perturb_mag_current_density_2.mw

I am trying to calculate the electric field E induced in a vibrating cantilever of conductive material, oscillating in the field of a permanent magnet.  However, I am having some difficulty getting pdsolve to work the way I want it to.  I'm also not sure if the partial differential eqations I derived from Maxwell's equations are correct, or if the boundary conditions for the electric field in the cantilever are correct.  Currently pdsolve gives me no solutions, which makes me think that either my PDEs or my BCs are not correct.  It may be that I need to try some sort of numerical method as well.  I am assuming that the z component of the electric field is just 0.  My third PDE comes from setting the divergence of the electric field to 0.  My first two PDEs come from the vector laplacian and its relation to the divergence and curl:

Laplacian * E = Div(E) -Curl(Curl(E))

The x and y components of this should be my first and second PDE, respectively.  Note that in this equation the divergence of E is 0, and the curl of E is -dB/dt, where B is the magnetic field.

My boundary conditions are simply that the components of the electric field at the surface of the cantilever is always tangent to the surface.

I have tried various simplifications, such as setting the right hand side of the PDEs to 0, and still I don't get any solution.

My question:  Are my PDEs and BCs sensible?  And if so, what do I need to do with pdsolve to get a proper solution?

Let us consider the following assumptions:

Any set of binomials $B \in R=K[x_1, \cdots, x_n]$ induces an equivalence relation on the set of monomials in $R$ under which $m_1∼m_2$ if and only if $m_1−tm_2\in \langle B \rangle$ for some non-zero $t\in K$. As a k-vector space, the quotient ring $R/B$ s spanned by the equivalence classes of monomials. Now let $f =x^2−y^2$ be a binomial in $K[x, y]$. Among monomials of total degree three, $x^3$ and $xy^2$, as well as $x^2y$ and $y^3$ become equal in $K[x, y] / \langle f\rangle$.

Why the degree three part in the quotient is two-dimensional with one basis vector per equivalence class?

Also, why does the polynomial $f=x^3+xy^2+y^3$ map to a binomial with a coefficient matrix [2, 1]? I think this matrix arises from the matrix [1, 1, 1, 0] by summing the columns corresponding to $x^3$ and $xy^2$ and those for $x^2y$ and $y^3$. 

How can I implement a simple code to obtain these results in {\tt Maple}?

I am looking forward to hearing any help and guidance.

Thank you in advance

Given a excel sheet with data for regression as input column Y will be a dependent variable 

Say a maximum of 120 independent variables are their 

A function that takes excel as input with headers as in the excel file

Do pick all possible subsets of maximum size 5 that is sizes 2,3,4,5 only 

Pick each and eleminate not to store them all together as otherwise storage will be a problem if more data

Copy only those subsets of independent variables to seperate seperate sheet

Only those subsets 

where the variables are independent pairwise between them

Step 2 function 

Then need to run a multiple linear regression on these subsets like training and test 

And choose the best models I each of cases of number of variable

That is best with 2 variables

Again with 3 variables

Similarly 4 and 5

Atleast if possible upto 2 to 3 variables it will be good kind help with your guidance and what is possible 

If you are not able give the program of train test regression with charts no issues 

Kind help with atleast storing the independent pairwise subsets of size 2 and 3 into seperate sheets in a Excel file atleast

I will do the regression at my end 

I will have excel sheet with minium 500 coulmns and 1000 rows say

For sample to explain my question I attach a demo excel

All my columns have headers

I am looking to find all 2 way multiplication and add them as columns to my excel sheet and return it as a new excel sheet say

The column names for the new 2 way column should be like the

header name of column you are multiply * the name of the other columsn

Now in sample file if i multiple column with name A with column with name B I get a new column with header A*B the header name should be inserted and

Below that all the elements of that A column multiplied  with that of B should come

I am looking to form columns for all possible2  way multiplication for the excel I will give.

As you can see the demo file

Excel_to_explain.xlsx

Kind help please

Hello!

I have changed the the global character size from 12 to 14 but it is not stable. Suddenly size 12 is coming up when a try to copy a row to a another row in the same worksheet.

It is very annoying!!

Any tips????

Regards

Kjell

Dear all

I have an equation obtained from partial derivable of some functions, I would like to compute the limit when my variable named Pe goes to infinity. 

I hope to get a more appreciate presentation of my code to obtain the limit (  Pe -> + infty)

limit_infinity.mw

All derivative are well compute, but How can I add the limit as Pe goes to infinity

Thank you 

Hey everyone,

I've been experiencing some issues with Mapleprimes on my laptop. Whenever I try to access the website, it takes an unusually long time to load, and sometimes it doesn't even load at all. This is quite frustrating as I need to use Mapleprimes for my research work. I've tried accessing the website on other devices, and it works fine, so I'm confident that the issue is with my laptop. Has anyone else experienced this problem? Any suggestions on how to fix it?

