I watched a webinar training:   Maple Training for Engineers, Researchers, and Scientists.

The file demonstrated topics and used collapsible regions with a colored band across the document and a + / - sign on the left to open/close the section or region.  Different than the document gray down arrow.

I have searched all the documentation and can not find how to do this.   I have done this in other programs like MathCAD to close and lock a region from viewing or editing of specific formulas.

Any help always appreciated.

Regards,

Bill

I'm currently working on building a Grid Layout for a project, and I'm having trouble coding in the RunWindow and GetFile elements into buttons under the grid layout. I've gone through the overviews and examples for them, but had no luck. I'm using Maple 2016.1 for OS X.

Additionally, the structure of the code is slightly different as to how many of the example worksheets structure their Grid Layout code, since the code originated from a Maplet Builder file. I.e. in the example worksheets they would follow as:

maplet := Maplet('onstartup' = 'Action1', 'reference' = 'Maplet1',
         BoxLayout('background' = "#D6D3CE", 'border' = 'false', 'halign' = 'center', 'inset' = '5', 'reference' = 'BoxLayout1', 'valign' = 'center', 'vertical' = 'false', 'visible' = 'true',
                       BoxColumn( BoxCell('hscroll' = 'never', 'value' = 'Button1', 'vscroll' = 'never'),
         GridLayout('background' = "#D6D3CE", 'border' = 'false','halign'='center','inset'='5', 'reference' = 'GridLayout1', 'valign' = 'center', 'visible' = 'true',
                   GridRow('valign' = 'top', GridCell('height' = '1', 'hscroll' = 'never', 'value' = 'BoxLayout1', 'vscroll' = 'never', 'width' = '1' ))),
         Window('layout'= 'GridLayout1', 'reference' = 'W1', 'resizable' = 'true', 'title' = "Maplet"),
          Action('reference' = 'Action1', RunWindow('window'= 'W1'))

However the structure for the code I am working with has action at the very start of the code, follwed by the the code for the buttons then layouts/window.  E.g. (the code has been shortened)

with (Maplets[Elements]):
maplet :=
Maplet('onstartup'='Action1','reference'='Maplet1',
Action('reference'='clickButton1'),
Action('reference'='clickButton9',
Evaluate('function'='plot3d(x^2*cos(y),x = -1 .. 1,y = -2*Pi .. 2*Pi)','target'='Plotter1','waitforresult'='true')),
Action('reference'='clickButton11'),
Action('reference'='clickButton12'),
Action('reference'='clickButton10'),
Button('background'="#D6D3CE",'caption'="Insert Molecular Geometry",'enabled'='true','foreground'="#000000",'onclick'='clickButton1','reference'='Button1','visible'='true'),

....

BoxLayout('background'="#D6D3CE",'border'='false','halign'='center','inset'='5','reference'='BoxLayout1','valign'='center','vertical'='false','visible'='true',
BoxColumn(
BoxCell('hscroll'='never','value'='Button1','vscroll'='never'),
BoxCell('hscroll'='never','value'='BoxLayout2','vscroll'='never'),
BoxCell('hscroll'='never','value'='BoxLayout3','vscroll'='never'),
BoxCell('hscroll'='never','value'='BoxLayout9','vscroll'='never'),
BoxCell('hscroll'='never','value'='BoxLayout14','vscroll'='never')),
BoxColumn(
BoxCell('hscroll'='never','value'='Label3','vscroll'='never'),
BoxCell('hscroll'='never','value'='Plotter1','vscroll'='never'),
BoxCell('hscroll'='never','value'='Slider1','vscroll'='never'))),
GridLayout('background'="#D6D3CE",'border'='false','halign'='center','inset'='5','reference'='GridLayout1','valign'='center','visible'='true',
GridRow('valign'='top',
GridCell('height'='1','hscroll'='never','value'='BoxLayout1','vscroll'='never','width'='1'))),
Window('layout'='GridLayout1','reference'='Window1','resizable'='true','title'="Maplet"),
Action('reference'='Action1',
RunWindow('window'='Window1'))):

Maplets[Display](maplet);

If anyone would be able to provide an example of code or some guidance I could follow that would be greatly appreciated! 

MAPLE 15 on Windows 10

I have a file on which I can no longer open. This happened after my computer made me long on again after being gone for a little while. Maple was not running when I got back on. This is not unusal and I just clinck on the file and restart.

This time this did not work.

It comes up with a message asking me to select an input mode. Whatever I select even 'Plain text' it just hangs.

I'd send you an image, but I don't see how to do it. The button provide only allows for something with  url and the snip I made is on my desktop.

I need to get thiis worksheet back. I've put a lot of effort into it.

