# Items tagged with studentstudent Tagged Items Feed

### CURVATURE OF GENERALIZED SASAKIAN SPACE FORMS...

July 02 2015
1 1

Given an almost contact metric manifold M(\phi,\xi,\eta, g), we say
that M is a generalized Sasakian-space-form if there exist three functions f1, f2, f3
on M such that the curvature tensor R is given by

R(X,Y)Z=f_1{g(Y,Z)X-g(X,Z)Y}+f_2{g(X,\phiZ)\phiY-g(Y,\phiZ)\phiX+2g(X,\phiY)\phiZ}+f_3{\eta(X)\eta(Z)Y-\eta(Y)\eta(Z)X+gg(X,Z)\eta(Y)\xi-g(Y,Z)\eta(X)\xi}

In (2n+1) dimensional generalized Sasakian space form M2n+1(f_1,f_2,f_3), we have the following relations.

S(X,Y)=(2nf_1+3f_2-f_3)g(X,Y)-(3f_2+(2n-1)f_3)\eta(X)\eta(Y)

S(X,\xi)=2n(f_1-f_3)\eta(X)

C\bar(\xi,X)Y=[f_1-f_3-(r/2n(2n-1))][g(X,Y)\xi-\eta(Y)X]

P(X,Y)Z=R(X,Y)Z-(1/(n-1))[S(Y,Z)X-S(X,Z)Y]

R(X,Y)\xi=(f_1-f_3){\eta(Y)X-\eta(X)Y}

R(\xi,X)Y=(f_1-f_3){g(X,Y)\xi-\eta(Y)X}

for any vector fields X, Y on M, where R, S, C\bar, and r denote the Riemannian curvature tensor, Ricci tensor, concircular curvature tensor and scalar curvature of M2n+1(f1, f2, f3), respectively

Using above equations I have to evaluate P(C\bar(\xi,X)Y,Z)U.

Manually It is tedious job. Can we find the value by maple? Is there any option to solve these type of problems?

If yes, I can solve many more, which helps a lot in my work.. Thanks in advance.

### Rational functions and CylindricalAlgebraicDecompo...

June 25 2015
0 2

Maybe a bit strange question (just exploring Maple and a new topic), but is there a way to use CylindricalAlgebraicDecompose with a rational functions, eg 1/x, where eg is x an integer? I tried to use it but always ended up with:

Error, invalid input: RegularChains:-SemiAlgebraicSetTools:-CylindricalAlgebraicDecompose expects its 1st argument, F, to be of type Or(list(list(Or(polynom(rational), polynom(rational) = polynom(rational), polynom(rational) <> polynom(rational), polynom(rational) <= polynom(rational), polynom(rational) < polynom(rational)))), list(polynom(rational))), but received [1/x = x, polynom(rational)]

### How to read some outputs from RegularChain package...

June 25 2015
1 4

Hi! I just started to use Maple and I play with some of its functions. I have seen in examples related to RegularChain package an output like  [regular_chain, [[-1, -1], [0, 0]]] and I wonder how I should read it. Thanks for any help and sorry if my question is very basic.

### How to input calculated coefficients to correspond...

June 12 2015
1 1

I have calculated coefficients in maple using a "for...end do" command. For example,

for n from 0 to 1 do A[n] = int(((2*n+1)*(1/2))*simplify(LegendreP(n, cos(theta)))*sin(theta), theta = 0 .. (1/2)*Pi) end do;

A[0] = 1/2

A[1] = 3/4

Here, I can calculate as many coefficients as I want. But, how do I use these coefficients in the following line? For example, I need to calculate a summation. But for each term in the summation, I want to input the coefficients above to the corresponding term in the sum. So. the following summation

A[0]+A[1]*r*cos(theta)+...

will automaticlly attach the numerical values of the coefficients calculated above to the corresponding term in the sum.

I hope this makes sense.

