## Difficulty with pdsolve and electromagnetics...

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?

## How to find roots of polynomials with a huge Groeb...

Hi everyone,

I am trying to find the roots of a system of 3 multivariate polynomials with 3 variables. I have used

G := Basis(P, tdeg(x6, x7, x8))

from the Groebner package and got a Groebner Basis with 29 elements (the length of output exceeds the limit). I want to find roots in the interval [0,1] with x<y<z. Is there a way to find solutions? Some of the polynomials in the Basis are of order 11 and I can't find a single variable polynomial in the basis. Is there an efficiet way to find such roots? Or should I do someting completely different?

Best

fabs

## How can I implement a simple code to obtain the di...

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.

## How to do the integration with substitution...

How to find G(0)??

M2.mw

## How do I solve this system of 4 nonlinear equation...

I simplified my setup as much as possible. Please check lambdas.mw.

While I think I managed to obtain some analytical solutions, they look a bit strange for two reasons:

1) They do not depend on the exogenous parameters as I expected. In fact, mu_jk and mu_ki should only depend on q_0jk and q_0ki, while lambda_jk and lambda_ki should only depend on BigSigma_0jk, BigSigma_0ki, smallsigma_ujk and smallsigma_uki.

2) Strong dependence on q_0jk and q_0ki: if I were to setup these two parameters to zero or to the same value I can't obtain solutions anymore (especially for the lambdas). Does it mean that they are not really "free" parameters?

I noticed that if I combine the two equations from the FOCs of mu_jk and mu_ki into one system (is this even legit?), I get q_0jk = - q_0ki * (lambda_jk / lambda_ki). This is also easy to see if I apply the calibration at the beginning of the script (remove hashtags on all the params with the exception of q_0jk and q_0ki) and then divide lambda_jk by lambda_ki. Why?

I am quite sure that the computations are correct (I checked multiple times), but I am now questioning my setup. In which ways does my setup differ from the one below?

Essentially, I am trying to extend the following problem. As you see below, mu depends only on p_0 (the one-dimensional equivalent of my q_0jk and q_0ki) and lambda depends only on BigSigma_0 and smallsigma_u (the one-dimensional equivalents of my BigSigma_0jk, BigSigma_0ki, smallsigma_ujk and smallsigma_uki).

Thank you.

## Picking up 2 or 3 element subsets for a larger nr...

Given a large number n

When I say n my elements will be {1,2,3,4..n}

take n, k where k will be 2 or 3

Picking up k  element subsets

In such a way it will return one subset at a time without storing in list to avoid memory usage more

A for loop like

Some place within the code where

I will be able to perform my task using  each 2 or 3 element subset

If we go for function may be we need to go for recursive function in such a way that at each call of function it will produce one 2 element subset I do my work with that and then do my next call of the same function again

## How to create a loop in Physics package with one ...

I am trying to create a loop in the Physics package where I am interested in looking at the components of a tensor with one index up and one down. However, when I run the loop it returns the expression with both indices down in my attempts to solve the issue.

I have been fighting with it for an hour now and cant seem to find a fix. Any help will be appreciated, I have attached the file I am working with.

LoopQuestion.mw

## How to substitute a variable into an expression co...

The following differential equation occurs during blending of two fluid in a continuous flow stirred tank

I want to replace the quantities in parenthesis on the RHS with the following variables (so-called deviation variables) where the overbar variables are constants and x1, x2 and x are variables.

When I use the subs command or algsubs command, it doesn't perform the substitution.

What is the best way to perform this operation?

## Create excel file with sheets of independent varia...

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

## How can I handle this error?...

I'm trying to solve a system of differential equations and encountered this error: Error, (in fsolve) {f1[0], f1[1], f1[2], f1[3], f2[0], f2[1], f2[2], f2[3]} are in the equation, and are not solved for. How can this error be rectified?

## Is there a way to make maple simply skip errors an...

For example when I run a worksheet, if there is an error, maple simply prints the error and moves on to the next step. Is there a way to do that with loops.
The try and catch statements are a bit cumbersome and sometimes you have to predict the kind of error statements you may face.

## transform PDEs using change of variable...

Dear all

I  have a PDE, I would like to substitute the funciton T by another funciton

How transform the old PDE to a new PDE

transfirm_equation_using_change_variable.mw

thank you

## Taking an excel sheet perform operation create new...

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

For sample to explain my question I attach a demo excel

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

## Global setting of character size in maple 2022...

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

## Why does the procedure maximize still return a wro...

Here is an apparent instance:

 > interface(version);
 >
 (1)
 >