st6.mw,st7.mwI want to obtain the analytical solution for this PDE by maple       . But I can not do it. Please help me

((d^2)T/dx^2)+ ((d^2)T/dy^2)+ ((d^2)T/dz^2)=-A*Q(x,y,z)

Where   0 <x<a ,  0 <y<b  ,  0 <z<l

With the boundary conditions:

(dT(0,y,z)/dx)=n-T(0,y,z)    (dT(a,y,z)/dx)=n-T(a,y,z)   (dT(x,0,z)/dy)=n-T(x,0,z)

(dT(x,b,z)/dy)=n-T(x,b,z)     (dT(x,y,0)/dz)=n-T(x,y,0)    (dT(x,y,l)/dz)=n-T(x,y,l)

where n is constant and A is set of parameters.

we have number from 1 to 2014. If we underline the number that divide by 3 and 4, how many pattern of two underlines that next to each other as example?(1,2,3,4,5,6,7,8,9,10,...,2014).

Hello all,

I have the following equation:

N*exp(-(1/2)*eta*epsilon*(N*alpha*epsilon*w+2*N*w*C[max]-alpha*epsilon*z-2*Q1*alpha)/(w*N))*S1*upsilon*w-N*S1*upsilon*w+K1^2*alpha*eta*z*epsilon+K1*alpha*eta*z*epsilon*S1 = 0

in which I need to find solution for epsilon (analytical solution) when epsilon>0.  

Thanks,

Dmitry

I have a nonlinear system with 4 equations and 4 unknowns. I am using fsolve. I know that there are multiple solutions for each variable but am only getting one. I need the others. what do I do??

This is my code:

R__1 := Matrix([[1, 0] , [0, 1] ]);

R__2 := Matrix([[1/2, sqrt(3)/2] , [-sqrt(3)/2, 1/2] ]);

R__3 := Matrix([[-1/2, sqrt(3)/2] , [-sqrt(3)/2, -1/2] ]);

R__4 := Matrix([[-1, 0] , [0, -1] ]);

R__5 := Matrix([[-1/2, -sqrt(3)/2] , [sqrt(3)/2, -1/2] ]);

d__1 := Vector( [ 0, 5.4] );

d__2 := Vector( [ 6.4, 4.539] );

d__3 := Vector( [ 11, 4.078] );

d__4 := Vector( [ 15.5, 2.079] );

d__5 := Vector( [ 19, 1.039] );

a := Vector( [ a__x, a__y] );

A__1:=R__1.a+d__1;

A__2:=R__2.a+d__2;

A__3:=R__3.a+d__3;

A__4:=R__4.a+d__4;

A__5:=R__5.a+d__5;

OO:=Vector([O__x,O__y]);

DA1:=A__2.A__2-A__1.A__1-2*(A__2-A__1).OO;

DA2:=A__3.A__3-A__1.A__1-2*(A__3-A__1).OO;

DA3:=A__4.A__4-A__1.A__1-2*(A__4-A__1).OO;

DA4:=A__5.A__5-A__1.A__1-2*(A__5-A__1).OO;

fsolve({DA1,DA2,DA3,DA4},{a__x,a__y,O__x,O__y});

Thanks for any tips you may be able to offer

How do I plot the following equations in Maple ?:

I already tried this: 

According to the given solution the plot should look like that: 

I think I have to tell maple that the function is defined from R^2 -> R, but I don't know how to do this. 

Thanks in advance for your kind help.

Hello people in mapleprimes,

I want to draw a graph of a procedure.

filter:=x->if x<10 then 1-x/10 else 0 fi;

plot('filter(x)',x=0..20);

works well. But, I don't know why it is needed for filter(x) is wrapped with foward quotte ' .

I changed that quote to back quote ` but, in this case the result hadn't appeared.

And, without the foward quote ', error appears.

And, even if I wrapped x with ' as in plot('filter(x)','x' =0..20),

a graph appeared properly, though I cannot understand why wrapped x, 'x' is right.

Please teach me the logic of the above code.

Best wishes.

taro yamada

AoA. How are you hope you will be fine. Sir the following matrix have been given

A := Matrix(2, 2, {(1, 1) = 1, (1, 2) = 2, (2, 1) = -1, (2, 2) = 2});

B := Matrix(2, 2, {(1, 1) = 1, (1, 2) = 0, (2, 1) = -2, (2, 2) = 3});

C := Matrix(2, 2, {(1, 1) = 0, (1, 2) = 0, (2, 1) = 0, (2, 2) = 0});

I want to write M by M matrix using the above matrices like this

P:=[[[A,B,B,...,B],[C,A,B,...,B],[C,C,A,...,B],[.,.,.,...,B],[C,C,C,...,A]]]

PhD (Scholar)
Department of Mathematics

AoA... I want to plot the following functions

f(x)=sin(x)

g(x)=sin(x)-x+x^2

h(x)=cos(x)-sin(x)

I(x)=exp(x)-x

J(x)=sin(x)+exp(x)

in one coordinate having the line style and legend like attached file.