### A happy Maple recipient...

June 12 2015 Maple
1
0

Last month, we received a very kind note from a recipient of one of our sponsorships. Maplesoft sponsors several academic and commercial events throughout the year, providing free copies of Maple or MapleSim to lucky attendees. Audrey was one of the winners of the Elgin Community College Calculus Contest, where she won a copy of Maple. Here’s what she had to say:

Thank you so much for the Maple license.  I have become familiar with Maple during the last school year.  At first the commands were like Chinese to me and I had a rough time getting anything done, but once I made a connection between the commands and what they were doing it was a lot easier.  Even without former knowledge of computer programing, the commands are increasingly intuitive.  Maple has been a huge help to me doing my homework and projects, and even as I was studying for the competition it was useful for checking my answers.  Another reason that I love Maple is that it provides visuals for the difficult concepts we learned in class, such as shell method in Calc II and mixed partial derivatives in Calc III.  I enjoy math, but I thank that Maple has enriched my experience along the way.

~Audrey~

It’s always nice to hear how students and professionals alike are succeeding with the help of Maple. If you’d like to share your experience, please send an email to customerservice@maplesoft.com or post it here on MaplePrimes.

### How to determine unknown value in boundary conditi...

June 11 2015
0 6

Hello everyone,

How can unknown values in boundary conditions of system ODEs be determine by using shooting technique. See the work sheet here Sht.mw

Thanks.

### Is there some kind of commands?...

June 05 2015
0 2

This command (Student[Calculus1][ShowSolution](Int(e^(-(s-1)*t)))) shows me solutions.

and, the command in the picture can make integral solution but not laplace

so i ask you that what command make solutions for Laplace transform

### Error, (in plot) two lists or Vectors of numerical...

June 03 2015
1 2

Hey there,

I've a numerical solved system of differential equations, which depend on one argument and one index. I can solve it, but when I try plot it I have this error: Error, (in plot) two lists or Vectors of numerical values expected.

Could anyone help me figure out what I'm doing wrong?

> restart;
> A := 115.1558549; B := .3050464658; n := 3; f0 := 0.5e-4;

>f:=theta->f0*(cos(arcsin(sin(theta)/n)))^2;
I0:=Ir(z)+sum(Is[k](z),k=1..20);

> alpha := [0, 1, 2, 3, 4, 5, 6];

Theta := [3*Pi*(1/180), 6*Pi*(1/180), 9*Pi*(1/180), 12*Pi*(1/180), 15*Pi*(1/180), 18*Pi*(1/180), 21*Pi*(1/180), 24*Pi*(1/180), 27*Pi*(1/180), 30*Pi*(1/180), 33*Pi*(1/180), 36*Pi*(1/180), 39*Pi*(1/180), 42*Pi*(1/180), 45*Pi*(1/180), 48*Pi*(1/180), 51*Pi*(1/180), 54*Pi*(1/180), 57*Pi*(1/180), 60*Pi*(1/180)];

>G:= theta->A*sin(theta)*cos(2*arcsin((sin(theta)/n)))/((1+sin(theta)^2/B^2)*cos(arcsin(sin(theta)/n)));