-Traruh

After running Maple in a shell file, I come up with this error that I do not understand on my Mac,

gap_long := 0.117647058823529 Pi

gap_lat := 0.0588235294117647 Pi

lat_begin := 0.441176470588235 Pi

long_begin := -Pi

lat_begin_0 := 0.441176470588235 Pi

long_begin_0 := -Pi

long_max := 0.882352941176471 Pi

lat_max := -0.441176470588235 Pi

33

Warning, `parameter` is implicitly declared local to procedure `set_par_eff`

distance eff distance_eff
im in has not
im in has not
im in has not
im in has not
im in has not
im in has not
im in has not
im in has not
im in has not
Im in has par
Im in has par
Error, invalid input: eval expects its 2nd argument, eqns, to be of type
{integer, equation, set(equation)}, but received par_eff_post
13

32

31

17

hou := 0

mini := 0

seci := 0

memory used=4.0MB, alloc=32.3MB, time=0.23



If needed, I can attach more files if my question is still a bit too cryptic. Please let me know asap as this is urgent. Thank you so much,
-Z

hi.please help me for solve this equation

i encounter with error''

Error, (in StringTools:-IsPrefix) second argument must be a string''

equations which be solved attached as pdf file

thanks

Kernel4.mw

root.pdf

Download Kernel4.mw

I'm tryinv to find the contents of specific bins in a maple histogram. I don't find this elementary 'function' anywhere in the help.

How do I do it? Surely it's possible w/o taking a ruler to the screen...

Hi, I want to ask. the maple program that i have done have something wrong somewhere.

for an example changes basis

 from e_{1}e_{1}=e_{1} , e_{1}e_{2}=e_{2} maple program reading :A1 : (1,1,1)=1,B1: (1,2,2)=1

to e_{2}e_{2}=e_{2} , e_{2}e_{1}=e_{1} maple program reading :A2: (2,2,2)=1,B2: (2,1,1)=1

these changes basis above are 2 operation, left product and right product

A1 and A2 are left product, while B1 and B2 are right product,

i need to make A1 isomorphic to A2, and B1 isomorphic to B2.

by using maple program, i should get identity in matrix form 2x2

[0 1] but i get [0         1]

[1 0],            [C_{21} 0],

For isomorphism, the determinant should not be zero

here's are my maple program:

>isom := proc (A1, A2, B1, B2, n)

local i, j, k, s, r, eqns, t, TEST, BChange, sols, m, S1, S2, C;

C := matrix(n, n);

BChange := matrix(n, n);

TEST := 0; eqns := {};

for i to n do for j to n do for m to n do

S1 := sum(A1[i, j, k]*C[k, m], k = 1 .. n); S2 := sum(C[i, r]*(sum(A2[r, s, m]*C[j, s], s = 1 .. n)), r = 1 .. n);

eqns := `union`(eqns, {S1 = S2})

end do end do end do;

for i to n do for j to n do for m to n do

S1 := sum(B1[i, j, k]*C[k, m], k = 1 .. n); S2 := sum(C[i, r]*(sum(C[j, s]*B2[r, s, m], s = 1 .. n)), r = 1 .. n);

eqns := `union`(eqns, {S1 = S2})

end do end do end do;

sols := [solve(eqns)];

t := nops(sols);

for i to t do for j to n do for k to n do

BChange[k, j] := subs(sols[i], C[k, j])

end do end do;

if simplify(linalg:-det(BChange)) <> 0 then print("BChange", BChange);

print("s1", S1); print("s2", S2); print("The det is", simplify(linalg:-det(BChange)));

TEST := 1 end if end do;

if TEST = 0 then print("These two algebras are not isomorphic")

end if end proc

input maple program:

> DENDA1 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1]);
> DENDB1 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 2, 2) = 1]);
> DENDA2 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(2, 2, 2) = 1]);
> DENDB2 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(2, 1, 1) = 1]);
> isom(DENDA1, DENDA2, DENDB1, DENDB2, 2);

Couldn't any question with title beginning with http be removed automatically? There has been quite a few containing nothing but spam.

Dear All,

I am going to solve the following systems of ODEs but get the error: Newton iteration is not converging.
Could you please share your idea with me. In the case of AA=-0.2,0,0.2,0.4,...; I could get the solution.
Thank you in advance.

restart;
with(plots);
Pr := 2; Le := 2; nn := 2; Nb := .1; Nt := .1; QQ := .1; SS := .1; BB := .1; CC := .1; Ec := .1; MM := .2;AA:=-0.4;

