I have theoretically 3(could eventually be more) layers with an incident wave with a wave equation for that wave.

It refracts into the 2nd layer from the first and now has a 2nd wave equation, then from the 2nd into the 3rd layer with a 3rd wave equation.

All the wave equations are of the form, Psi(z) = A_1psi_1(z) + B_1psi_2(z); this is just a general solution where psi_1&2 are linearly independant solutions that make up the general equation above and A_1 and B_1 are constant coefficients that would be A_2,B_2 and A_3,B_3 for the 2nd and 3rd layers respectively.

Transfer matrix method gives A_1,B_1 in terms of A_2,B_2(as it transfers from layer 1 to 2 they equate under boundary conditions so you can solve the simultaneous equations for results). You create a matrix of these results and multiply it with the respective matrix of the 2nd layer to 3rd layer to give you the overall transfer matrix from one side of the system to the other.

I think something to do with transfer function but not sure how to use it or set up the problem. 

Thanks in advance for any pointers.

Bonjour,

Je veux savoir comment augmenter la mémoire du maple sachant que j'ai un calculateur puissant (4 CPU de 2G pour chacun+2 RAM de 146 G pour chacune).

En vérité, il s'agit de résoudre un système polynomial à 7 équations et 4 variables ; voici les deux messages du Maple après l'exécution : "Kernel connection has been lost" "execution stopped:memory allocation failed.please see ?alloc for more detail."

Quelles sont les paramètres ci-dessous de kernelopts qu'il faut modifier et comment :

===========================================

> kernelopts(maxdigits);

                             38654705646

> kernelopts(wordsize);

                                  64

> kernelopts(dagtag=4);

                                FLOAT

> kernelopts(dagtag=SERIES);

                                  15

> kernelopts(cputime);

                               0.010998

> kernelopts(datalimit=64*Unit( megabyte )):
> kernelopts(datalimit=64*Unit( mebibyte ));

                                62500

> kernelopts(datalimit=10000*Unit( kibibyte ));

                                65536

> kernelopts(datalimit);

                                10000

> kernelopts(cpulimit=10*Unit( minute )):
> kernelopts(cpulimit);

                                 600

============================================
Avec mes plus vifs remerciements,

Gérard.

Hi, 

Apologies if this is a very simple question and I am being a bit stupid, but how do I plot two functions of r on one graph, if they operate over different values of r? 

Say I have the functions:

FOO = r→APOT*exp(-r/rho)-CPOT/r^6+4*E2/r 

g = r→(c1*exp(d1*r)+c2*exp(d2*r)+c3*exp(d3*r)+c4*exp(d4*r))/r 

where FOO takes values of r between 0.5 and 2, and g takes values of r between o.2 and 0.5. 

Any help would be appreicated!

product.mw

Experts, I pose a question:

Separate the numbers 3,4,5,6,7,8,28,30,35 into three groups of three numbers each, so that the
product of the numbers in each group is equal.

The idea is to select numbers where the variance between the 3 groups is minimized.

my attempt doesn't get the anwer directly, there must be a better approach

f(f(z,a),b) = f(z, a + b) 

i googled this axiom is diff(x(t),t) = xi(f);

then i think 

diff(x(t),t$2) = xi(f);

is it f(f(f(z,a),b),c) = f(z, a + b+c) ?

then think again

whether  f(f(f(z,a),b),c) + f(f(z,a),b) = f(z, a + b+c)  is diff(x(t),t$2)+diff(x(t),t)= xi(f);

however do not know how to construct right hand side  f(z, a + b+c), this is my guess

any books teaching this?

i think that if any matrix group be created from  f(f(f(z,a),b),c) + f(f(z,a),b)

that can help to convert to differential equations

hope that there is a solvable group which can represent solvable differential equation or differential system

if xi is Infinitesimal in maple,

how to find Infinitesimal from f(f(z,a),b) = f(z, a + b) ?

Is there an easy way, where I can generate a 3d cube when I have already defined a 3d polygon surface?

I would like to sweep my surface 20 cm in the z-axis, preferably without having to define the cube from it's 8 corners.

