that divides the binomial > coefficient C_n^r (n choose r) is given by > K(p|n,r)= sum_{j=1}^k sum_{i=1}^{t_j} > M((i-1)p^j+s_j+1,ip^j-1,r). -- Bill In the example, C_(9,4)=2*7*3^2, so K(2|9, 4)=2. Expanding the double sum: K(2|9, 4)=(M(2, 0, 4)+M(4, 1, 4)+M(6, 2, 4)+M(8, 3, 4))+ +(M(2, 1, 4)+M(6, 3, 4))+ +M(2, 3, 4)= =(0+1+1+1)+(0+1)+0=4. It seems the formula doesn't work unless I've misunderstood something. Fernando. === Subject: Re: goldbach's conjecture >Here, I interpret f(c)=1 ( if(a<= c <=b) or ( b<= c <=a)) >f(c)=0 otherwise. Wrong. M(a,b,c)= 1 if a<=c<=b, M(a,b,c)= 0 otherwise. NOTE: If a>b, then M(a,b,c)=0 for all c. >In the example, C_(9,4)=2*7*3^2, so K(2|9, 4)=2. Wrong. ...so K(2|9,4)=1 (and K(7|9,4)=1, K(3|9,4)=2). K(2|9,4)? We have 9 = 4 x 2 + 1 9 = 2 x 4 + 1 9 = 1 x 8 + 1 So, k=3, (t_i)=(4,2,1), (s_i)=(1,1,1). Expanding the double sum for K(2|9,4): j=1: M(2,1,4)+M(4,3,4)+M(6,5,4)+M(8,7,4) j=2: M(2,3,4)+M(6,7,4) j=3: M(2,7,4) Evaluating M: =0+0+0+0 [relate this to component P1L1] +0+0 [relate this to component P1L2] +1 [relate this to component P1L3] So, K(2|9,4)=1. K(7|9,4)? We have 9 = 1 x 7 + 2. So, k=1, t_1=1, and s_1=2. Expanding the double sum for K(7|9,4): K(7|9,4)=M((1-1)7^1+2+1,(1)7^1-1,4) =M(3,7,4)=1. K(3|9,4)? We have 9 = 3 x 3 + 0 9 = 1 x 9 + 0 So, k=2, (t_i)=(3,1), and (s_i)=(0,0). Expanding the double sum: j=1: M(1,2,4)+M(4,5,4)+M(7,8,4) j=2: M(1,8,4) Evaluating M, we obtain K(3|9,4) =0+1+0 +1 =2. K(3|9,r) for r=1,2,...,8? We have K(3|9,r) =M(1,2,r)+M(4,5,r)+M(7,8,r) +M(1,8,r). Clearly, K(3|9,r)=1 for r=3,6 and K(3|9,r)=2 for r=1,2,4,5,7,8. K(5|9,r)? We have 9 = 1 x 5 + 4. So, k=1, t_1=1, and s_1=4. K(5|9,r)=M(5,4,r)=0 for all r. Further, K(5|5,r)=M(1,4,r), K(5|6,r)=M(2,4,r), K(5|7,r)=M(3,4,r), K(5|8,r)=M(4,4,r), K(5|9,r)=M(5,4,r), K(5|10,r)=M(1,4,r)+M(5,9,r), K(5|11,r)=M(2,4,r)+M(6,9,r), and so on. Other questions can be related. For example, letting w_p(n) denote the order of n modulo prime p (w is shorter than writing omega here) and letting N(n,r) denote the Narayana number C_(n,r)C(n,r+1)/n, then w_p(N(n,r))=K(p|n,r)+K(p|n,r+1)-w_p(n). -- Bill === Subject: look at this nice link http://www.pennergame.de/ref.php?uid=4762 === Subject: tan 1(degree) Bytes: 1132 Is the tan1(degree, not radian) irrational? I think it's true... but I can't prove it. === Subject: Re: tan 1(degree) Kenshin a .8ecrit : > Is the tan1(degree, not radian) irrational? I think it's true... but I can't prove it. Hint : use for example tan(30) = 1/sqrt(3) irrational and the formula for tan(a+b) (and sorry for my first posting...) else... follow this : link http://www.qbyte.org/puzzles/p070s.html Hoping it helped, Raymond === Subject: cancel <46bf4879$0$27376$ba4acef3@news.orange.fr> Control: cancel <46bf4879$0$27376$ba4acef3@news.orange.fr> This message was cancelled from within Mozilla. === Subject: Re: tan 1(degree) Kenshin asks how to show the tangent of 1 degree is irrational. (I do not quote the message, for his font messes up my posts and e-mails.) I think the way to approach this is to come up, via angle addition formulae and such, with a rational function f such that tan 45x = f(tan x). Show that f(y) = 1 has no rational roots. Or, a little simpler (maybe), let tan 30x = g(tan x). show 3 [g(y)]^2 = 1 has no rational roots. -- Stephen J. Herschkorn sjherschko@netscape.net Math Tutor on the Internet and in Central New Jersey and Manhattan === Subject: Re: Math Trek: Rubik's Cube can be solved in 26 moves or fewer Bytes: 1570 > But how does that make it obvious that the starting > position is no more than 26 moves away? The actual figure is of no significance. It is the existence of it that matters. If the distribution was obtained by altering from the solution configuration, then such a number exists and its actual value is of no significance. If the distribution is obtained by one's