Eq1 := diff(f(eta), `$`(eta, 3))+f(eta).(diff(f(eta), `$`(eta, 2)))-2.*nn/(nn+1).((diff(f(eta), eta))^2)-MM.(diff(f(eta), eta)) = 0; Eq2 := 1/Pr.(diff(theta(eta), `$`(eta, 2)))+f(eta).(diff(theta(eta), eta))-4.*nn/(nn+1).(diff(f(eta), eta)).theta(eta)+Nb.(diff(theta(eta), eta)).(diff(h(eta), eta))+Nt.((diff(theta(eta), eta))^2)+Ec.((diff(f(eta), `$`(eta, 2)))^2)-QQ.theta(eta) = 0;
Eq3 := diff(h(eta), `$`(eta, 2))+Le.f(eta).(diff(h(eta), eta))+Nt/Nb.(diff(theta(eta), `$`(eta, 2))) = 0;

bcs := f(0) = SS, (D(f))(0) = 1+AA.((D@@2)(f))(0), theta(0) = 1+BB.(D(theta))(0), phi(0) = 1+CC.(D(phi))(0), (D(f))(etainf) = 0, theta(etainf) = 0, phi(etainf) = 0

Error, (in dsolve/numeric/ComputeSolution) Newton iteration is not converging

how to translate python code which use scipy, numpy to maple code

import numpy as np
from scipy.sparse.linalg import svds
from functools import partial


def emsvd(Y, k=None, tol=1E-3, maxiter=None):
    """
    Approximate SVD on data with missing values via expectation-maximization

    Inputs:
    -----------
    Y:          (nobs, ndim) data matrix, missing values denoted by NaN/Inf
    k:          number of singular values/vectors to find (default: k=ndim)
    tol:        convergence tolerance on change in trace norm
    maxiter:    maximum number of EM steps to perform (default: no limit)

    Returns:
    -----------
    Y_hat:      (nobs, ndim) reconstructed data matrix
    mu_hat:     (ndim,) estimated column means for reconstructed data
    U, s, Vt:   singular values and vectors (see np.linalg.svd and 
                scipy.sparse.linalg.svds for details)
    """

    if k is None:
        svdmethod = partial(np.linalg.svd, full_matrices=False)
    else:
        svdmethod = partial(svds, k=k)
    if maxiter is None:
        maxiter = np.inf

    # initialize the missing values to their respective column means
    mu_hat = np.nanmean(Y, axis=0, keepdims=1)
    valid = np.isfinite(Y)
    Y_hat = np.where(valid, Y, mu_hat)

    halt = False
    ii = 1
    v_prev = 0

    while not halt:

        # SVD on filled-in data
        U, s, Vt = svdmethod(Y_hat - mu_hat)

        # impute missing values
        Y_hat[~valid] = (U.dot(np.diag(s)).dot(Vt) + mu_hat)[~valid]

        # update bias parameter
        mu_hat = Y_hat.mean(axis=0, keepdims=1)

        # test convergence using relative change in trace norm
        v = s.sum()
        if ii >= maxiter or ((v - v_prev) / v_prev) < tol:
            halt = True
        ii += 1
        v_prev = v

    return Y_hat, mu_hat, U, s, Vt

     It is known that ODE boundary value problem is similar to the problem of solving systems of nonlinear equations. Equations are the boundary conditions, and the variables are the values of the initial data.
For example:

y '' = f (x, y, y '), 0 <= x <= 1,

y (0) = Y0, y (1) = Y1;

Where y (1) = Y1 is the equation, and Z0 is variable, (y '(0) = Z0).

     solve () and fsolve () are not directly suitable for such tasks. Directly should work the package of optimization in relation to a system of nonlinear equations. (Perhaps it has already been implemented in Maple.)
Personally, I am very small and unprofessional know Maple and cannot do it. Maybe there is someone who would be interested, and it will try to implement this approach to solving ODE boundary value problems?  

Hi,

I did some hypothesis testing exercises and I cross checked the result with Maple. I just used following vectors for an unpaired test

a := [88, 89, 92, 90, 90];
b := [92, 90, 91, 89, 91];

I ended up with the following solution:

HFloat(1.5225682336585966)
HFloat(-3.122568233658591)
for a 0.95 confidence interval.

Using

TwoSampleTTest(a, b, 0, confidence = .95, summarize = embed)

and

TwoSampleTTest(a, b, 0, confidence = .975, summarize = embed)

I get following results:

-2.75177 .. 1.15177

-3.13633 .. 1.53633

respectively. I can not explain the discrepancy.

Best regards,

Oliver

PS:

Maple Code in case files won´t be attached.

