How to find the integral
,

assuming k and n  integer?
It is known (McCrea W. H., Whipple F. J. W.Random paths in two and three dimensions, Proc. Roy. Soc. Edinburgh. 1940. V. 60. P. 281–298) that

G(n,n)=2/Pi*sum(1/(2*k-1),k=1..n).

The general case is reduced to the case k=n.
This is not a creature of pure reason: the one appears in electric circuits
(see M. Skopenkov, A. Paharev, A. Ustinov, Through resistor net, Mat. pros. Issue 18 (2014), 33-65, in Russian, http://www.mccme.ru/free-books/matpros/pdf/mp-18.pdf).
I found G(8,8) = 182144/(45045*Pi) in 657.797 s and G(9,9) = 3186538/(765765*Pi) in 4157.687 s on my comp by

restart; s := time():(1/2)*VectorCalculus:-int((1-cos(9*Pi*x)*cos(9*Pi*y))/(sin((1/2)*Pi*x)^2+sin((1/2)*Pi*y)^2), [x, y] = Rectangle(0 .. 1, 0 .. 1)); time()-s;
Mathematica 10.3.0 does G(9,9) in 250.391 s on my comp.

Hello,

I have a question about poincare sections. I have this piece of code i need to analyse and I want to use a poincare section in order to so. How could I do it? I am interested in theta and omega. Any help is greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

Download New_Poincare_section.mw

http://www.maplesoft.com/support/help/Maple/view.aspx?path=Physics/.

i see bra and ket expression are so beautiful,

however,

how do real valued eigenvectors involve in calculation of bra and ket style computation?

Download Bryson_sesson1_p6.mw

Maple's isprime is not a definitive primality test. The input has to pass a "strong pseudo-primality test" and "one Lucas test". This is well documented. I thought I remembered that there is also a way to get Maple to perform a true primality test, but I don't remember how and don't see anything about this in the Maple help system.

Is my memory faulty, or is there no definitive primality test in Maple?

Thanks in advance,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

Hello,

How to change the length underline in latex ?

For example in this environment :

$\underline{\mathcal{G}}$

Thank you,

Gérard.

So I am trying to apply the Optimization function to a rather complicated problem I am currently working on, and having some trouble getting maple to cooporate. This is the part of the code that is giving me the error, with error included. All of the variables imputtet when calling OptimizeSpring are constants. If there is any other details I should add, please say so and I will add them promptly :) Thanks alot!

I suspect that it might be related to this suggestion, but I am not sure how to apply it http://www.mapleprimes.com/posts/95113-Optimization-Workaround-For-Operator-Form

I'm trying to solve a beam vibration problem. I am relatively new to Maple and trying to solve PDE's. I feel like I'm pretty close, but I don't understand what's wrong here.

This is my maple file.

Thesis_Pde2_attempt.mw

as a note, I made some simplifying assumptions. I am just using part of this equation since it is less complex. And my boundary conditions are simply supported on both ends so no displacement and no 2nd derivative at the ends.

Any help would be greatly appreciated!!

Hello everyone, 

I have some problems with the "isolve" command on Maple. I am trying to solve for integer a very easy system of equations. When I type the commands

restart; 

n := 2;
isolve({sum(a[k], k = 1 .. n)-1 = 1}, d)

I get the expected {a[1] = 2-d, a[2] = d}. However, if I add conditions a[1],a[2] >= 0, that is the commands

restart;
n := 2;
isolve({ge(a[1], 0), ge(a[2], 0), sum(a[k], k = 1 .. n)-1 = 1}, d)

I get the warning "Warning, solutions may have been lost". What am I doing wrong? Is there a way to get Maple to give me the possible values?

Thank you in advance,

David

I'm trying to solve a system of equations thats expressed as a summation (the original has the summation symbol as opposed to 'sum'):

d_actual := solve(W_actual = sum(W_guess(def-asp_rad_inverse[i], E, asp_rad[i]), i = 1 .. n), def);

When n<5, I get an answer after a few seconds, but when n is higher, the program sits and 'evaluates' forever...I've waited up to 30 min. 

Background:

I have a plate with a number of hemispheres on the surface (# of impacted hemispheres given a force = n). Each has a unique radius and they're listed from largest to smallest in 'asp_rad[]'. I have an equation for the deflection of a single hemisphere as a function of Force and material properties that I have rearranged with respect to Force (W_guess(deflection, E, r)). There's an opposing plate that stays parallel to the original plate while pushing down on the asperities with Force W_actual. The total deflection of the opposing plate is the sum of: 1) the difference between the tallest radius and the impacted radius in question (asp_rad_inverse[]), and 2) the deflection of the impacted radius in question. 

I'm attempting to solve for the total deflection of the opposing plate via solving for the 'def' in the summation above, but when I run it, the program is not able to compute a solution.

Thanks in advance.

Hello,

I'm a very new beginner, and I have a question about getting the data of a curve from a JPG, without using manual measures an too getting more accurate datas.

I wish to fit the curve with a model. The JPG joined, from EU 2015, is about human thermoregulation. I still try to found a model with Mathematica but am uncertain seeing the result as illogic.

Did anyone write something to read curves from a JPG and get coordinates from these curves ? In the JPG, the curve is above, as an 'U'.

Thanks for your advice,

Milos.

Hello,

I have an error in my code. I don't know where it came from. Earlier today I loaded this and it worked fine and now an error comes up. Any help is greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

Download Poincare_section.mw

Hi everyone,

Consider this maple 18 doc: Euler18.mw

The code is regular code for Julia sets of the exponential.

To see how the Julia set behaves at infinity, I apply the transform mu(z)=1/z.

The plot3d command correctly plots the Julia set at an appropriate neighborhood of infinity, but:

1) Axes are not transformed

2) Saving as .eps produces an empty plot, sans the axes (plot is saved correctly, when not applying mu(z))

Is there any trick to force the axes to also show correctly with the transformed ranges?

Seems that this misalignment is bothering the .eps renderer, which probably plots the graph in twilight zone, given the false ranges of the untransformed axes.

Any ideas on how to force the saveas .eps to work in this case?

Many thanks,

Yiannis

Hi

If I have this equation

and I need to use different Z, it's like

how can I solve it

Many Thanks

Amal

Dear Maple users

Physical experiment: I dropped a ball with low mass from a height of approximately 7 meters and wanted to test if the air resistance was proportional to the square of the velocity. I filmed the fall and used the program Logger Pro to collect data: a number of datapoints (time,height) was collected. I copy/pasted the datapoints into MS Excel, from where I could import data into Maple via Tools > Assistants > Import Data ... Then I wanted to make a fit with the theoretical solution, given by a function having just one parameter: the Drag coefficient. Unfortunately I received an error "complex values encountered" (see below). I can solve the problem manual by making a number of guesses for the drag coefficient, until the theoretical curve approximates the data points well. I wanted to make Maple do the fitting job, though. I will appreciate if someone could give an idea how to fit the data properly.

NB! Mass m and g is defined above in the Maple document. The Statistics and plots package is called too.