Hi,

I am working on a project and really need help from you guys how to rearrange/factorize an equation. So I got a form of expression as shown below, where

W__1 + W__2 = -sin(-beta + alpha)*((H^2 - h^2)*gamma + h^2*psi)/(2*sin(beta)*sin(alpha))

How can I rearrange it into a similar form of

W__1 + W__2 = -H^2*sin(-beta + alpha)*((1 - h^2/H^2)*gamma + h^2*psi/H^2)/(2*sin(beta)*sin(alpha))

where I just bring out value of H^2? I realize it's very simple to do by hand but I just need to learn how to handle Maple for my work.

Really hope anyone can help me. Thank you very much for your time and assistance.

Kind regards

Faiz Farhan

I have some difficulties with exporting a 3d plot from Maple in a pdf format without loosing the whole settings. As a simple example consider the following.

plot3d(sin(x)*10^y, x = -4 .. 4, y = -2 .. 2, view = [-4 .. 4, -2 .. 2, 0 .. 2], labelfont = ["TimesNewRoman", 26], labels = [x, Typesetting:-Typeset(log[10](y)), typeset()])

I tried two approaches, each has a drawback.

1- Right clicking on the figure, choosing `Export`, then `PDF`. Unfortunately, Maple changes the font size of labels!

2- Right clicking on the figure, choosing `Export`, then `Encapsulated Postcript`. Then I open the resulted `eps` file in GSview. Convert it to pdf. The result is a large-size pdf file which is heavy to render. Even when it gets rendered, scrolling up and down (for example in Adobe reader) is not good, because it seems the picture is going to get rendered again!

So how should one export a 3d plot from Maple in a pdf format, But not loosing the settings of the plot such as the font size of the labels and also not ending up with a heavy file?

Try to convert the old worksheet to the modern linear algebra package ( student )? 

Download uitw_03_m_recent.mw

Hi,

I have a random variable that follows Uniform(1,4). Now I have a function which is of the following type:

g := a*alpha+b*t/alpha+exp(alpha)

where,

A := RandomVariable(Uniform(c, d));
                 RandomVariable(Uniform(c, d))
f := proc (alpha) options operator, arrow; PDF(A, alpha) end proc;
alpha -> PDF(A, alpha)
#Defining expectation fuction
E := proc (alpha) options operator, arrow; int(alpha*f(alpha), alpha = c .. d) end proc;
alpha -> int(alpha f(alpha), alpha = c .. d)
#g is a function of random variable α, where a and b are parameter

now I want to find the expectation of g and the first derivative of expectation of g,

E(g)

diff(E(g), t)

I understand the way I have defined E(alpha) is improper. But please understand my intent and help! here is the maple file also doubt_1.mw

How I can remove RootOf from the solution?

thanks.

root.mw

Given two metric equations, How can I find the transformation equation between these two metrices using maplesoft software?

Why in geom3d[FindAngle] we cannot get the value of the angle of a triangle greater than Pi / 2?
For example, I build a chord of a circle of unit radius along the sides of the triangle and calculate the center angle that corresponds to the given angle of the triangle. But it's not very convenient.
TR_ANGLE.mw

Is there any way to simplify this code?  even with small number at discretization this take forever to solve  :(

restart;

with(plots);

numero := 5;

# Valores Calculados / Retirados da internet

viscosidade := Vector[row](10, [0.000024, 0.00001113, 0.89*10^(-5), 0.00001779, 0.017299, 0.00001028, 0.927*10^(-5), 0.818*10^(-5), 0.749*10^(-5), 0.7*10^(-5)]);

H := Vector[row](8, [-0.1414243148*10^8, -0.1677843875*10^8, -0.2177577229*10^8, -0.3078557121*10^8, -0.4007777822*10^8, -0.4007777822*10^8, -0.5832487417*10^8, 0.84247483*10^7]);

a := [524, 879, 1271, 1099, 1779, -163, 241, -258, 1200, 1200];

b := [1.3383, 4.1117, 0.8467, -0.47, 0.0333, 6.78, 5.6683, 7.5933, 3, 3];
c := [-0.0008, 0.00015, -0.00145, 0.00105, 0.0008, -0.00475, -0.002, -0.00455, 0, 0];
d := [0.166667*10^(-6), -0.666667*10^(-6), 0.833333*10^(-6), -0.5*10^(-6), -0.333333*10^(-6), 0.15*10^(-5), 0.166667*10^(-6), 0.116667*10^(-5), -0.888178*10^(-15), -0.888178*10^(-15)];