Is there a command I can use for this purpose?

it seems impossible to draw all DE system in one time.

quite easy to get error when can not solve

> newsys := [Diff(x1(t), t) = VectorCalculus[`-`](VectorCalculus[`*`](2, x3(t)^2)), Diff(x2(t), t) = VectorCalculus[`-`](u(t)), Diff(x3(t), t) = u(t), Diff(u(t), t) = 0];
[ d 2 d d
[--- x1(t) = -2 x3(t) , --- x2(t) = -u(t), --- x3(t) = u(t),
[ dt dt dt

d ]
--- u(t) = 0]
dt ]
> DEplot3d(value(newsys), [x1(t), x2(t), x3(t), u(t)], t = 0 .. 1, [[x1(0) = 1, x2(0) = 1, x3(0) = 1, u(0) = 1]], scene = [x1(t), x2(t)]);
Error, (in DEtools/DEplot) 'scene' must specify three variables in DEplot3d: scene = [x1(t), x2(t)]
> Sol := dsolve(`union`(newsys, {u(0) = .5, x1(0) = .5, x2(0) = .5, x3(0) = .5}), range = 0 .. 15, numeric); plots:-odeplot(Sol, [x1(t), x2(t), x3(t), u(t)], t = 0 .. 15);
Error, invalid input: `union` received [Diff(x1(t), t) = -2*x3(t)^2, Diff(x2(t), t) = -u(t), Diff(x3(t), t) = u(t), Diff(u(t), t) = 0], which is not valid for its 1st argument
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

How can I get and install grtensor for MAPLE12 on WIN7 32bit platform,

I tried with http://grtensor.phy.queensu.ca, downloaded grtii6.exe, now how to proceed further???

got error when draw root locus

and would like to know how to set feasibility tolerance, less than 0.1 is also ok

with(DynamicSystems):

x11 := [1.05657970467127, .369307407127487, .400969917393968, .368036162749865, .280389875142339, .280523489139136, .283220960827744, .373941285224253, .378034013792196, .384412762008662, .358678988563716, .350625923673556, .852039817522304, .362240519978640, 1.03197080591829, .343650441408896, .982510654490390, .404544012440991, .422063867224247, 1.20938803285209, .455708586000668, 1.22503869712995, .388259397947667, .472188904769827, 1.31108028794286, 1.19746589728366, .572669348193002];

y11 := [.813920951682113, 10.3546712426210, 2.54581301217449, 10.2617298458172, 3.82022939508992, 3.81119683373741, 3.90918914917183, 10.5831132713329, 10.8700088489538, 11.0218056177585, 10.5857571473115, 9.89034057997145, .271497107157453, 9.77706473740146, 2.23955104698355, 4.16872072216206, .806710906391666, 11.9148193656260, 12.0521411908477, 2.52812993540440, 12.6348841508094, 2.72197067934160, 5.10891266728297, 13.3609183272238, 3.03572692234234, 1.07326033849793, 15.4268962507711];

z11 := [8.93290500985527, 8.96632856524217, 15.8861149154785, 9.16576669760908, 3.20341865536950, 3.11740291181539, 3.22328961317946, 8.71094047480794, 8.60596466961827, 9.15440788281943, 10.2935566768586, 10.5765776143026, 16.3469510439066, 9.36885507010739, 2.20434678689869, 3.88816077008078, 17.9816287534802, 10.1414228793737, 10.7356141216242, 4.00703203725441, 12.0105837616461, 3.77028605914906, 5.01411979976607, 12.7529165152417, 3.66800269682059, 21.2178824031985, 13.9148746721034];

u11 := [5.59, 5.74, 5.49, 5.19, 5.37, 5.56, 5.46, 5.21, 5.55, 5.56, 5.61, 5.91, 5.93, 5.98, 6.28, 6.24, 6.44, 6.58, 6.75, 6.78, 6.81, 7.59, 7.73, 7.75, 7.69, 7.73, 7.79];

a1 := Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t)+k4*u1(t);

b1 := Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t)+k8*u1(t);

c1 := Diff(z1(t),t) = k8*x1(t)+ k9*y1(t)+ k10*z1(t)+k12*u1(t);

d1 := Diff(u1(t),t) = 0;

ICS:=x1(1)=x11[1],y1(1)=y11[1],z1(1)=z11[1],u1(1)=u11[27];

sol:=dsolve({a1,b1,c1,d1,ICS}, numeric, method=rkf45, parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12],output=listprocedure);