Unpaired t Test
restart;
Unpaired test-test dataset
a := [88, 89, 92, 90, 90];
b := [92, 90, 91, 89, 91];
The se² estimate is given by:
se²=var(a)+var(b)+2*cov(a*b)=var(a)+var(b)
se²=
sigma[a]^2/Na+sigma[b]^2/Nb;
with Na, Nb being the length of vector a and b respectively.
                             2                              2
  sigma[[88, 89, 92, 90, 90]]    sigma[[92, 90, 91, 89, 91]]
  ---------------------------- + ----------------------------
               Na                             Nb             
sigma[a]^2;
 and
sigma[b]^2;
 are approximated by
S[a]^2;
 and
S[b]^2;
                                             2
                  sigma[[88, 89, 92, 90, 90]]
                                             2
                  sigma[[92, 90, 91, 89, 91]]
                                           2
                    S[[88, 89, 92, 90, 90]]
                                           2
                    S[[92, 90, 91, 89, 91]]
with
S[X]^2;
 defined as
S[X]*`²` = (sum(X[i]-(sum(X[j], j = 1 .. N))/N, i = 1 .. N))^2/N;
                                 2
                             S[X]
                                                 2
                      /      /         N       \\
                      |      |       -----     ||
                      |  N   |        \        ||
                      |----- |         )       ||
                      | \    |        /    X[j]||
                      |  )   |       -----     ||
                      | /    |       j = 1     ||
                      |----- |X[i] - ----------||
                      \i = 1 \           N     //
             S[X] ￂﾲ = ----------------------------
                                   N              
with(Statistics);
Sa := Variance(a);
                   HFloat(2.1999999999999993)
Sb := Variance(b);
                   HFloat(1.3000000000000003)
Now we are ready to do hypothesis testing (0.95).
We have (with k=min(Na,Nb)=5):
C = mean(a)-mean(b); Deviation := t_(alpha/a, k-1)*se(Sa/k-Sb/k);
c := Mean(a)-Mean(b); deviation := 2.776*sqrt((1/5)*Variance(a)+(1/5)*Variance(b));
                  HFloat(-0.7999999999999972)
                   HFloat(2.3225682336585938)
upperlimit := c+deviation; lowerlimit := c-deviation;
                   HFloat(1.5225682336585966)
                   HFloat(-3.122568233658591)

Execution of built in student test
TwoSampleTTest(a, b, 0, confidence = .95, summarize = embed);

where i can found oscilloscope icon for cisuit simulation?thanks

I am unable to solve the attached optimal control problem,please any one who many help  me in guideing .tnx

restart:
unprotect('gamma');

L:=b[1]*c(t)+b[2]*i(t)+w[1]*(u[1])^2/2+w[2]*(u[2])^2/2+w[3]*(u[3])^2/2;
1 2 1 2 1 2
b[1] c(t) + b[2] i(t) + - w[1] u[1] + - w[2] u[2] + - w[3] u[3]
2 2 2
H:=L+lambda[1](t)*((1-p*Psi)*tau+phi* v + delta *r-lambda*(1-u[3])*s-u[1]*varphi*s -mu*s ) +lambda[2](t)*(p*Psi*tau + u[1]*vartheta*s -gamma*lambda* (1-u[3])*v-(mu+phi)*v ) +lambda[3](t)*( (1-u[3])*rho*lambda* (s +gamma*v)+(1-q)* u[2]*eta*i -(mu +beta +chi)*c ) +lambda[4](t)* ((1-rho)*(1-u[3])*lambda*( s +gamma*v) +chi*c - u[2]*eta*i - (mu +alpha )*i) +lambda[5](t)*( beta*c + u[2]*q*eta*i -(mu +delta)*r);
1 2 1 2 1 2
b[1] c(t) + b[2] i(t) + - w[1] u[1] + - w[2] u[2] + - w[3] u[3] + lambda[1](t
2 2 2

) ((1 - p Psi) tau + phi v + delta r - lambda (1 - u[3]) s - u[1] varphi s

- mu s) + lambda[2](t) (p Psi tau + u[1] vartheta s

- gamma lambda (1 - u[3]) v - (mu + phi) v) + lambda[3](t) ((1 - u[3]) rho

lambda (s + gamma v) + (1 - q) u[2] eta i - (mu + beta + chi) c) + lambda[4](t

) ((1 - rho) (1 - u[3]) lambda (s + gamma v) + chi c - u[2] eta i

- (mu + alpha) i) + lambda[5](t) (beta c + u[2] q eta i - (mu + delta) r)
du1:=diff(H,u[1]);

w[1] u[1] - lambda[1](t) varphi s + lambda[2](t) vartheta s
du2:=diff(H,u[2]);du3:=diff(H,u[3]);
w[2] u[2] + lambda[3](t) (1 - q) eta i - lambda[4](t) eta i

+ lambda[5](t) q eta i
w[3] u[3] + lambda[1](t) lambda s + lambda[2](t) gamma lambda v

- lambda[3](t) rho lambda (s + gamma v)