Massas := Vector[row](10, [44.01, 16.04, 2.02, 28.01, 18.01, 28.05, 30.07, 44.1, 58.12, 84]);

nu := Matrix(11, 8, [[-1, -2, -2, -3, -4, -4, -6.05, -1], [-3, -4, -5, -7, -9, -9, -12.23, 1], [1, 2, 2, 3, 4, 4, 6.05, -1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1]]);

A := Vector[row](8, [65.56165, 0.045, 0.001144, 0.119*10^(-5), 0.184*10^(-9), 0.659*10^(-8), 0.198*10^(-7), 0.0000378]);
E := Vector[row](8, [83523.900, 65017, 49782, 34885.500, 27728.900, 25730.100, 23564.300, 58826.300]);
m := Vector[row](8, [0.60950, 0.37330, -0.02830, 0.43540, 0.03530, -0.25150, 0.81870, -0.36200]);
n := Vector[row](8, [-0.46790, -0.26130, 0.19130, 0.08760, 1.11630, 0.00920, 0.03420, 1.26390]);

Conc[CO] := 40.65;
Conc[H2] := 78.91;
Conc[N2] := 119.5;

DensidadeCO := 6.712;
DensidadeN2 := 6.736;
DensidadeH2 := 0.0483;

Cpcte := [1.064, 14.51, 1.954, 2.889, 2.227, 2.596, 2.583, 2.619, 2.619, 2.619, 0.856, 1.056];
viscosidade := Vector[row](12, [0.0000252, 0.0000252, 0.0000252, 0.0000163, 0.0000154, 0.0000154, 0.0000154, 0.0000154, 0.0000154, 0.000023, 0.000023, 0.0000251]);
massas := Vector[row](12, [0.02801, 0.00202, 0.01801, 0.01604, 0.02805, 0.03007, 0.0441, 0.05812, 0.05812, 0.084, 0.04401, 0.02801]);

#Constantes
Rcte := 8.314;
varepsilon[B] := 0.4;
beta := 0.255;
phi := 4/3;
delta[wall] := 0.004;
lambda[wall] := 60;
h[water] := 1000;
Temp[water] := 498;
rho[B] := 380;
dt := 0.0157;
dp := 0.00015;

#Equações Auxiliares
for k to 11 do
    Y[k](t, z) := Rcte*C[k](t, z)*T(t, z)/1000000;
end do;

Cp[mix] := (t, z) -> 1000*Cpcte[12];
mu[mix] := (t, z) -> viscosidade[12];
M[mix] := (t, z) -> massas[12];

h[int] := (t, z) -> rho[mix](t, z)*0.458/varepsilon[B]/((Cp[mix](t, z)*mu[mix](t, z))^4.074*(dp/mu[mix](t, z))^4.407);
Reynolds := (t, z) -> dp*rho[mix](t, z)/mu[mix](t, z);
f := (t, z) -> 172/Reynolds(t, z) + 4.36/Reynolds(t, z)^0.12;
U := (t, z) -> 1/(1/h[water] + delta[wall]/lambda[wall] + 1/h[int](t, z));
P[CO] := (t, z) -> 1000000*Y[1](t, z);
P[H2] := (t, z) -> 1000000*Y[2](t, z);
for j to 8 do
    R[j](t, z) := A[j]*exp(-E[j]/(Rcte*T(t, z)))*P[CO](t, z)^m[j]*P[H2](t, z)^n[j];
end do;

#EDP's

for k to 11 do
    edp[k] := diff(C[k](t, z), t) = -v(t, z)*diff(C[k](t, z), z) + rho[B]*beta*add(nu[k][j]*R[j](t, z), j = 1 .. 8);
end do;
edp[12] := diff(T(t, z), t) = -v(t, z)*diff(T(t, z), z) + rho[B]*beta*add(add(-H[j]*nu[i][j]*R[j](t, z), i = 1 .. 10), j = 1 .. 8)/(rho[mix](t, z)*Cp[mix](t, z)) - 4*U(t, z)*(T(t, z) - Temp[water])/(dt*rho[mix](t, z)*Cp[mix](t, z));
edp[13] := diff(v(t, z), z) = -v(t, z)*diff(rho[mix](t, z), z)/rho[mix](t, z);
edp[14] := diff(rho[mix](t, z), z) = M[mix](t, z)/Rcte*(-1000000*diff(T(t, z), z)/T(t, z)^2);
edp[15] := diff(PT(t, z), z) = -f(t, z)*v(t, z)^2*rho[mix](t, z)/dp;

