## find a weak form to Navier equations...

I want to find a weak form to Navier equations and obtain a solution formulation . I am interested in solving this problem using a finite element solver for which we need to introduce these equations in weak form. Can anyone help me in this regard? What is a higher-order continuity in the FEM approximation. This is challenge with the FEM which is based the Lagrange basis functions. To overcome the shortcomings, should we use the isogemetric analysis being based on the NURBS basis functions? How FEM cover this shortage for solving this type of equations?

## Verification of solved Maple system of PDEs...

HI all, I obtained a solution to a system solved by Maple but it seems not to be correct. And I couldn't detect where the mistake lies!

solution_bug_or.....mw

## Which version or brand of maple has geometric cons...

I find some book named automatic construction of graph for CAD

Then searched some paper related with it about geometric constraint solver

Do maple has these things?

I have no idea in design, which input should be for these automatic design from nothing?

is there any mechanical knowledge as constraint by default in this automatic design?

## Is it possible to write a table type together with...

We can write a list, set, MutableSet and array type together with their entries types. For example `list(polynom)` or `array(array(integer))`. But what about a table? For example how can I emphasize a type table with indices of the type integer and entries a list of integers? I was guessing `table(integer,list(integer))` which is not working, so my guess is not correct. I tried some other combinations which they didn't work too. I can't see anything in the programming guide and the help of Maple or a post here that is addressing this question.

Example:

```test:=table([1=[1,2,3],2=[6,5,4]]):
type(test,table(integer,list(integer))): # which of course is not working.```

## HazardRate does not work for convolution...

Hello,

HazardRate seems not to work for a convolution - it always returns zero.

restart;
with(plots);
with(Statistics);
X1 := RandomVariable(Uniform(0, 1));
X2 := RandomVariable(Uniform(0, 1));
HazardRate(1/2*X1 + 1/2*X2, 0.4); #returns zero
plot(HazardRate(1/2*X1 + 1/2*X2, t), t = 0 .. 0.9, legend = "Hazard Rate"); #plots zero
#writing hazard rate explicitly works fine
plot(PDF(1/2*X1 + 1/2*X2, t)/(1 - CDF(1/2*X1 + 1/2*X2, t)), t = 0 .. 0.9, legend = "Hazard Rate explicitly");

Thank you!

## Geometry :equilateral triangle...

Let $\triangle ABC$ be an equilateral triangle and $\angle BAC$=$20^\circ$, take point $D$ is on $AC$ such that $AD$ $=$ $BC$. Find $\angle ABD$= ?

## How to approximate the most dominant eigenvalue o...

Use the Symmetric Power method to approximate the most dominant eigenvalue of the matrix A=Matrix([[4, 2, -1], [2, 0, 2], [-1, 2, 0]]) , Use x_0 = (-1,0, 1)^t.  Iterate until a tolerance of 10^-4 is achieved or until the number of iterations exceeds 25.

I tried but failed to get full evaluation (numbers only).

with(LinearAlgebra);

A := Matrix([[4, 2, -1], [2, 0, 2], [-1, 2, 0]]);
x_0 := <-1, 0, 1>;
Tol := 0.0001;
k := 15;
y_k := evalf(A*x[k - 1]);
mu_k := evalf(Transpose(x_k - 1)*y_k);
x_k = y_k/Norm(y_k, 2);

Q5_Ch_9.3.pdf

## How to animate velocity and acceleration ...

Hi,

An important application of vectors is their use to represent velocity and acceleration.it would ideal to see how the velocity and acceleration vectors behave and how they interact, as a point moves along a curved path. I want to create an animation to do that.

I have some difficulties with arrow animations.

Ideas?

Thanks

TESTAnimVitesse.mw

## How to remove several entries from an array effici...

Consider 1-dimensional arrays in Maple. To add one element at the end of an array, there is a pre-defined command `ArrayTools:-Append` (or using `ArrayTools:-Insert` if one wants to add an element at another location of the array) and to remove one entry from an array there is another pre-defined command `ArrayTools:-Remove`. Now let's say I want to add several elements and remove several elements. If I want to add all of the new elements at the end of the array, there is a predefined command `ArrayTools:-Extend`. If I want to remove several entries that are sequal, then I can give the second argument of `ArrayTools:-Remove` as a range `n1..n2`. But now let's say I want to remove several entries that are not sequal, for examples entries with indices in `[5,8,14]`. Is there any special efficient way to do it or just defining a loop to do the removals one by one? Removing by a loop is not very nice since the number of indices will change after each removal. Then another idea is to redefine the whole array using a `select` or a `seq`. But I'm guessing that none of these are the best way to do so. If I was dealing with `MutableSet`, I would use `&minus`, but I can't use MutableSets in every situation, because MutableSets change the order of elements and have more special properties like no repeated elements etc.

## Why am I getting a negative pdf?...

Hello,

I plot a pdf of the average of two iid random variables, and get that it is negative. What am I doing wrong?

Here is an example:

restart;
with(plots);
with(Statistics);
plot([PDF(X1, t), PDF(0.5*X1 + 0.5*X2, t)], t = 0 .. 1, color = [red, blue], legend = ["PDF X1", "PDF average"]);

## How to plot with variables ...

Hello everyone

I have the following issue :

I want to create a different plots (2d/3d) with varying variables ( I mean expression contains different variables and I am changing their values in order to get different results )

for example:

u=a*x^2+b*y^2

a=1

b=1

plot3d(u, x = -2 .. 2, y = -2 .. 2)

and I am getting an error

could you please tell me how to plot in that way , that first i define the function with unknown variables , then i am giving them different values ( idea is that i have lots of variables and lots of ranges so it will not be convenient to change them manually into the expression ) and at the end to have a plot

Thank you very  very much

## How to accelerate matrix construction?...

Hello everyone!

I want to construct column vector which elements should be square matrices (m x n each one). So, i use cycle "for" to set such construction.

My question is: what is the fastest way to construct matrices if each matrix elements are independent from each other and also they are results of numerical integration, like is shown in attached file?

Acceleration.mw

## How I can solve PDE equation on three straight and...

how I can solve this PDE equation with four boundary conditions mentioned in the attached file?

It seems that this pde needs four boundary conditions. One of them is defined on a curved domain that its function is provided.

Data related to function phi in boundary condition is attached as an excel file.

a similar procedure is provided in this paper

townsend.pdf

Thanks

pde.mw

Book1.xlsx

## How find Eigenvectors by considering some points a...

By considering matrix A and having three conditions mentioned in maple file, Matrix A  has four zero eigenvalues ​​and one non-zero eigenvalue that are reported in maple file by applying three conditions.

The goal is to obtain five Eigenvectors (V__1` ,`V__2` ,`V__3` ,`V__4` ,`V__5`) corresponding to these five eigenvalues ​​such that they have following form.

1-The first Eigenvector should be v1 = [-, -, -, 0,0] that the three dashes can be whatever, but the last two numbers must be 0 and 0.

2- The second Eigenvector should be v2 = [-, -, -, 0,0] where the three dashes can be anything but the last two numbers must be 0 and 0.

3- The third Eigenvector must be v3 = [-, -, -, 1,0], which three dashes are whatever , but the last two numbers must be 1 and 0.

4-The fourth Eigenvector should be v4 = [-, -, -, 0,1] that those three dashes can be whatever, but the last two numbers must be 0 and 1.

5-The fifth  Eigenvector should be v5 = [-, -, -, 0,0] that those three dashes can be whatever, but the last two numbers must be 0 and 0.

for more details please see maple file.

How I can find this Eigenvectors by considering mentioned points.

Thanks

EIGENVECTOR.mw