- lambda[4](t) (1 - rho) lambda (s + gamma v)

ddu1 := -A[1] u[1] + psi[1](t) beta x[1] x[3] - psi[2](t) beta x[1] x[3]

ddu2 := -A[2] u[2] - psi[3](t) k x[2]
sol_u1 := solve(du1, u[1]);
s(t) (lambda[1](t) varphi - lambda[2](t) vartheta)
--------------------------------------------------
w[1]
sol_u2 := solve(du2, u[2]);sol_u3 := solve(du3, u[3]);
eta i (-lambda[3](t) + lambda[3](t) q + lambda[4](t) - lambda[5](t) q)
----------------------------------------------------------------------
w[2]
1
---- (lambda (-lambda[1](t) s - lambda[2](t) gamma v + lambda[3](t) rho s
w[3]

+ lambda[3](t) rho gamma v + lambda[4](t) s + lambda[4](t) gamma v

- lambda[4](t) rho s - lambda[4](t) rho gamma v))
Dx2:=subs(u[1]= s*(lambda[1](t)*varphi-lambda[2](t)*vartheta)/w[1] ,u[2]= eta*i*(-lambda[3](t)+lambda[3](t)*q+lambda[4](t)-lambda[5](t)*q)/w[2], u[3]=-lambda*(lambda[1](t)*s+lambda[2](t)*gamma*v-lambda[3](t)*rho*s-lambda[3](t)*rho*gamma*v-lambda[4](t)*s-lambda[4](t)*gamma*v+lambda[4](t)*rho*s+lambda[4](t)*rho*gamma*v)/w[3] ,H );
2 2
s (lambda[1](t) varphi - lambda[2](t) vartheta)
b[1] c(t) + b[2] i(t) + -------------------------------------------------
2 w[1]

2 2 2
eta i (-lambda[3](t) + lambda[3](t) q + lambda[4](t) - lambda[5](t) q)
+ ------------------------------------------------------------------------- +
2 w[2]

1 / 2
------ \lambda (lambda[1](t) s + lambda[2](t) gamma v - lambda[3](t) rho s
2 w[3]

- lambda[3](t) rho gamma v - lambda[4](t) s - lambda[4](t) gamma v

/
\ |
+ lambda[4](t) rho s + lambda[4](t) rho gamma v)^2/ + lambda[1](t) |(1
\

/ 1
- p Psi) tau + phi v + delta r - lambda |1 + ---- (lambda (lambda[1](t) s
\ w[3]

+ lambda[2](t) gamma v - lambda[3](t) rho s - lambda[3](t) rho gamma v

- lambda[4](t) s - lambda[4](t) gamma v + lambda[4](t) rho s

\
+ lambda[4](t) rho gamma v))| s
/

2 \
s (lambda[1](t) varphi - lambda[2](t) vartheta) varphi |
- ------------------------------------------------------- - mu s| +
w[1] /

/
|
lambda[2](t) |p Psi tau
\

2
s (lambda[1](t) varphi - lambda[2](t) vartheta) vartheta /
+ --------------------------------------------------------- - gamma lambda |1 +
w[1] \

1
---- (lambda (lambda[1](t) s + lambda[2](t) gamma v - lambda[3](t) rho s
w[3]

- lambda[3](t) rho gamma v - lambda[4](t) s - lambda[4](t) gamma v

\
\ |
+ lambda[4](t) rho s + lambda[4](t) rho gamma v))| v - (mu + phi) v| +
/ /

// 1
lambda[3](t) ||1 + ---- (lambda (lambda[1](t) s + lambda[2](t) gamma v
\\ w[3]

- lambda[3](t) rho s - lambda[3](t) rho gamma v - lambda[4](t) s

\
- lambda[4](t) gamma v + lambda[4](t) rho s + lambda[4](t) rho gamma v))|
/

1 / 2 2
rho lambda (s + gamma v) + ---- \(1 - q) eta i (-lambda[3](t)
w[2]

\ \
+ lambda[3](t) q + lambda[4](t) - lambda[5](t) q)/ - (mu + beta + chi) c| +
/

/
| / 1
lambda[4](t) |(1 - rho) |1 + ---- (lambda (lambda[1](t) s
\ \ w[3]

+ lambda[2](t) gamma v - lambda[3](t) rho s - lambda[3](t) rho gamma v

- lambda[4](t) s - lambda[4](t) gamma v + lambda[4](t) rho s

\
+ lambda[4](t) rho gamma v))| lambda (s + gamma v) + chi c
/

2 2
eta i (-lambda[3](t) + lambda[3](t) q + lambda[4](t) - lambda[5](t) q)
- ------------------------------------------------------------------------
w[2]