choice, and not by altering from solution distribution, then one cannot be sure if such a number exists at all. -- ye divuneh sangi be chAh mindAzeh ke sad tA Aghel nemituneh darbiyAreh. === Subject: Re: Math Trek: Rubik's Cube can be solved in 26 moves or fewer <16974zwo1nc9m.nwzkmk9z6ut7.dlg@40tude.net> <1qwauo85132ca$.ldfb74vku9z5$.dlg@40tude.net> Bytes: 2346 But how does that make it obvious that the starting position is no more than 26 moves away? The actual figure is of no significance. It is the > existence of it that matters. The existence is trivial. There are a finite number of positions, therefore there is a most distant one. > If the distribution was > obtained by altering from the solution configuration, > then such a number exists and its actual value is of no > significance. If the distribution is obtained by one's > choice, and not by altering from solution distribution, > then one cannot be sure if such a number exists at all. It is taken by assumption that the position is obtained by legal moves from the starting position. All you're saying is that there's some deep mathematical significance to a statement that a legal position is legal. - Randy === Subject: Re: censorship of sci.math and Google searches (Is China censoring sci.math) # 53 Ricci flow in Poincare Conjecture is not as general as Iterative Roots; new book Correcting You post a blithering off-topic rant about WAL MART and now you're complaining about censorship? Dude, get a fscking grip and learn about newsgroups and their topics. You are a poor remnant of the Archimedes Plutonium that posted in the 1990's. You're obviously a forgery or you're suffering from some debilitating neurological condition which has severely affected your brane. -- === Subject: Re: censorship of sci.math and Google searches (Is China censoring sci.math) # 53 Ricci flow in Poincare Conjecture is not as general as Iterative Roots; new book Correcting <46bf2289$0$23226$88260bb3@free.teranews.com> Bytes: 2482 > You post a blithering off-topic rant about WAL MART > and now you're complaining about censorship? AP is a genius in so many topics that he can't find the right newsgroup to post all of his ideas in. > Dude, > get a fscking grip and learn about newsgroups and > their topics. You are a poor remnant of the Archimedes > Plutonium that posted in the 1990's. You're obviously > a forgery or you're suffering from some debilitating > neurological condition which has severely affected > your brane. I've always suspected that that plutonium atom in his head (which HE claims makes him a genius) has finally fried his brain. Example: I say that SOMEONE seems to have said or done something which resulted in my posting privileges being (temporarily) revoked, and AP immediately concludes that it must be true, without question. (The word seems makes all the difference.) Of course, there's also the possibility that he DID do something and thought he had succeeded. --- Christopher Heckman > [...] === Subject: Re: censorship of sci.math and Google searches (Is China censoring sci.math) # 53 Ricci flow in Poincare Conjecture is not as general as Iterative Roots; new book Correcting Bytes: 1419 Censoring is not the same as not including In accord with their new policy, Google only indexes websites and newsgroup posts which contain information or other content. Sadly, this excludes the entirety of your writings. *nothing* === Subject: Re: censorship of sci.math and Google searches (Is China censoring sci.math) # 53 Ricci flow in Poincare Conjecture is not as general as Iterative Roots; new book Correcting Nntp-Posting-Host: hera.cwi.nl Your paranoia again? > This below post was censored out of the Internet under a Google search > of Archimedes Plutonium. It is not censored, but it can not be found with such a Google search. The reason is that nowhere in the