Thanks in advance for your help!

Kind help to implement the attached flowchart

Finding_Detour_using_alorigthm.pdf

Just experienced a strange response from Maple when I changed the Font anti-aliasing to enabled.

With Font anti-aliasing disabled I ran evalf(Pi,100) and Maple returned 100 digits - no problem.  I then did some other errands in other programs leaving Maple idle, when I came back I thought I would change anti-aliasing to enabled and see if maybe that's the reason why some users are experiencing icons disappearing etc..

Well I re entered and evalueated evalf(Pi,100) and Maple only output 10 digits.  Huh??? What!? Why?  changed font anti-aliasing back but no joy.  So I closed Maple and I got a pop up

Maybe it was hiding behind Maple I don't know but I don't think it was there until I closed Maple.  It seems this OpenJDK platform I believe is causing a lot of Maple issues.

Whoa!  That's really odd.  My restart was with Maple Font anti-aliasing enabled I performed a evalf(Pi,100) and no problem.  I changed to Font anti-aliasing disabled and evalf(Pi,100) presented me with 10 digits!

What the heck is going on.  This font anti-aliasing enabled caused my Maple to slow down as the screen filled up (as I recorded in a earlier post months ago) and now toggling anti-aliasing causes the outputs to not work as expected.  It's gotta be an open JDK issue. (FYI closing Maple did not produce the same pop-up as earlier - I expect idling maple for a while might)

I found a new problem in Maple 2023 on windows 10.  But it is more of an annoyonus. This is what happens:

I can have a worksheet open and running somecode with lots of output generated on the screen. Everything displays fine.

Now I go and open a new application not related to Maple at all, for example if I open the task manager, this causes the Maple screen to immediately go all BLANK ! Yes, all the display is gone. I have no idea why opening a new application in new window could cause this.

Everything disappears from the worksheet except for the worksheet frame. All the menus are gone also.

But resizing the worksheet window makes everything to appear agin due to the repaint process, But I need to resize the worksheet few times to get everything to repaint fully.

So the content is still there, but it just do not show/repaint.

Note that Maple does NOT freeze or anything, it is still running and the content is there, it is just that the content becomes not visible due to opening a new application window on the side.

I have never seen anything like this in any other application on windows. I also never had this problem on same PC with Maple 2022.2.

Anyone else noticed this problem?  This is reproducible all the time. Sometimes the content will display again on its own after short amount of time, but will be missing many menu items and missing side content and so on so I have to resize the windows to make repaint eveything again. 

May be it is a Java problem. I do not know.

I have the same system as described in this post 

I will make a movie to show this very soon but I am waiting for something to finish running before I do this so I can save all my work.

Windows 10 pro, running Maple 2023 with two monitors.

Here is a small movie. I made very small example which prints number on the screen in a loop. I added a Sleep in between so it does not take over the CPU just for illustration. In my real code there is no such Sleep command.

In this movie, we see that when I open the task manage window how the display in the worksheet is gone. In this example it comes back after few seconds but all the other items in the worksheet (menus etc..) are still missing. Resizing the windows makes them appear again. In my actual code, due to the larger content, the whole worksheet remain not visible for much longer each time (I waited 5 minutes and more for it to repaint), but still had to resize it to make everything visible as in this example.

Can someone else reproduce this?

for n from 1 to 1000000 do
    print("n=",n);
    Threads:-Sleep(2);
od;

Hi, I am looking to illustrate my lecture with Maple figures. This is in a French context, using French vocabulary. I am including my mathematical development in an appendix. I would appreciate any suggestions. Thank you for your help

G2MathDvlpt.pdf  G2.mw

> int((1 - x)^r*(-2*x + (-2 + x)*log(1 - x))/(2*x*log(1 - x)^2), x = 0 .. 1) assuming 0 <= r

Expected result is:

1 + r - r * ln(1 + r) - 1/2 * ln(2 * Pi * (1 + r)) + lnGAMMA(1 + r)

Hi,

Can anybody explain why

with(Units):
A := 1, 2, 3:
B := 4, 5, 6:
AB := B - A;

outputs 11, but the output is 3, 3, 3 without the Units package?

Best regards,

Mikkel

For two nonempty lists (of the same length), 

F~(list1, ` $`, list2); # space-dollarsign

is (almost) equivalent to 

zip(F, list1, list2);

However, it appears that in practice, using `~` can be faster than its equivalent zip version.
Here is a typical test: 

Download `~`_and_zip.mw

But I cannot find any explanations in the documentation (as well as What is Maple's equivalent to Mathematica's MapThread?). Does anyone know why?