\ /
| |
- (mu + alpha) i| + lambda[5](t) |beta c
/ \

+

2 2
eta i (-lambda[3](t) + lambda[3](t) q + lambda[4](t) - lambda[5](t) q) q
--------------------------------------------------------------------------
w[2]

\
|
- (mu + delta) r|
/
ode1:=diff(lambda[1](t),t)=-diff(H,s);ode2:=diff(lambda[2](t),t)=-diff(H,v);ode3:=diff(psi[3](t),t)=-diff(H,c);ode4:=diff(lambda[4](t),t)=-diff(H,i);ode5:=diff(lambda[5](t),t)=-diff(H,r);
d
--- lambda[1](t) = -lambda[1](t) (-lambda (1 - u[3]) - u[1] varphi - mu)
dt

- lambda[2](t) u[1] vartheta - lambda[3](t) (1 - u[3]) rho lambda

- lambda[4](t) (1 - rho) (1 - u[3]) lambda
d
--- lambda[2](t) = -lambda[1](t) phi
dt

- lambda[2](t) (-gamma lambda (1 - u[3]) - mu - phi)

- lambda[3](t) (1 - u[3]) rho lambda gamma

- lambda[4](t) (1 - rho) (1 - u[3]) lambda gamma
d
--- psi[3](t) = -lambda[3](t) (-mu - beta - chi) - lambda[4](t) chi
dt

- lambda[5](t) beta
d
--- lambda[4](t) = -lambda[3](t) (1 - q) u[2] eta
dt

- lambda[4](t) (-u[2] eta - mu - alpha) - lambda[5](t) u[2] q eta
d
--- lambda[5](t) = -lambda[1](t) delta - lambda[5](t) (-mu - delta)
dt
restart:
#Digits:=10:

unprotect('gamma');
lambda:=0.51:
mu:=0.002:
beta:=0.0115:
delta:=0.003:
alpha:=0.33:
chi:=0.00274:
k:=6.24:
gamma:=0.4:
rho:=0.338:;tau=1000:;Psi:=0.1:;p:=0.6:;phi:=0.001:;eta:=0.001124:q:=0.6:varphi:=0.9:;vatheta:=0.9:
b[1]:=2:;b[2]:=3:;w[1]:=4:;w[2]:=5:;w[3]:=6:
#u[1]:=s(t)*(lambda[1](t)*varphi-lambda[2](t)*vartheta)/w[1]:
#u[2]:=eta*i*(-lambda[3](t)+lambda[3](t)*q+lambda[4](t)-lambda[5](t)*q)/w[2]:;u[3]:=lambda*(-lambda[1](t)*s-lambda[2](t)*gamma*v+lambda[3](t)*rho*s+lambda[3](t)*rho*gamma*v+lambda[4](t)*s+lambda[4](t)*gamma*v-lambda[4](t)*rho*s-lambda[4](t)*rho*gamma*v)/w[3]:
ics := s(0)=8200, v(0)=2800,c(0)=1100,i(0)=1500,r(0)=200,lambda[1](20)=0,lambda[2](20)=0,lambda[3](20)=0,lambda[4](20)=0,lambda[5](20)=0:
ode1:=diff(s(t),t)=(1-p*Psi)*tau+phi* v(t) + delta *r(t)-lambda*(1-u[3])*s(t)-u[1]*varphi*s(t) -mu*s(t),
diff(v(t), t) =p*Psi*tau + u[1]*vartheta*s(t) -gamma*lambda* (1-u[3])*v(t)-(mu+phi)*v(t) ,
diff(c(t), t) =(1-u[3])*rho*lambda* (s(t) +gamma*v(t))+(1-q)* u[2]*eta*i(t) -(mu +beta +chi)*c(t),
diff(i(t), t) =(1-rho)*(1-u[3])*lambda*( s(t) +gamma*v(t)) +chi*c(t) - u[2]*eta*i(t) - (mu +alpha )*i(t),
diff(r(t), t) = beta*c(t) + u[2]*q*eta*i(t) -(mu +delta)*r(t),
diff(lambda[1](t), t) = -lambda[1](t)*(-lambda*(1-u[3])-u[1]*varphi-mu)-lambda[2](t)*u[1]*vartheta-lambda[3](t)*(1-u[3])*rho*lambda-lambda[4](t)*(1-rho)*(1-u[3])*lambda,diff(lambda[2](t),t)=-lambda[1](t)*phi-lambda[2](t)*(-gamma*lambda*(1-u[3])-mu-phi)-lambda[3](t)*(1-u[3])*rho*lambda*gamma-lambda[4](t)*(1-rho)*(1-u[3])*lambda*gamma,diff(lambda[3](t),t)=-lambda[3](t)*(-mu-beta-chi)-lambda[4](t)*chi-lambda[5](t)*beta,diff(lambda[4](t),t)=-lambda[3](t)*(1-q)*u[2]*eta-lambda[4](t)*(-u[2]*eta-mu-alpha)-lambda[5](t)*u[2]*q*eta,diff(lambda[5](t),t)=-lambda[1](t)*delta-lambda[5](t)*(-mu-delta);
d
--- s(t) = (1 - p Psi) tau + phi v(t) + delta r(t) - lambda (1 - u[3]) s(t)
dt