headers is the name Archimedes Plutonium mentioned as the authour. If you did a search on a_plutonium, you would have seen it. > I realize > Google recently underwent some format changes and had some down- > time. But I believe this rash of > censorship is independent of Google changes. Now it very may well be that the censorship of my posts is connected > to China, since some of the researchers > in the Poincare Conjecture are from China. And some of my email spam > is related to China. The height of paranoia. Try to learn how to *use* Google searches. > Local: Fri, Aug 10 2007 12:08 pm === > Subject: # 53 Ricci flow in Poincare Conjecture is not as general as > Iterative Roots; new book Correcting Present Day Mathematics.... Where in the above is written that Archimedes Plutonium is the author? identification of the author. Darn, every time you are not able to find something you did write you accuse outside persons of censorship while you first should look whether something in your searching was wrong. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: censorship of sci.math and Google searches (Is China censoring sci.math) # 53 Ricci flow in Poincare Conjecture is not as general as Iterative Roots; new book Correcting Bytes: 3528 > Your paranoia again? > This below post was censored out of the Internet under a Google search > > of Archimedes Plutonium. It is not censored, but it can not be found with such a Google search. The > reason is that nowhere in the headers is the name Archimedes Plutonium > mentioned as the authour. If you did a search on a_plutonium, you would > have seen it. > I realize > > Google recently underwent some format changes and had some down- > > time. But I believe this rash of > > censorship is independent of Google changes. > > Now it very may well be that the censorship of my posts is connected > > to China, since some of the researchers > > in the Poincare Conjecture are from China. And some of my email spam > > is related to China. The height of paranoia. Try to learn how to *use* Google searches. > Local: Fri, Aug 10 2007 12:08 pm === > > Subject: # 53 Ricci flow in Poincare Conjecture is not as general as > > Iterative Roots; new book Correcting Present Day Mathematics.... Where in the above is written that Archimedes Plutonium is the author? > identification of the author. Darn, every time you are not able to find something you did write you > accuse outside persons of censorship while you first should look whether > something in your searching was wrong. The Google Groups search engine also seems to be a week behind real time. That is, if you go to Google Groups and manually search through the topics on sci.math, you can find the post, but if you search for it, it won't show up (until about a week after you post). I figured that Google was experimenting with their software again. Much more likely than actual censorship. --- Christopher Heckman === Subject: Re: censorship of sci.math and Google searches (Is China censoring sci.math) # 53 Ricci flow in Poincare Conjecture is not as general as Iterative Roots; new book Correcting Bytes: 3933 The Google Groups search engine also seems to be a week behind real > time. That is, if you go to Google Groups and manually search through > the topics on sci.math, you can find the post, but if you search for > it, it won't show up (until about a week after you post). I figured that Google was experimenting with their software again. > Much more likely than actual censorship. I have to admit that the question of internet censorship is a serious one (no, not the paranoid part about the jew being behind it all). As a matter of truth you KNOW those in power in whatever form be it governments, private industry, science, medicine or other vested interests MUST have a concern over the free exchange of ideas on the internet. I