## MaplePrimes Questions

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## Heat equation initial/boundary conditions...

What would be the IBC conditions for the 1D heat equation describing the temperature distribution along a circular rod with a heat source at its base?

## computing all principal minor of a Hessian Matrix...

Hi,

I have 6 by 6 Hessian matrix H. I want to check whether it is a negative definite. The rule of negative definite is "if and only if its n leading principlal minors alternate in sign with the kth order leading principal minor should have same sign as (-1)^k".

In my Hessian H, some leading principal minor of H is zero while the nonzero ones follows above rule. So negative definite test fails and Now I have to check negative semidefinite test which state that "H is negative semidefinite if and only if every principal minor of odd order is <=0 and every principal minor of even orderis >=0". So I have to check sign of every principal minor ( instead of just leading principal minor) to check for negative semidefinite of H matrix.

Can anyone help me how can I compute sign of all principal minor of a 6 by 6 square Hessian matrix.

Thanks and Regards,

Nilesh

## modify an expression...

Hello people in mapleprimes,

I want to single out omega^epsilon from and modify the rhs of the following expression
to the expression where the  the part without omega^epsilon and  another part of  omega^epsilon
are multiplied.

Y = -L*epsilon^epsilon*(1-epsilon)^(1-epsilon)*(-omega^(-1+epsilon)*k*theta+(1-theta)*omega^epsilon)/(1-epsilon-theta)

I am glad if you teach me this.

taro

## Another engine dispatch i dont understand...

I found this error extremely confusing when using the solve function:

Error, (in Engine:-Dispatch) cannot determine if this expression is true or false: 1000 < 5^(1/2)

## RootOf Error needing to be dispatched to the engin...

Hi, i encountered this, error, and the link to the help page was broken.

Error, (in RootOf) expression independent of _S000100

## How do I display the numeric value for a trig func...

when I enter a trig function as cos(pi/2) I get as a return the same input.  What I would like is the numeric answer displayed. also there are times when I don't want pi in the answer but a numeric value calculated based on pi * whatever.

Thanks

Bill

## Proof of Least Square Equation ...

I am trying to prove the equation of the least square estimator. For example, I have:

X := Matrix(2,3,symbol=p)

Y:= Matrix(2,1,symbol=f)

b:= Matrix(2,1,symbol=n)

or Y=X.b

The known estimation of b results from the minimization of the objective function:

S:=Transpose(X.b-Y).(X.b-Y).

We take the derivative of the above expression and set it equals with zero.

Then the estimator is: b=MatrixInverse(Transpose(X).X).Transpose(X).Y

How can I get this expression using commands οn maple?

My final task is to change the objective function to see the different estimations. For example if I have the below objective function which is the results of estimation as equation:

S:=Transpose(X.b-Y).MatrixInverse(C).(X.b-Y)

where C:=Matrix(2,2,symbol=w)

Ofcorsse I know the answer, but I am not sure for more complicated objective functions.

## modification of an expression...

Hello people in maple primes,

I have an expression,

e1_1:=-gamma*r*theta/(w*beta*(theta-1))

, which I want to put in order as

gamma*r*theta/(w*beta*(1-theta))

Isn't there any ways to do the modification above?

taro

## NonLinearFit - Operator mode...

Hi!

Here below is the code I got problems:

#################################

Dens := proc(v)
local theta, r;
evalf[8](
Int(
Int(
4*r/(1-0.84*cos(theta)^2)^(1/2)*exp(-r*(6.25-5.245*cos(theta)^2)^(1/2))
, theta = 0. .. 2*Pi)
, r = 0. .. v)
) assuming v>=0
end proc;

#
#

FitFinalDens := NonlinearFit(
b*(1+a*u)/u*Dens(u/(1+a*u))
, depth
, veloc
, [u]
, initialvalues = [a = 1.4, b = 0.13]
, parameternames = [a, b]
, output = [leastsquaresfunction, residuals, parametervector]
, parameterranges=[a=1.1..3.0,b=0.02..0.8]
);

#################################

Then, I obtain two sort of errors:

First error message:

Error, (in Statistics:-NonlinearFit) invalid input: no implementation of NonlinearFit matches the arguments in call, 'NonlinearFit(0.13*(1.+1.4*u)*(int(int(4*r/..........

etc...

Second error message:

Error, (in Statistics:-NonlinearFit) complex value encountered

So, really I don't known how to correct the code.

I tried a lot  of things such as using  "value" command,  "Re" command, etc.

Do you have a solution?

Sincerely yours.

Jacqr

## invalid input: LinearAlgebra:-Basis expects its 1s...

invalid input: LinearAlgebra:-Basis expects its 1st argument, V, to be of type {Vector, set(Vector), list(Vector)

A:=<<5,5,5>|<1,2,3>|<-5,1,2>>;
Basis(A);

## how can i solve with ShowSolution...

restart;
with(Student[Calculus1]);
a := Int(exp(cos(x)), y = 0 .. sin(x), x = 0 .. (1/2)*Pi);
ShowSolution(a);
i get error

## Can't solve arctan equation...

Trying to solve:

solve (arctan((2*x^2-1)/(2*x^2+1)) = 0, x);

The answer I get is the original function:

arctan((2*x^2-1)/(2*x^2+1))

This example is from the Maple book by Keck, and he shows the Maple V answer as

1/2 sqrt(2) -1/2 sqrt(2)

Suggestions?

## Solve the PDE with conditions......

Hi every body :

I want to slove this below PDE with conditions 1&2, can every body help me, tnx.

PDE := diff(u(x, t), t)+6*u(x, t)*(diff(u(x, t), x))+diff(u(x, t), x, x, x) = 0;

1.x=0

2.assume t is step function(Heaviside).

with regards....

## How to simplify this solution?...

```restart;
sol:=dsolve(diff(y(x),x)= x/(sqrt(x^2-16))*1/(2*y(x)),y(x));
```

Gives

But the solution can also be written as

I just do not know how to transform the first solution to the second simpler one. I tried:

```sol:=map(x->rhs(x),[sol]);
```

The simpler solution can be found as follows

```restart;
sol:=dsolve(diff(y(x),x)= x/(sqrt(x^2-16))*1/(2*y(x)),y(x),'implicit');
```

But the term in the middle above is

Therefore the solution is really

```eq:=y(x)^2-sqrt(x^2-16)-_C1 = 0;
solve(eq,y(x));```

Which gives

What command to simplify the long solution to the shorter one obtained from the implicit?

## where did the 3 come from? dsolve question....

The solution by Maple below is correct, but non-the-less, a little strange.

```restart;
dsolve(diff(y(x),x)=3*x^2*(y(x)^2+1),y(x));
```

Gives

Ofcourse 3*constant is still constant. But it is a little strange and have no reason for it to be there.  When I solve it by hand

What could made Maple put the 3 in there? Again, solution is 100% correct, but it could be simpler.

Maple 2017.1

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