d
- u[1] varphi s(t) - mu s(t), --- v(t) = p Psi tau + u[1] vartheta s(t)
dt

d
- gamma lambda (1 - u[3]) v(t) - (mu + phi) v(t), --- c(t) = (1 - u[3]) rho lambda
dt

(s(t) + gamma v(t)) + (1 - q) u[2] eta - (mu + beta + chi) c(t), 0 = (1

- rho) (1 - u[3]) lambda (s(t) + gamma v(t)) + chi c(t) - u[2] eta - mu

d d
- alpha, --- r(t) = beta c(t) + u[2] q eta - (mu + delta) r(t), ---
dt dt

lambda[1](t) = -lambda[1](t) (-lambda (1 - u[3]) - u[1] varphi - mu)

- lambda[2](t) u[1] vartheta - lambda[3](t) (1 - u[3]) rho lambda

d
- lambda[4](t) (1 - rho) (1 - u[3]) lambda, --- lambda[2](t) =
dt
-lambda[1](t) phi - lambda[2](t) (-gamma lambda (1 - u[3]) - mu - phi)

- lambda[3](t) (1 - u[3]) rho lambda gamma

d
- lambda[4](t) (1 - rho) (1 - u[3]) lambda gamma, --- lambda[3](t) =
dt
d
-lambda[3](t) (-mu - beta - chi) - lambda[4](t) chi - lambda[5](t) beta, ---
dt

lambda[4](t) = -lambda[3](t) (1 - q) u[2] eta

- lambda[4](t) (-u[2] eta - mu - alpha) - lambda[5](t) u[2] q eta,

d
--- lambda[5](t) = -lambda[1](t) delta - lambda[5](t) (-mu - delta)
dt

sol := dsolve({c(0) = 0, i(0) = 0, r(0) = .1, s(0) = 0, v(0) = 0, diff(c(t), t) = (1-u[3])*rho*lambda*(s(t)+gamma*v(t))+(1-q)*u[2]*eta*i(t)-(mu+beta+chi)*c(t), diff(i(t), t) = (1-rho)*(1-u[3])*lambda*(s(t)+gamma*v(t))+chi*c(t)-u[2]*eta*i(t)-(mu+alpha)*i(t), diff(r(t), t) = beta*c(t)+u[2]*q*eta*i(t)-(mu+delta)*r(t), diff(s(t), t) = (1-p*Psi)*tau+phi*v(t)+delta*r(t)-lambda*(1-u[3])*s(t)-u[1]*varphi*s(t)-mu*s(t), diff(v(t), t) = p*Psi*tau+u[1]*vartheta*s(t)-gamma*lambda*(1-u[3])*v(t)-(mu+phi)*v(t), diff(lambda[1](t), t) = -lambda[1](t)*(-lambda*(1-u[3])-u[1]*varphi-mu)-lambda[2](t)*u[1]*vartheta-lambda[3](t)*(1-u[3])*rho*lambda-lambda[4](t)*(1-rho)*(1-u[3])*lambda, diff(lambda[2](t), t) = -lambda[1](t)*phi-lambda[2](t)*(-gamma*lambda*(1-u[3])-mu-phi)-lambda[3](t)*(1-u[3])*rho*lambda*gamma-lambda[4](t)*(1-rho)*(1-u[3])*lambda*gamma, diff(lambda[3](t), t) = -lambda[3](t)*(-mu-beta-chi)-lambda[4](t)*chi-lambda[5](t)*beta, diff(lambda[4](t), t) = -lambda[3](t)*(1-q)*u[2]*eta-lambda[4](t)*(-u[2]*eta-mu-alpha)-lambda[5](t)*u[2]*q*eta, diff(lambda[5](t), t) = -lambda[1](t)*delta-lambda[5](t)*(-mu-delta), lambda[1](20) = 0, lambda[2](20) = 0, lambda[3](20) = 0, lambda[4](20) = 0, lambda[5](20) = 0}, type = numeric);
Error, (in dsolve/numeric/process_input) invalid specification of initial conditions, got 1 = 0

sol:=dsolve([ode1,ics],numeric, method = bvp[midrich],maxmesh=500);