#Discretização do Modelo
hh := 0.11/numero;
for k to 11 do
    dis[k] := diff(C[k](t, z), z) = (x[k, i](t) - x[k, i - 1](t))/hh;
end do;
dis[12] := diff(T(t, z), z) = (x[12, i](t) - x[12, i - 1](t))/hh;
dis[13] := diff(rho[mix](t, z), z) = (x[13, i](t) - x[13, i - 1](t))/hh;
dis[14] := diff(v(t, z), z) = (x[14, i](t) - x[14, i - 1](t))/hh;
dis[15] := diff(PT(t, z), z) = (x[15, i](t) - x[15, i - 1](t))/hh;
for k from 16 to 26 do
    dis[k] := C[k - 15](t, z) = x[k - 15, i](t);
end do;
dis[27] := T(t, z) = x[12, i](t);
dis[28] := rho[mix](t, z) = x[13, i](t);
dis[29] := v(t, z) = x[14, i](t);
dis[30] := PT(t, z) = x[15, i](t);
listadis := seq(dis[k], k = 1 .. 30);
for k to 15 do
    equacao[k] := eval(edp[k], {listadis});
end do;

#Resolução 

ci[1, i] := x[1, i](0) = Conc[CO];
ci[2, i] := x[2, i](0) = Conc[H2];
for k from 3 to 11 do
    ci[k, i] := x[k, i](0) = 0;
end do;
ci[12, i] := x[12, i](0) = 503;
ci[13, i] := x[13, i](0) = 0.005165;
ci[14, i] := x[14, i](0) = 0.33*DensidadeH2 + 0.17*DensidadeCO + 0.5*DensidadeN2;
ci[15, i] := x[15, i](0) = 1000000;
cis := seq(seq(eval(ci[k, i], i = j), k = 1 .. 15), j = 1 .. numero);
unassign(i);
eqs := seq(seq(eval(equacao[k], i = j), k = 1 .. 15), j = 2 .. numero);
final[1] := x[1, 1](t) = Conc[CO];
final[2] := x[2, 1](t) = Conc[H2];
for k from 3 to 11 do
    final[k] := x[k, 1](t) = 0;
end do;
final[12] := x[12, 1](t) = 503;
final[13] := x[13, 1](t) = 0.005165;
final[14] := x[14, 1](t) = 0.33*DensidadeH2 + 0.17*DensidadeCO + 0.5*DensidadeN2;
final[15] := x[15, 1](t) = 1000000;
seqfinal := seq(final[k], k = 1 .. 15), eqs;
sol := dsolve({cis, seqfinal}, numeric, stiff = true, range = 0 .. 180);
odeplot(sol, [t, x[12, 4](t)], t = 0 .. 180);

Modelo_discretizado_com_t_e_tudo_constante.mw

Thank you already

Got a lot of worksheets who are not complete anymore once opened in maple 2020

It can be only opened with a old version of Maple
Can it be imported in Maple 2020?

example 

Dynmod03.mws

Is there a way to verify the following Fourier transform property: F[f(x) exp(i b x)](k) = F[f(x)](k − b)? This is what I tried:
 

Download First_Shifting_Theorem.mw

Is there a way to specify options or something to change the definition of fourier and invfourier to have a 1/sqrt(2Pi) factor instead? I don't want to manually multiply the result by 1/sqrt(2Pi) every time in case I forget to do it and it leads to a mistake in the future.

Dear all,

Please I want only 8 points to show on this curve, how do I specify it?

plot(ln(1+sin(Pi*x)), x = 0 .. 1, legend = numerical, style = point, symbol = box, color = blue, symbolsize = 15, numpoints = 8);

Thank you all and kind regards.

Please do keep safe amidst this global pandemic.

I would appreciate to know how to compute the following in Maple:

Sequence of distinct primes (starting term is 2) such that each subsequent term is the smallest prime not yet seen whose leading digits and the sum of the digits of the previous term are the same. It starts: 2,23,5,53,83,11,29..
 

it should be interesting to see which primes with first digit 3 appear (given that 3 is not a term). I would also like to be able to change the first term (eg to 3).

Best regards

David.

Found in old studymaterial about Loka-volterra ode 

dsolve({D(N)(t)=r*N(t)-k*N(t)^2,N(0)=N[0]},N(t));

Seems to me not logical notation to use a D operator  : D(N)(t)  for this ode : makes it unneeded complicated this notation..or do i miss something?

Please can you help me in resolving this error?

Here is the codeOptimal_control_model_of_DF_and_LP_2.mw