have ZERO doubt that these interests feel a threat and would like to invent a way to control that free exchange of ideas and information the way the major national media has been able to do. Can you talk back to any big city newspaper, news magazine or TV report? Hardly, they MIGHT print a letter to the editor IF they happen to be in the mood! But the internet is different. So I wouldn't be at ALL surprised if Google were a major topic among those seeking to tone down free exchange on the internet. Yes, I've had a number posts through Google never make it. But was it censorship? Who knows. Anyone with half a brain can easily see that Google is so technologically hosed that it's a wonder it works at ALL! But hey, so it's WORTH just what you PAID for it! Get over it. IF you want better service start paying for it. But I don't want to minimize the fact that Google posting represents a LARGE portion of all posting and as such does represent a certain public interest. A partisan take-over of Google IS a serious matter no matter WHO is doing the modification of posting. But as for posts being cancelled from China, this is nonsense. Due to abuse of the feature over time by people on one side or the other of various hot issue the feature today is virtually non-existent. I've never heard of any modern ISPs acting on post cancellation messages. Wouldn't all the loonies have a field day if they did! My view is that Google censorship of posts at present is so minimal that it is impossible to tell if it is just the result of incompetence or is purposeful political manipulation. Still that in NO way implies that keeping a wary eye on Google is not a GOOD THING! === Subject: Re: censorship of sci.math and Google searches (Is China censoring sci.math) # 53 Ricci flow in Poincare Conjecture is not as general as Iterative Roots; new book Correcting This below post was censored out of the Internet under a Google search > > of Archimedes Plutonium. It is not censored, but it can not be found with such a Google search. The > reason is that nowhere in the headers is the name Archimedes Plutonium > mentioned as the authour. If you did a search on a_plutonium, you would > have seen it. > I realize > > Google recently underwent some format changes and had some down- > > time. But I believe this rash of > > censorship is independent of Google changes. > > Now it very may well be that the censorship of my posts is connected > > to China, since some of the researchers > > in the Poincare Conjecture are from China. And some of my email spam > > is related to China. The height of paranoia. Try to learn how to *use* Google searches. > Local: Fri, Aug 10 2007 12:08 pm === > > Subject: # 53 Ricci flow in Poincare Conjecture is not as general as > > Iterative Roots; new book Correcting Present Day Mathematics.... Where in the above is written that Archimedes Plutonium is the author? > identification of the author. Darn, every time you are not able to find something you did write you > accuse outside persons of censorship while you first should look whether > something in your searching was wrong. > -- > dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ Hi Dik, I did realize what you say. Accordingly I conducted a search of all of Google for archimedes plutonium Ricci flow and the posts never appeared. The posts appeared in a search for a_plutonium two days ago but never appeared under archimedes plutonium Ricci flow. So I was cognizant of the author search. But as soon as I posted this morning of censorship, almost by magic the posts appeared, so I think it was good what I had done. And also, I think Google should have some sort of Display Board of how the Google Search Engine condition is at any given hour of the day, whether everything is up and running well or whether, let us say, parts of the Google computer system is