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 

Hi everyone.

I always used simple command to plot graphs with parametric function:

> plot([seq([i, t, t=0..11-i], i=1..10)], thickness=3, color=blue); 

And I always obtained this:

But yesterday I installed second update for Maple 18, and now I get only error:

"Error, (in plot) invalid input: ToInert expects 1 or 2 arguments, but received 0"

What command I should use now?

I'd like to implement this in Maple, but being a newbie having hard time getting the syntax right:

This is what I tried:

a:='a';
f:= i->product( `if`(evalb(i<>j),(a-z(j))/(z(i)-z(j)),NULL),j=1..3);

but it is not skipping the i=j case, since when I call it with f(1) I get division by zero.

f(1);
Error, (in product) numeric exception: division by zero

Tried also

f:= i->product(`if`(evalb(not(i=j)),(a-z(j))/(z(i)-z(j)),NULL),j=1..3);
and few other things. I think the reason it fails is deeper than my level of Maple undertstanding.

How would you do this in Maple?

hello, I have a list of numbers, for example [1.2,5.6,7.2,0.5,-0.25,-4,6]. I would like to find the position of it in the list where the number is closest to zero. May I know if there is a function for this please? Thanks.

Hi,

I am interested to know if Abel equation of the form:

y'=a*y^3+(b*x+c)*y^2+d*y+(g*x+f)    where: a,b,c,d,g,f are constants. 

is belonging to any solvable classes? I noticed that most of the classes solved in the literature using invariant analysis has a rational coefficients in x and they do not have the full form as the one abov. Any suggestions for this ?

Regards

Hamada

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

PhD (Scholar)
Department of Mathematics

AoA. How are you? I want to solve the following equation in one step and convenient way please help

psi(x):=Matrix(1,3,[x,x-1,x^(2)-x-1])

P := Matrix(3, 3, [1, 2, 1, 0, 1, 1, -1, 2, 3])

U := Matrix(3, 3, [a[1, 1], a[1, 2], a[1, 3], a[2, 1], a[2, 2], a[2, 3], a[3, 1], a[3, 2], a[3, 3]])

u := psi(x)^T*(P^2)^T*U*P^2*psi(t)-t*psi(x)^T*(P^2)^T*U*P^2*psi(1)-x*psi(1)^T*(P^2)^T*U*P^2*psi(t)+t*x*psi(1)^T*(P^2)^T*U*P^2*psi(1)

If you reduce my computational work or have any suggestion to solve please give.

PhD (Scholar)
Department of Mathematics

AoA. How are you? Hope you will be fine. I want write the following in Loop for any M

F[r,s]:=2^(k+2) m sqrt((c[r-1])/(c[s-1])) for r=2...(M+1), s=1..r-1 and (r+s)=odd;

F[r,s]:=0  otherwise

Novice question

I have two sets of inequalties:

s1:= (0<x, x<100)

s2:= (5<x, x<95)

I want each set to define a "range", so I can do set operations on the ranges. For example I want to determine that S2 is a subset of S1, S1 - S2 would give me (0<x, x<=5, 95<=x, x<100), S1 Union S2 = (0<x, x<100), etc

I assume these are simple things that can be done with Maple - but I am not sure how! Any suggestions?

I under stand how to do the calculus that's easy enough, but Maple is stil giving me a hard time.  The math par t is let the radius of the cylinder be r cms. 0<r<10 Then the height is 2 * Sqrt 100-r^2, the volume is V(r)=2PIr^2* sqrt 100-r^2 cm^3

Differentiante V(r) with respect to r we get V' (r) =2PIr^2(1/(2*sqrt(100-r^2)))(-2r) + (2PIsqrt(100-r^2))(2r)

V'(r)=(-2PIr^3 +4PIr(100-r^2))/sqrt (100-r^2)      V'(r)=2PIr(200-3r^2)/sqrt 100r^2         to find the critical point find the value of r when V(r) =0     2PI(200-3r^2)/sqrt 100-r^2 =0   2PIr(200-3r^2) = 0   r(200-3r^2)=0 

r=0 or 200-3r^2 =0     r=0 or r^2=200/3 r=sqrt(200/3) =10sqrt(2/3)   r is not in the interval so ignore it.  The critical point for 0<r<10 occurs at r = 10sqrt(2/3)       Since V'(r) >0 for 0<r<10sqroot(2/3) and V'(r) <0<10sqrt(2/3)<10

The dimensions are r=10sqrt(2/3) =8.16 cm and h=20/sqrt3 = 11.55 cm the volume is 4000PI/3*sqrt3=2418.4 cm^3

So how do I translate this into maple? Any help is greatly appreciated.

I am really baffled by this. I was starting to think Maple control system is good, only to find I get an error when I try to obtain the controllability Gammian for a state space system which is time varying.  Maple only seem to support a non-time varying A,B,C,D for this function.  Can someone please confirm this, or may be I am doing something wrong?

I was trying to verify my hand solution for a HW using Maple.

----------------------
restart:
alias(DS=DynamicSystems):
A:=Matrix( [[2,-exp(t)],[exp(-t),1]]);
B:=Matrix([[0],[1]]);
sys:=DS:-StateSpace(A,B);  #created OK
m:=DS:-Grammians(sys);

Error, (in DynamicSystems:-Grammians) symbolic value(s) in model: t, exp(t), exp(-t)
---------------------------------------------------

If the system is time invariant, then it works. Example from help:

-------------------------------------------------
restart:
alias(DS=DynamicSystems):
aSys := DS:-StateSpace( <<-5,3>|<3,-4>>, <<2,3>>, <<1,0>|<0,1>>, <<0,0>> ):
m:=DS:-Grammians(aSys);
---------------------------------

The main advantage of using computer algebra system for control system is to be able to do things using symbolic which is much more powerful than just numerical computation as with Matlab. There is nothing in the above linked to help page that says Maple does not support time varying state space for this function (unless I missed it).

Is it possible to add support for LTV in Maple 19?

ps. note that the ControllabilityMatrix works on LTV:

m:=DS:-ControllabilityMatrix(sys); #OK

But I wanted the Grammian.

Hello,

I have a question: Why gives Maple no result for:

expr2 := sin(k*(t-tau))*sin(k*tau);
Int(simplify(expr2, symbolic), tau = 0 .. t);

It is possible with Wolfram Alpha: http://www.wolframalpha.com/input/?i=Int%28sin%28sqrt%28k%2Fm%29*%28t-tau%29%29*sin%28sqrt%28k%2Fm%29*tau%29%2C+tau+%3D+0+..+t%29

Thanks!

Download mmgf_part1.mw

Any help???

Suppose I have installed maple on a directory in Windows 7 64 Bit. Now I use the command mode in windows, by typing maplew "D:\xx.mw" > xx.txt, it doesn't work. 

Excuse me, how to run maplew on command mode?