X,Y,Z,U:=op(subs(sol,[x1(t),y1(t),z1(t),u1(t)]));

tim := [seq(n, n=1..27)];

N:=nops(tim):

ans:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12) sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);

 add((X(tim[i])-x11[i])^2,i=1..N)+add((Y(tim[i])-y11[i])^2,i=1..N)+add((Z(tim[i])-z11[i])^2,i=1..N)+add((U(tim[i])-u11[i])^2,i=1..N)

 end proc;

ans(.001,.002,.003,.001,.002,.003,.001,.002,.003,.001,.002,.003);

result1 := Optimization:-Minimize(ans,initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.001,.002,.003]);

x11 := [1.05657970467127, .369307407127487, .400969917393968, .368036162749865, .280389875142339, .280523489139136, .283220960827744, .373941285224253, .378034013792196, .384412762008662, .358678988563716, .350625923673556, .852039817522304, .362240519978640, 1.03197080591829, .343650441408896, .982510654490390, .404544012440991, .422063867224247, 1.20938803285209, .455708586000668, 1.22503869712995, .388259397947667, .472188904769827, 1.31108028794286, 1.19746589728366, .572669348193002];

y11 := [.813920951682113, 10.3546712426210, 2.54581301217449, 10.2617298458172, 3.82022939508992, 3.81119683373741, 3.90918914917183, 10.5831132713329, 10.8700088489538, 11.0218056177585, 10.5857571473115, 9.89034057997145, .271497107157453, 9.77706473740146, 2.23955104698355, 4.16872072216206, .806710906391666, 11.9148193656260, 12.0521411908477, 2.52812993540440, 12.6348841508094, 2.72197067934160, 5.10891266728297, 13.3609183272238, 3.03572692234234, 1.07326033849793, 15.4268962507711];

z11 := [8.93290500985527, 8.96632856524217, 15.8861149154785, 9.16576669760908, 3.20341865536950, 3.11740291181539, 3.22328961317946, 8.71094047480794, 8.60596466961827, 9.15440788281943, 10.2935566768586, 10.5765776143026, 16.3469510439066, 9.36885507010739, 2.20434678689869, 3.88816077008078, 17.9816287534802, 10.1414228793737, 10.7356141216242, 4.00703203725441, 12.0105837616461, 3.77028605914906, 5.01411979976607, 12.7529165152417, 3.66800269682059, 21.2178824031985, 13.9148746721034];

u11 := [5.59, 5.74, 5.49, 5.19, 5.37, 5.56, 5.46, 5.21, 5.55, 5.56, 5.61, 5.91, 5.93, 5.98, 6.28, 6.24, 6.44, 6.58, 6.75, 6.78, 6.81, 7.59, 7.73, 7.75, 7.69, 7.73, 7.79];

k1 := result1[2][1];

k2 := result1[2][2];

k3 := result1[2][3];

k4 := result1[2][4];

k5 := result1[2][5];

k6 := result1[2][6];

k7 := result1[2][7];

k8 := result1[2][8];

k9 := result1[2][9];

k10 := result1[2][10];

k11 := result1[2][11];

k12 := result1[2][12];

a1 := Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t)+k4*u1(t);

b1 := Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t)+k8*u1(t);

c1 := Diff(z1(t),t) = k8*x1(t)+ k9*y1(t)+ k10*z1(t)+k12*u1(t);

d1 := Diff(u1(t),t) = 0;

diff_eq := [a1, b1, c1, d1];

sys6 := DiffEquation(diff_eq, [x1(t), y1(t), z1(t), u1(t)], [x1(t), y1(t), z1(t), u1(t)]);

sys6 := DiffEquation(diff_eq, [x1(t), y1(t), z1(t)], [x1(t), y1(t), z1(t), u1(t)]);

ResponsePlot(sys6, Step(), parameters = params);

RootLocusPlot(sys6);

> sys6 := DiffEquation(diff_eq, [], [x1(t), y1(t), z1(t), u1(t)]);

Error, (in DynamicSystems:-DiffEquation) unrecognized diff-equation type: 9

> sys6 := DiffEquation(diff_eq, [x1(t), y1(t), z1(t), u1(t)], [x1(t), y1(t), z1(t), u1(t)]); sys6 := DiffEquation(diff_eq, [x1(t), y1(t), z1(t)], [x1(t), y1(t), z1(t), u1(t)]);