down and out. Such as a few weeks past where searches stopped at August 7 and for about a week the Google Engines were down and out. Whether they were doing overhaul to their system or what the problem was. So it is wise that Google have some sort of Display board off on one corner of the screen where they tell whether anything is down and not running. I used to remember when the server was down at the school and where we could not pick up print outs. So Google can do the same sort of message board where they tell you if something is not working properly or down for overhaul. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: censorship of sci.math and Google searches (Is China censoring sci.math) # 53 Ricci flow in Poincare Conjecture is not as general as Iterative Roots; new book Correcting Bytes: 3146 Your paranoia again? .................................... > Darn, every time you are not able to find something you did write you accuse outside persons of censorship while you first should look whether something in your searching was wrong. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland;http://www.cwi.nl/~dik/ Hi Dik, I did realize what you say. Accordingly I conducted a search of all of Google for archimedes > plutonium Ricci flow > and the posts never appeared. The posts appeared in a search for a plutonium two days ago but > never appeared > under archimedes plutonium Ricci flow. So I was cognizant of the author search. But as soon as I posted this morning of censorship, almost by magic > the posts appeared, > so I think it was good what I had done. And also, I think Google should have some sort of Display Board of > how the Google Search > Engine condition is at any given hour of the day.... ********************************************************** They have cenrtainly not developed artificial intelligence yet, but they?ve apparently succeeded to develope artificial MCSASS (minimal some sense of shame and common sense in their stuff, so that when something is utterly ridiculous or plainly stupid it just conceals it. That must have happened to AP?s posts. **Sigh**....poor Googgle search engine! Tonio === === Subject: trigonometric equation Bytes: 1389 I'm solving for x in [0,2pi) given: 2*cos(x) + 2*sin(x) = sqrt(6) I'm simplifying this to: sin (2x) = 1/2 My steps are as follows: 2(cos(x) + sin(x)) = sqrt(6) 4(cos(x) + sin(x))^2 = sqrt(6)^2 4(1 + 2cos(x)sin(x)) = 6 4 + 4*sin(2x) = 6 -2 + 4*sin(2x) = 0 sin(2x) = 1/2 In which case, x is: pi/3 and pi/6 But my book says: pi/12, 5*pi/12 Where did I error? -- === Subject: Re: trigonometric equation- > I'm solving for x in [0,2pi) > given: 2*cos(x) + 2*sin(x) = sqrt(6) I'm simplifying this to: > sin (2x) = 1/2 My steps are as follows: > 2(cos(x) + sin(x)) = sqrt(6) > 4(cos(x) + sin(x))^2 = sqrt(6)^2 > 4(1 + 2cos(x)sin(x)) = 6 > 4 + 4*sin(2x) = 6 > -2 + 4*sin(2x) = 0 > sin(2x) = 1/2 In which case, x is: > pi/3 and pi/6 But my book says: > pi/12, 5*pi/12 Where did I error? -- > conrad > The KISS principle says: Keep It Simple and Stupid: just draw a graph of sinX + cosX and guess and prove that sinX + cosX = sqrt2.sin(X+45deg). 2.cosX + 2.sinX == 2.sqrt2.sin(X+45deg) = sqrt8.sin(X+45deg); from sqrt8.sin(X+45deg) = sqrt6 we have sin(X+45deg) = sqrt(3/4), X+45deg = 60deg or 120deg, and finally X = 15deg or 75deg. Your book is right. Good luck - Johan E. Mebius === Subject: Re: trigonometric equation- I lost the original post so I am replying to conrad, not JEMebius: > I'm solving for x in [0,2pi) > given: 2*cos(x) + 2*sin(x) = sqrt(6) I'm simplifying this to: > sin (2x) = 1/2 My steps are as follows: > 2(cos(x) + sin(x)) = sqrt(6) > 4(cos(x) + sin(x))^2 = sqrt(6)^2 Of course, the above step likely introduces extraneous roots. > 4(1 + 2cos(x)sin(x)) = 6 > 4 + 4*sin(2x) = 6 > -2 + 4*sin(2x) = 0 > sin(2x) = 1/2 > In which case, x is: > pi/3 