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

dsolve[':-interactive']({});
Error, `:=` unexpected
sol:=dsolve([ode1,ics],numeric, method = bvp[midrich],maxmesh=500);
Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

eq1:=diff(s(t), t)=(1-p*Psi)*tau+phi* v(t) + delta *r(t)-lambda*(1-u[3])*s(t)-u[1]*varphi*s(t) -mu*s(t);
eq2:diff(v(t), t) =p*Psi*tau + u[1]*vartheta*s(t) -gamma*lambda* (1-u[3])*v(t)-(mu+phi)*v(t);
eq3:=diff(c(t), t) =(1-u[3])*rho*lambda* (s(t) +gamma*v(t))+(1-q)* u[2]*eta*i(t) -(mu +beta +chi)*c(t);
eq4:=diff(i(t), t) =(1-rho)*(1-u[3])*lambda*( s(t) +gamma*v(t)) +chi*c(t) - u[2]*eta*i(t) - (mu +alpha )*i(t);
eq5:=diff(r(t), t) = beta*c(t) + u[2]*q*eta*i(t) -(mu +delta)*r(t);

d
--- s(t) = (1 - p Psi) tau + phi v(t) + delta r(t) - lambda (1 - u[3]) s(t)
dt

- u[1] varphi s(t) - mu s(t)
d
--- v(t) = p Psi tau + u[1] vartheta s(t) - gamma lambda (1 - u[3]) v(t)
dt

- (mu + phi) v(t)
d
--- c(t) = (1 - u[3]) rho lambda (s(t) + gamma v(t)) + (1 - q) u[2] eta i(t)
dt

- (mu + beta + chi) c(t)
d
--- i(t) = (1 - rho) (1 - u[3]) lambda (s(t) + gamma v(t)) + chi c(t)
dt

- u[2] eta i(t) - (mu + alpha) i(t)
d
--- r(t) = beta c(t) + u[2] q eta i(t) - (mu + delta) r(t)
dt
eq6:=diff(Q(t),t)=b[1]*c(t)+b[2]*i(t)+w[1]*(u[1])^2/2+w[2]*(u[2])^2/2+w[3]*(u[3])^2/2;
d 1 2 1 2 1 2
--- Q(t) = b[1] c(t) + b[2] i(t) + - w[1] u[1] + - w[2] u[2] + - w[3] u[3]
dt 2 2 2
ics:=s(0)=8200, v(0)=2800,c(0)=1100,i(0)=1500,r(0)=200,Q(0)=6700;
s(0) = 8200, v(0) = 2800, c(0) = 1100, i(0) = 1500, r(0) = 200, Q(0) = 6700
sol0:=dsolve({eq1,eq2,eq3,eq4,eq5,eq6,ics},type=numeric,stiff=true,'parameters'=[u[1],u[2],u[3]],abserr=1e-15,relerr=1e-12,maxfun=0,range=0..50):
Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations
with(plots):
Q0:=6700;
6700
obj:=proc(u)
global sol0,Q0;
local ob1;
try
sol0('parameters'=[u[1],u[2],u[3]]):
ob1:=subs(sol0(20.),Q(t)):
catch :
ob1:=0;
end try;
#ob1:=subs(sol0(20.),Q(t));
if ob1>Q0 then Q0:=ob1;print(Q0,u);end;
ob1;
end proc;
proc(u) ... end;
obj([1,1,1]);
0
obj([3,2.5],4);
0
u0:=Vector(3,[0.,0.,0.],datatype=float[8]);
Vector[column](%id = 85973880)

Q0:=0;
Q0 := 0
with(Optimization);
[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, NLPSolve,

QPSolve]
sol2:=NLPSolve(3,obj,initialpoint=u0,method=nonlinearsimplex,maximize,evaluationlimit=100):
sol0('parameters'=[3.18125786060723, 2.36800986932868]);
sol0(parameters = [3.18125786060723, 2.36800986932868])
for i from 1 to 3 do odeplot(sol0,[t,x[i](t)],0..20,thickness=3,axes=boxed);od;
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

Hi

I want to write the functional Z of J with in terms of the fourier transform of J: .

Actually I'm in Minkowski space and all the integrals should be over 4 dimensions, x,y,k,p should all be four-vectors, but I wanted to keep things short. (The only way I have found to express a 4D integral is using Physics-Intc with the singleparameters of the four vector. Is there a more convenient way to get ?) But still in 1D I cannot solve it.

To find the solution, an exponential of only one integral, is actually pretty easy, since there are integrals over e. g. deliver a delta distribution, but I cannot reproduce this in Maple since he doesn't perform the integral over x.

I have found that I can/have to use the command inttrans-fourier to gain the delta distribution, but when I try to use it for the problem mentioned above I run into all kinds of problems. Not to mention that I cannot manage to perform a fourier transformation in 4D.

Does anybody know how to solve this problem? Thanks!