1-s2.0-S0377042714003331-main.pdf

PhD (Scholar)
Department of Mathematics

I want to get the result of multi-matrix multiply like followed below,

but error "final value in for loop must be numeric or character"

(*n is arbitrary and B[1],B[2],...,B[n] have been obtained*)

A:=LinearAlgebra:-IdentityMatrix(n);
#using the multiplication operation of matrix
for i from 1 to n do
   A:=LinearAlgebra:-Multiply(A,B[i]);
od:

return A

help me 

thanks

Hello

I have a loop with the do structure but there is an error in the loop .

how can I continue the loop by error or disregard it?

What is Groebner? That was asked in different forms several times in MaplePrimes and MathStackExchange (for example, see http://math.stackexchange.com/questions/3550/using-gr?bner-bases-for-solving-polynomial-equations ). In view of this I think the presented post on Groebner basis will be useful. This post consists of two parts: its mathematical background and examples of solutions of polynomial systems by hand and with Maple.

Let us start. Up to Wiki http://en.wikipedia.org/wiki/Gr%C3%B6bner_basis ,Groebner basis computation can be seen as a multivariate, non-linear generalization of both Euclid's algorithm for computing polynomial greatest common divisors, and Gaussian elimination for linear systems. This is implemented in Maple trough the Groebner package.
The simplest introduction to the topic I know is a well-written book of Ivan Arzhantsev (https://zbmath.org/?q=an:05864974) which includes the proofs of all the claimed theorems and the solutions of all the exercises. Here is its digest groebner.pdf done by me (The reader is assumed to be familiar with the ideal notion and ring notion (one may refresh her/his knowledge, looking in http://en.wikipedia.org/wiki/Ideal_%28ring_theory%29)). It should be noted that there is no easy reading about this serious matter.
Referring to the digest as appropriate, we solve the system
S:={a*b = c^2+c, a^2 =a+ b*c, a*c = b^2+b} by hand and with the Groebner package.
For the order a > b > c we construct its ideal
J(S):=<f1 = a*b-c^2-c,f2 = a^2-a-b*c, f3 = a*c-b^2-b>.
The link between f1 and f2 gives
f1*a-f2*b = (-c^2-c)*a + (a + b*c)*b = a*b -a*c + b^2*c -
a*c^2 =f4.
The reduction with f1 produces
f4 ->-a*c^2- a*c + b^2*c + c^2 +c =: f4.
Now the reduction with f3 produces
f4 -> -b^2- b - b*c +c^2 + c =:f4.
The link between f2 and f3 gives:
f2*c - f3*a = a*b +a*b^2 -a*c -b*c^2 = f5.
The reduction with f1 produces
f5 -> -a*c + c*b +c^2 +c =:f5.
The reduction with f3 produces
f5 -> -b^2 -b + c*b +c^2 +c =:f5.
The reduction with f4 produces
f5 -> 2b*c =: f5.
The link between f1 and f3
f1*c - f3*b = b^3 + b^2 -c^3 -c^2=:f6.
The reduction with f4 produces
f6 -> 2b*c + 2b*c^2 -2c^3 -2c^2=:f6.
At last, we reduce f6 by f5, obtaining f6:= -2c^3 -2c^2.
We see the minimal reduced Groebner basis of S consists of
a^2 -a -b*c, -b^2 -b- b*c +c^2 +c, -2c^3 - 2c^2.
Now we find the solution set of the system under consideration. The equation -2c^3 - 2c^2 = 0 implies
c=0, c=0, c=-1. The the equation -b^2 - b - b*c +c^2 + c = 0 gives
b = 0 , b = -1, b = 0, b = -1, b = 0, b = 0 respectively.
At last, knowing b and c, we find a from a^2 -a -b*c = 0.
Hence,
[{a = 0, b = 0, c = 0}, {a = 1, b = 0, c = 0}, {a = 0, b = -1, c = 0}], [{a = 0, b = 0, c = 0}, {a = 1, b = 0, c = 0}, {a = 0, b = -1, c = 0}], [{a = 0, b = 0, c = -1}].
The solution of the system under consideration by the Groebner package is somewhat different because Maple does not find the minimal reduced Groebner basis directly.

Download groebner.mw

Hello, Im trying to do a jocobian

http://www.maplesoft.com/support/help/Maple/view.aspx?path=VectorCalculus/Jacobian

but when I try the example code

jacobian([rcos(t), rsin(t), r^2*t], [r, t])

i only get the output as 

jacobian([rcos(t), rsin(t), RandomMatrix(4, 4*density = .75, outputoptions = [shape = tringular*lowe])^2*t], [RandomMatrix(4, 4*density = .75, outputoptions = [shape = tringular*lowe]), t])

I want the output as a matrix as in the example url.