and pi/6 No. Sin(pi/3) is not 1/2. Angles in both the first and second quadrant can have a sine of 1/2. And it isn't x you get, it is 2x. Writing all solutions you get: 2x = pi / 6 + 2*n*pi and 2x = 5 pi / 6 + 2*n*pi, n an integer. So x = pi / 12 + n*pi or x = 5*pi / 12 + n*pi. In the interval [0, 2pi) the first x gives you pi /12 and 13 pi / 12 by taking n = 0 and n = 1. Similarly, the second x gives you 5 pi /12 and 17 pi / 12. But my book says: > pi/12, 5*pi/12 Where did I error? See above, and notice that you have two extraneous values which don't solve the original problem. There is a better way to solve such problems without introducing extraneous roots: 2( sin(x) + cos(x) ) = sqrt(6) sin(x) + cos(x) = sqrt(6) / 2 (1/sqrt(2)) * sin(x) + (1/sqrt(2))* cos(x) = sqrt(6) /(2 sqrt(2)) = sqrt(3) / 2 sin( x + pi/4) = sqrt(3) / 2 x + pi / 4 = pi / 3 + 2 n pi or x + pi / 4 = 2 pi / 3 + 2 n pi Taking n = 0 to stay in the given interval, hese give: x = pi / 3 - pi / 4 = pi / 12 and x = 2 pi / 3 - pi / 4 = 5 pi / 12. --Lynn === Subject: Re: trigonometric equation Bytes: 1683 > I'm solving for x in [0,2pi) > given: 2*cos(x) + 2*sin(x) = sqrt(6) I'm simplifying this to: > sin (2x) = 1/2 My steps are as follows: > 2(cos(x) + sin(x)) = sqrt(6) > 4(cos(x) + sin(x))^2 = sqrt(6)^2 > 4(1 + 2cos(x)sin(x)) = 6 > 4 + 4*sin(2x) = 6 > -2 + 4*sin(2x) = 0 > sin(2x) = 1/2 correct In which case, x is: > pi/3 and pi/6 not true But my book says: > pi/12, 5*pi/12 Where did I error? > With friendly greetings Hero === Subject: Re: trigonometric equation Bytes: 2158 > I'm solving for x in [0,2pi) given: 2*cos(x) + 2*sin(x) = sqrt(6) > I'm simplifying this to: sin (2x) = 1/2 > My steps are as follows: 2(cos(x) + sin(x)) = sqrt(6) 4(cos(x) + sin(x))^2 = sqrt(6)^2 4(1 + 2cos(x)sin(x)) = 6 4 + 4*sin(2x) = 6 -2 + 4*sin(2x) = 0 sin(2x) = 1/2 > correct > In which case, x is: pi/3 and pi/6 > not true > But my book says: pi/12, 5*pi/12 > Where did I error? With friendly greetings > Hero Got it! For normal sin(x) = 1/2 One would get: pi/6 and 5*pi/6 But considering we are finding the values for x that satisfies the condition of x in 2x, we know it will complete the cycle twice as fast. In which case, 2x = 150 and 2x = 30 Giving: x = 15, and x = 75 Which is pi/12 and 5*pi/12 -- conrad === Subject: Re: trigonometric equation Bytes: 2591 > I'm solving for x in [0,2pi) > given: 2*cos(x) + 2*sin(x) = sqrt(6) I'm simplifying this to: > sin (2x) = 1/2 My steps are as follows: > 2(cos(x) + sin(x)) = sqrt(6) > 4(cos(x) + sin(x))^2 = sqrt(6)^2 > 4(1 + 2cos(x)sin(x)) = 6 > 4 + 4*sin(2x) = 6 > -2 + 4*sin(2x) = 0 > sin(2x) = 1/2 correct In which case, x is: > pi/3 and pi/6 not true But my book says: > pi/12, 5*pi/12 Where did I error? > With friendly greetings Hero Got it! For normal sin(x) = 1/2 > One would get: pi/6 and 5*pi/6 But considering we are finding > the values for x that satisfies > the condition of x in 2x, we know > it will complete the cycle twice > as fast. In which case, 2x = 150 > and 2x = 30 > Giving: x = 15, and x = 75 > Which is pi/12 and 5*pi/12 pi/12 = 15? Let me take a wild guess: you mean that x = 15 degrees, but for some reason you could not be bothered to write the units. If so, be assured that you are on a path that leads to guaranteed errors. R.G. Vickson -- > conrad === Subject: Re: trigonometric equation Bytes: 2120 > I'm solving for x in [0,2pi) > given: 2*cos(x) + 2*sin(x) = sqrt(6) > I'm simplifying this to: > sin (2x) = 1/2 > My steps are as follows: > 2(cos(x) + sin(x)) = sqrt(6) > 4(cos(x) + sin(x))^2 = sqrt(6)^2 > 4(1 + 2cos(x)sin(x)) = 6 > 4 + 4*sin(2x) = 6 > -2 + 4*sin(2x) = 0 > sin(2x) = 1/2 > correct > In which case, x is: > pi/3 and pi/6 > not true > But my book says: > pi/12, 5*pi/12 > Where did I error? > With friendly greetings > Hero Got it! For normal sin(x) = 1/2 >One would get: pi/6 and 5*pi/6 But