>for j from 1 to 7 do
d1 := diff(Ir(z), z) = -sum(G(Theta[k])*Ir(z)*Is[k](z)/I0,k=1..20)-alpha[j]*Ir(z)-sum(f(Theta[k])*Ir(z),k=1..20):
d2 := diff(Is[1](z), z) = G(Theta[1])*Ir(z)*Is[1](z)/I0-alpha[j]*Is[1](z)+f(Theta[1])*Ir(z):
d3 := diff(Is[2](z), z) = G(Theta[2])*Ir(z)*Is[2](z)/I0-alpha[j]*Is[2](z)+f(Theta[2])*Ir(z):
d4 := diff(Is[3](z), z) = G(Theta[3])*Ir(z)*Is[3](z)/I0-alpha[j]*Is[3](z)+f(Theta[3])*Ir(z):
d5 := diff(Is[4](z), z) = G(Theta[4])*Ir(z)*Is[4](z)/I0-alpha[j]*Is[4](z)+f(Theta[4])*Ir(z):
d6 := diff(Is[5](z), z) = G(Theta[5])*Ir(z)*Is[5](z)/I0-alpha[j]*Is[5](z)+f(Theta[5])*Ir(z):
d7 := diff(Is[6](z), z) = G(Theta[6])*Ir(z)*Is[6](z)/I0-alpha[j]*Is[6](z)+f(Theta[6])*Ir(z):
d8 := diff(Is[7](z), z) = G(Theta[7])*Ir(z)*Is[7](z)/I0-alpha[j]*Is[7](z)+f(Theta[7])*Ir(z):
d9 := diff(Is[8](z), z) = G(Theta[8])*Ir(z)*Is[8](z)/I0-alpha[j]*Is[8](z)+f(Theta[8])*Ir(z):
d10 := diff(Is[9](z), z) = G(Theta[9])*Ir(z)*Is[9](z)/I0-alpha[j]*Is[9](z)+f(Theta[9])*Ir(z):
d11 := diff(Is[10](z), z) = G(Theta[10])*Ir(z)*Is[10](z)/I0-alpha[j]*Is[10](z)+f(Theta[10])*Ir(z):
d12 := diff(Is[11](z), z) = G(Theta[11])*Ir(z)*Is[11](z)/I0-alpha[j]*Is[11](z)+f(Theta[11])*Ir(z):
d13 := diff(Is[12](z), z) = G(Theta[12])*Ir(z)*Is[12](z)/I0-alpha[j]*Is[12](z)+f(Theta[12])*Ir(z):
d14 := diff(Is[13](z), z) = G(Theta[13])*Ir(z)*Is[13](z)/I0-alpha[j]*Is[13](z)+f(Theta[13])*Ir(z):
d15 := diff(Is[14](z), z) = G(Theta[14])*Ir(z)*Is[14](z)/I0-alpha[j]*Is[14](z)+f(Theta[14])*Ir(z):
d16 := diff(Is[15](z), z) = G(Theta[15])*Ir(z)*Is[15](z)/I0-alpha[j]*Is[15](z)+f(Theta[15])*Ir(z):
d17 := diff(Is[16](z), z) = G(Theta[16])*Ir(z)*Is[16](z)/I0-alpha[j]*Is[16](z)+f(Theta[16])*Ir(z):
d18 := diff(Is[17](z), z) = G(Theta[17])*Ir(z)*Is[17](z)/I0-alpha[j]*Is[17](z)+f(Theta[17])*Ir(z):
d19 := diff(Is[18](z), z) = G(Theta[18])*Ir(z)*Is[18](z)/I0-alpha[j]*Is[18](z)+f(Theta[18])*Ir(z):
d20 := diff(Is[19](z), z) = G(Theta[19])*Ir(z)*Is[19](z)/I0-alpha[j]*Is[19](z)+f(Theta[19])*Ir(z):
d21 := diff(Is[20](z), z) = G(Theta[20])*Ir(z)*Is[20](z)/I0-alpha[j]*Is[20](z)+f(Theta[20])*Ir(z):
dsys := {d1, d10, d11, d12, d13, d14, d15, d16, d17, d18, d19, d2, d20, d21, d3, d4, d5, d6, d7, d8, d9}:
dSol[j] := dsolve({op(dsys), Ir(0) = 1, Is[1](0) = 0.1e-1, Is[2](0) = 0.1e-1, Is[3](0) = 0.1e-1, Is[4](0) = 0.1e-1, Is[5](0) = 0.1e-1, Is[6](0) = 0.1e-1, Is[7](0) = 0.1e-1, Is[8](0) = 0.1e-1, Is[9](0) = 0.1e-1, Is[10](0) = 0.1e-1, Is[11](0) = 0.1e-1, Is[12](0) = 0.1e-1, Is[13](0) = 0.1e-1, Is[14](0) = 0.1e-1, Is[15](0) = 0.1e-1, Is[16](0) = 0.1e-1, Is[17](0) = 0.1e-1, Is[18](0) = 0.1e-1, Is[19](0) = 0.1e-1, Is[20](0) = 0.1e-1}, [Ir(z), Is[1](z), Is[2](z), Is[3](z), Is[4](z), Is[5](z), Is[6](z), Is[7](z), Is[8](z), Is[9](z), Is[10](z), Is[11](z), Is[12](z), Is[13](z), Is[14](z), Is[15](z), Is[16](z), Is[17](z), Is[18](z), Is[19](z), Is[20](z)], numeric);
end do:

