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) ?

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

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.

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

I've found the following project: http://www.parallella.org/

It is a very cheap but impressive computer ( 64-cores, they say it gives about 90 GFLOPS of computing power). The problem is the very limited amount of memory (1GB). See: http://www.parallella.org/board/ for specifications.

Now my question is: do you think Maple will run on this machine (acoording to the site it will run Ubuntu) and if so then does it make sense to try it given the small amount of memory it has? Or in another words: do there exist problems that could be solved by Maple on this powerful machine and that cannot be solved on a regular machine with let's say 4GB of RAM?

Hello everybody

I'm new at using Maple

so what I'm trying to do is " solve system of differential equations numerically " and plot the result 

I use the floweing code

PDEtools[declare]((u, v, w)(t), prime = t)

> params := z = 0;

Omega= 2.2758;

tau = 13.8;

T2 = 200; s = 1;

r = 0.7071;

\[CapitalDelta] = 1.7758;

s = 2.2758;

Eta= 1.05457173*10^-34;

omega = 0.5; k = 1666666.667;

> sys1 := {diff(u(t), t) = Omega*v(t)-u(t)/T2,

diff(v(t), t) = -Omega*u*{t}-2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*w(t)-v(t)/T2,

diff(w(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*v(t)};

Cs1 := {u(-20) = 0, v(-20) = 0, w(-20) = -1}

> ans1 := dsolve*RealRange(Open({ICs1, sys1}), {u(t), v(t), w(t)});
%;
Error, (in RealRange) invalid arguments

plot([u(t),t=-20..20])
plot([v(t),t=-20..20])
plot([w(t),t=-20..20])

:::::::::

also I need to use the result of v(t) in another equation as,

x=2*v(t)*cos(k*z-omega*t)

How I can do that ?

Hello,

I was wondering if I can call Matlab R2012b with maple 14 on my macos 10.7.5.

When I try to do this:

> Matlab[setvar]("x", 3.14);

I get this:

Error, (in Matlab:-setvar) there was a problem finding or loading matlink.so. Refer to ?Matlab,setup for help configuring your system to work with the Matlab-link.

I read that I may have to change a script. Where are those scripts located?

Regards,

Three families grow vegetables in their backyards,and agree to form a small closed economy by sharing their produce. family andrews grow artichokes, family brown grows beans and family Cuthbert grows corn.Family Andrews receives 70% of its artichokes, 30% of the beans and 30% of the corn.Family Brown receives 20% of the artichokes,60% of the beans and 10% of thr corn.Family Cuthbert receives the remainder of the vegetables.

a) Write down the exchange matrix A.

b) If production is measured in doolars ,define the variables
                                    x[1]
,
                                    x[2]
,
                                    x[3]
 of the production vector X.

c) Find all solution of the Leontief closed with matrix equation (I-A)^-1¤X=0.

d) If family Cuthbert produces $100 worth of corn, how much will familes Andrews and Brown need to produce (in dollars) in order foe the economy to be in equilibrium?

hello 

please say me how can i make diff and implicit diff with Set Point answer?

for example how can i write these?

(x^2+y^2=6)' => 2*x+2*y*y'=0 => y'(-2,5)=2/5

or

(y=x^3+4*x)' => y'=3*x^2+4 => y'(3)=31

thanks very much

I am trying to solve the rate equations for A<=>B<=>C with k1,k2,k3,k4 as the rate constants.  I put in the equations into Maple but can't seem to get it to solve them.  The initial conditions for A(0) = S, B(0)=C(0)=0

Here is what I plugged into the program:

Parameters(S, k1, k2, k3, k4);

sys_ode := d*A(t)/dt = -k1*A(t)+k2*B(t), d*B(t)/dt = k1*A(t)+(-k2-k3)*B(t)+k4*C(t), d*C(t)/dt = k3*B(t)-k4*C(t);

d A(t)
------ = -k1 A(t) + k2 B(t),
dt

d B(t)
------ = k1 A(t) + (-k2 - k3) B(t) + k4 C(t),
dt

d C(t)
------ = k3 B(t) - k4 C(t)
dt

ics := A(0) = S, B(0) = 0, C(0) = 0;
A(0) = S, B(0) = 0, C(0) = 0

dsolve({ics, sys_ode});
Error, (in dsolve) found functions with same name but depending on different arguments in the given DE system: . It is required an indication of the dependent variables

Hellp

for a task about the launch of a rocket we had to make a matrix OPL3 with in the first column the time T and in the second column the height of the rocket at that time.

I must Maple find the time where the rocket is at his highest point.

I can find how high the highest point is, but didn't succeed to find the corresponding time.
Can Maple tell me at wich time (= row # o/t matrix OPL3) the rocket is at his highest point.

I used the following to find the highest point.

ymin:=min(seq(abs(OPL3(i,2)),i=64..830));

Note: the diff equitation is numerically solved, so I can't use solve(....=0) (am I right here?)

Thanks!

How  can you create a loop for Monty Hall Problem when you have 3 door (1 opening) and then 4 Doors (with 2 openings and possible 2 switches)

I have this kind of problem. When I try to solve my command:

is there any way to avoid this? in order to get the answer directly...