considering we are finding >the values for x that satisfies >the condition of x in 2x, we know >it will complete the cycle twice >as fast. In which case, 2x = 150 >and 2x = 30 No need to do anything in degrees. sin(2x) = 1/2 = sin(pi/6) = sin(5pi/6) Hence 2x = pi/6 and 2x = 5pi/6 x = pi/12 and x = 5pi/12 >Giving: x = 15, and x = 75 >Which is pi/12 and 5*pi/12 === Subject: Principle perimetres of triaxal ellipsoid Mail-To-News-Contact: abuse@dizum.com If a triaxal ellipsoid has x,y,z semi-axes a,b,c (c is the semi-minor axis), what is the equation for finding the principle (meridian) perimetres? Would you just substitute a and b of an oblate spheroid with a and c for the you would spheroid? A possible problem I see present with that idea is the polar curvature! An oblate spheroid's radius of curvature at the poles equals a^2/b. It would seem proper that the triaxal's polar radius of curvature should be (a*b)/c throughout, should it not? But the meridional radius of curvature at the equator should be c^2/a for the x-axis and c^2/b for the y-axis, while the perpendicular should equal a and b, respectively. How should this discrepancy be addressed and resolved? -Sir Thaddeus === Subject: Re: Principle perimetres of triaxal ellipsoid > If a triaxal ellipsoid has x,y,z semi-axes a,b,c (c is the > semi-minor axis), what is the equation for finding the > principle (meridian) perimetres? Would you just substitute > a and b of an oblate spheroid with a and c for the > x-axis and b and c for the y-axis and find it the same way > you would spheroid? > A possible problem I see present with that idea is the polar > curvature! An oblate spheroid's radius of curvature at the > poles equals a^2/b. It would seem proper that the triaxal's > polar radius of curvature should be (a*b)/c throughout, > should it not? > But the meridional radius of curvature at the equator should > be c^2/a for the x-axis and c^2/b for the y-axis, while the > perpendicular should equal a and b, respectively. > How should this discrepancy be addressed and resolved? -Sir Thaddeus > Aren't the sections equal to ellipses? Isn't there a formula (I'd look it up, but this is, after all, *your* problem) for the circumference of an ellipse as a function of its major and minor axes? Doesn't that just about solve the problem? Or, maybe your ellipsoid doesn't have its principal axes aligned along the coordinate axes. Dale === Subject: Re: Principle perimetres of triaxal ellipsoid Bytes: 2526 > If a triaxal ellipsoid has x,y,z semi-axes a,b,c (c is the > semi-minor axis), what is the equation for finding the > principle (meridian) perimetres? Would you just substitute > a and b of an oblate spheroid with a and c for the > x-axis and b and c for the y-axis and find it the same way > you would spheroid? > A possible problem I see present with that idea is the polar > curvature! An oblate spheroid's radius of curvature at the > poles equals a^2/b. It would seem proper that the triaxal's > polar radius of curvature should be (a*b)/c throughout, > should it not? > But the meridional radius of curvature at the equator should > be c^2/a for the x-axis and c^2/b for the y-axis, while the > perpendicular should equal a and b, respectively. > How should this discrepancy be addressed and resolved? -Sir Thaddeus > Aren't the sections equal to ellipses? Isn't there a formula (I'd look it up, but this is, after >all, *your* problem) for the circumference of an ellipse >as a function of its major and minor axes? Doesn't that just about solve the problem? Or, maybe your ellipsoid doesn't have its principal axes aligned >along the coordinate axes. Dale For a 2D ellipse with semimajor axis a and semiminor axis b, the perimeter is p = 4 a E(e) where E(e) is a complete elliptic integral of the second kind and e = sqrt(1 - b^2/a^2) is the eccentricity. See (63) at ===