>for j from 1 to 7 do
dSol[j](0.4);
as:='as':
for l from 1 to 20 do
as[l]:=[Theta[l],rhs(dSol[j](0.4)[2+l])];
od:
plo[j]:=convert(as,listlist);
od:

>plot(plo[2],plo[1]);
Error, (in plot) two lists or Vectors of numerical values expected

### What does unable store mean?...

June 01 2015
1 9

Hello everyone,

I'm trying to solve system of ODE but it return this Error, (in fproc) unable to store 'YP[4]' when datatype=float[8]
How can this be corrected, see the worksheet YP.mw

Thanks.

### Changing significant digits gives different answer...

June 01 2015
0 5

Hi,

Why does maple do this? For example:

>Digits := 4

>.67*((6918*(.856*11+1.08))/(42.2*2600^.36))^5;

=7.216 10^9

But with the Digit set to default it gives me:

>.67*((6918*(.856*11+1.08))/(42.2*2600^.36))^5;

=7.204144575 10^9

thanks!

### Error, (in dsolve/numeric/process_input) system mu...

May 31 2015
1 3

I can't solve this problem, can someone explain me whats worng and how to fix it, here is what i've done:

with(plots);
with(DEtools);
sist := diff(x1(t), t) = -4*x1(t)+x2(t), diff(x2(t), t) = -x1(t)+7*x2(t);
d                             d
--- x1(t) = -4 x1(t) + x2(t), --- x2(t) = -x1(t) + 7 x2(t)
dt                            dt

condi := [x1(0) = 0, x2(0) = 3], [x1(0) = 2, x2(0) = 1], [x1(0) = 7, x2(0) = 9];
[x1(0) = 0, x2(0) = 3], [x1(0) = 2, x2(0) = 1],

[x1(0) = 7, x2(0) = 9]
for i to 3 do sol[i] := dsolve({sist, condi[i]}, {x1(t), x2(t)}, numeric); gra := odeplot(sol[i], [x1(t), t], t = -1 .. 1); display(gra) end do;

### expand differential operators...

May 29 2015
0 6

I just wanted to ask whether one can get out of the expansion

(D-f(x))@@2(g)(x)=(D@@2)(g)(x)-(D((f(x))(g)))(x)-((f(x))(D(g)-(f(x))(g)))(x)

the intended result

(D@@2)(g)(x)-D(f*g)(x)-f(x)*D(g)(x)+f(x)^2*g(x)

### How do I solve s systems of pdes in maple...

May 27 2015
0 13

The model of fixed-bed adsorption column

Fluid phase:

PDE:= diff(U(x, tau),tau)+ psi*Theta*diff(U(x, tau),x)-(1/Pe)*psi*Theta*diff(U(x, tau),$(x, 2))=-3*psi*xi*(U(x, tau)-Q/K); IBC:={U(x, 0) = 0,U(0, tau) = 1+(1/Pe)*(D[1](U))(0, tau),(D[1](U))(1, tau)=0}; Particle: PDE:= diff(Q(r, tau), tau) = diff(Q(r, tau),$(r, 2))+(2/r)*diff(Q(r, tau),r);

IBC:={Q(r, 0) = 0,(D[1](Q))(0, tau) = 0,(1/K)*(D[1](Q))(1, tau)=xi*(U-Q(1, tau)/K)};

Pe:=0.01:

psi:=6780:

Theta:=3.0:

xi:=10000:

I will really appreciate your help. Thanks in anticipation.

### QPochhammer wrong type of arguments...

May 26 2015
0 4

I'm just using it this way:

with(QDifferenceEquations):
QPochhammer(-1,5,10)

Error, (in QDifferenceEquations:-QPochhammer) wrong type of arguments

Am I doing something terribly wrong???

### whats the problem...

May 22 2015
0 2

i dont know whats wrong with it help me guys

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