Thanks

I have the following system of non-linear equations and want to find their solutions experimenting with my parameters. I also want to restrict the solutions to be non-negative. I have done the following, but i am sure it exist a more efficient way. Can somone help on this? 

eqns := [A = (gr_c+delta)*kh^(1-alpha)/sav_rate, theta = Rk*(Rh-Rk)/(gamma*((Rh-Rk)^2+sigma^2)), theta = 1*1+kh, Rk = 1+rk-delta, Rh = 1+rh-delta, rk = A*alpha*kh^(alpha-1), rh = A*(1-alpha)*kh^alpha, sigma = sigmay/theta, varrho = Rap^((eps-1)*eps/(1-gamma)), Rap = Rk^(1-gamma)+(1-gamma)*Rk^(-gamma)*theta*(Rh-Rk)-.5*Rk^(-gamma-1)*gamma*(1-gamma)*theta^2*((Rh-Rk)^2+sigma^2), R = Rk+theta*(Rh-Rk), beta = ((1+gr_c)/R)^(1/eps)/varrho];
print(`output redirected...`); # input placeholder
[
[
[
[
[ (1 - alpha)
[ (gr_c + delta) kh
[A = ----------------------------,
[ sav_rate
[

Rk (Rh - Rk)
theta = ---------------------------, theta = 1 + kh,
/ 2 2\
gamma \(Rh - Rk) + sigma /

Rk = 1 + rk - delta, Rh = 1 + rh - delta,

(alpha - 1) alpha
rk = A alpha kh , rh = A (1 - alpha) kh ,

/(eps - 1) eps\
|-------------|
sigmay \ 1 - gamma /
sigma = ------, varrho = Rap , Rap =
theta

(1 - gamma) (-gamma)
Rk + (1 - gamma) Rk theta (Rh - Rk) - 0.5

(-gamma - 1) 2 / 2 2\
Rk gamma (1 - gamma) theta \(Rh - Rk) + sigma /,

/ 1 \]
|---|]
\eps/]
/1 + gr_c\ ]
|--------| ]
\ R / ]
R = Rk + theta (Rh - Rk), beta = ---------------]
varrho ]
]
vals := [alpha = .36, delta = 0.6e-1, sigmay = sqrt(0.313e-1), gamma = 3, eps = .5, gr_c = 0.2e-1, sav_rate = .23];
eval(eqns, vals);
print(`output redirected...`); # input placeholder
[
[
[
[ 0.64 Rk (Rh - Rk)
[A = 0.3478260870 kh , theta = -----------------------,
[ / 2 2\
[ 3 \(Rh - Rk) + sigma /

0.36 A
theta = 1 + kh, Rk = 0.94 + rk, Rh = 0.94 + rh, rk = ------,
0.64
kh

0.36 0.1769180601
rh = 0.64 A kh , sigma = ------------,
theta

0.1250000000
varrho = Rap ,

1 2 theta (Rh - Rk)
Rap = --- - -----------------
2 3
Rk Rk

2 / 2 2\
3.0 theta \(Rh - Rk) + sigma /
+ --------------------------------, R = Rk + theta (Rh - Rk),
4
Rk

2.000000000]
/1\ ]
1.0404 |-| ]
\R/ ]
beta = ---------------------]
varrho ]
]
eqns := [A = .3478260870*kh^.64, theta = (1/3)*Rk*(Rh-Rk)/((Rh-Rk)^2+sigma^2), theta = 1+kh, Rk = .94+rk, Rh = .94+rh, rk = .36*A/kh^.64, rh = .64*A*kh^.36, sigma = .1769180601/theta, varrho = Rap^.1250000000, Rap = 1/Rk^2-2*theta*(Rh-Rk)/Rk^3+3.0*theta^2*((Rh-Rk)^2+sigma^2)/Rk^4, R = Rk+theta*(Rh-Rk), beta = 1.0404*(1/R)^2.000000000/varrho];
print(`output redirected...`); # input placeholder
[
[
[
[ 0.64 Rk (Rh - Rk)
[A = 0.3478260870 kh , theta = -----------------------,
[ / 2 2\
[ 3 \(Rh - Rk) + sigma /

0.36 A
theta = 1 + kh, Rk = 0.94 + rk, Rh = 0.94 + rh, rk = ------,
0.64
kh

0.36 0.1769180601
rh = 0.64 A kh , sigma = ------------,
theta

0.1250000000
varrho = Rap ,

1 2 theta (Rh - Rk)
Rap = --- - -----------------
2 3
Rk Rk

2 / 2 2\
3.0 theta \(Rh - Rk) + sigma /
+ --------------------------------, R = Rk + theta (Rh - Rk),
4
Rk

2.000000000]
/1\ ]
1.0404 |-| ]
\R/ ]
beta = ---------------------]
varrho ]
]

solve(eqns, [Rk, Rh, varrho, Rap, beta, R, A, sigma, theta, rk, rh, kh]);

hello . i have a Partial differential equation i need some help with 

This is how it goes 

AoA. How are you? Sir want to generate the attached square matrix for any value of M. Please help.

PhD (Scholar)
Department of Mathematics