Error, (in DynamicSystems:-DiffEquation) unrecognized diff-equation type: 9

Error, (in DynamicSystems:-DiffEquation) unrecognized diff-equation type: 9

> ResponsePlot(sys6, Step(), parameters = params); RootLocusPlot(sys6);

Error, invalid input: DynamicSystems:-ResponsePlot expects value for keyword parameter parameters to be of type ({set, list})(name = complexcons), but received params

Error, (in Verify:-CommonExports) system object is not a module

I am not sure why Maple gives this:

r:=int( 1/(x+sqrt(x)),x);

Using Mathematica and Matlab, the answer should be

   2 Log[1 + Sqrt[x]]

At x=1, Maple result is not defined, since log(0), but Mathematica gives a numerical value for 2*log(2)

Is this a brach cut issue? Could someone please verify this. I am using Maple 17.02

The real part of both solutions agree for x>1, but Maple answer ofcourse has a complex part, and that is what I am wondering about. Is Maple correct, and Mathematica should have returned that? May be a Math expert can comment.

Bonjour,

Je veux savoir comment augmenter la mémoire du maple sachant que j'ai un calculateur puissant (4 CPU de 2G pour chacun+2 RAM de 146 G pour chacune).

Merci d'avance,

Gérard.

I am trying to solve a system of equations with Maple 16, but it keeps returning an error message. I have the following very simple code:

_________________________________________

assume(lambda > 0);
assume(kappa > 0);
assume(omega > 0);

assume(a >= 0);
assume(alpha, 'real');
assume(b >= 0);
assume(beta, 'real');
assume(m >= 0);
assume(mu, 'real');
assume(n >= 0);
assume(nu, 'real');
assume(t >= 0);
assume(tau, 'real');
assume(p >= 0);
assume(psi, 'real');
assume(d >= 0);
assume(delta, 'real');
assume(r >= 0);
assume(rho, 'real');
assume(x >= 0);
assume(xi, 'real');

solve({d^2*lambda^2+r^2*kappa^2+(x^2-1)*omega^2 = 0, (a^2-1)*lambda^2+m^2*kappa^2+t^2*omega^2 = 0, a*exp(-I*alpha)*b*exp(I*beta)*lambda^2+m*exp(-I*mu)*n*exp(I*nu)*kappa^2+t*exp(-I*tau)*p*exp(I*psi)*omega^2 = 0, a*exp(-I*alpha)*d*exp(I*delta)*lambda^2+m*exp(-I*mu)*r*exp(I*rho)*kappa^2+t*exp(-I*tau)*x*exp(I*xi)*omega^2 = 0, b*exp(-I*beta)*d*exp(I*delta)*lambda^2+n*exp(-I*nu)*r*exp(I*rho)*kappa^2+p*exp(-I*psi)*x*exp(I*xi)*omega^2 = 0}, {a, b, d, m, mu, n, nu, p, psi, r, rho, t, tau, x, xi, alpha, beta, delta}, useassumptions, maxsols = 10)

_________________________________________

When this piece of code is executed, I receive the following error message:

Error, (in Engine:-Tarjan) invalid input: subs received {0 <= x_8, 0 <= x_10, 0 <= x_12}, which is not valid for its 1st argument

What does this mean? How can I find solutions to this system of equations? (I know that there exists at least one solution, and I am figuring out whether there exist more.)

Any help would be greatly appreciated.

Hi

I want to solve two odes with their boundary condition. I wrote the code below:

restart:

eq2:=diff(T(eta),eta,eta)+Nb*diff(T(eta),eta)*diff(phi(eta),eta)+Nt*diff(T(eta),eta)*diff(T(eta),eta);

eq3:=diff(phi(eta),eta,eta)+Nt/Nb*diff(T(eta),eta,eta);

sys_ode:=  eq2=0,eq3=0;
bcs := phi(0)=0,phi(h)=1,T(0)=0,T(h)=1;
sol:=dsolve([sys_ode, ics]);

however, this code doesnt get my desired results (the results are complex!). but when I (with hand) integrate Eq3 twice and substitute boundary conditions and replace in Eq2 the answer is easy and straightforward.

How can I change the following algorithm to get my results?

Thanks for your attention in advance

Amir

How can I calculate GR tensors and geodesic equations for adS schwarzschild spacetime.