As I am trying to solve this integration:

restart; with(linalg); with(stats); with(plots); with(Statistics); with(LinearAlgebra); with(Optimization);
lambda0 := proc (t) options operator, arrow; gamma0+gamma1*t+gamma2*t^2 end proc;
lambda := lambda0(t)*exp(beta*s);
t1 := 145; t3 := 250; t2 := (t1+t3)*(1/2);
s := 1/(273.16+50); s1 := 1/(273.16+t1); s3 := 1/(273.16+t3); s2 := 1/(273.16+t2); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0; beta := -3800;
c := 300; n := 200;
Theta := solve(1-exp(-(gamma0*tau1+(1/2)*gamma1*tau1^2+(1/3)*gamma2*tau1^3)*exp(beta*s1)) = 1-exp(-(gamma0*a+(1/2)*gamma1*a^2+(1/3)*gamma2*a^3)*exp(beta*s2)), a);

a := Theta[1];

Delta := solve(1-exp(-(gamma0*(a+tau2-tau1)+(1/2)*gamma1*(a+tau2-tau1)^2+(1/3)*gamma2*(a+tau2-tau1)^3)*exp(beta*s2)) = 1-exp(-(gamma0*b+(1/2)*gamma1*b^2+(1/3)*gamma2*b^3)*exp(beta*s3)), b);

b := Delta[1];

A1 := `assuming`([unapply(int(exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1))/(gamma0+gamma1*t+gamma2*t^`2`), t = N .. M), N, M)], [N > 0, M > 0]);
A2 := unapply(int(exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2))/(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2), t = N .. M), N, M);
A3 := unapply(int(exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3))/(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2), t = N .. M), N, M);
B1 := `assuming`([unapply(int(t^2*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1))/(gamma2*t^2+gamma1*t+gamma0), t = N .. M), N, M)], [N > 0, M > 0]);
B2 := unapply(int((a+t-tau1)^2*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2))/(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2), t = N .. M), N, M);
B3 := unapply(int((b+t-tau2)^2*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3))/(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2), t = N .. M), N, M);

F0 := A1(0, tau1)+A2(tau1, tau2)+A3(tau2, c);
F1 := B1(0, tau1)+B2(tau1, tau2)+B3(tau2, c);

NLPSolve(1/(n^3*(F0*F1-F1)), tau1 = 115 .. 201, tau2 = 237 .. 273);

I need to have tau1 tau2 as varibles to get there optimal values ..

But this error keeps coming :

Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got HFloat(1.0) = HFloat(158.0) .. HFloat(255.0)

Please Help ..

Please help me to solve two equations in uploaded find and find two expressions for ‘T’ and ‘n’ as a function of other parameters.

maple.mw

I am a problem with solve differential equation, please help me: THANKS 

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);

dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, numeric, output = array([0.]));

              Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

****************FORMAT TWO ********************************************************

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);
dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, method = bvp[midrich], output = array([0.]));
%;
                                   Error, (in dsolve) too many levels of recursion

I DONT KNOW ABOUT THIS ERROR

PLEASE HELP ME

THANKS A LOT

what conditions are necessary that a group G has stabilisers?

Good morning.

I request your kind suggestion to my query posted.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Hi all.

I'm a student learning Algebra.

I've been searching everywhere and cannot work out how to plot and analyze a function graphically in Maple.

For example, you can see in this video, There is a point for the Vertex of a parabola on the example

http://www.maplesoft.com/TeacherResource/topic.aspx?m=1&c=1&cha=3&sec=9&top=31

I would like to put things like this on my graph (Vertex, or X-Intercepts, or the intersection of 2 lines)

I can certainly find this information by using Algebra (vertex form, etc) but it would help my understanding to also visualize the functions graphically.

Hi,

I wonder if there is a way to achieve this, say I have 4 Maple worksheets,

sheet1.mw

sheet2.mw

sheet3.mw

sheet4.mw

all of them can run seperately. Each of them runs on lots of data, and takes a big chuck of time. I hope to run them one by one. After each file is completed, save (Export) as PDF file, and move on to the next one.

On my own PC, I use Maple X64 windows version. I have never used the command line, but I suppose that will be done in this version, instead of the GUI version?

On the school server, it's Maple X64 linux version. So it's also has the maple command line version as well as the xmaple version.

Thanks,

casper

restart:
seq1:=seq(i,i=1..5);
seq2:=seq(i,i=2..6);
dseq:=seq2-seq1;
seq1:=seq(i,i=1..5);
seq2:=seq(i,i=1..5);
dseq:=seq2-seq1;
seq1:=[seq(i,i=1..5)];
seq2:=[seq(i,i=1..5)];
dseq:=seq2-seq1;

Is that possible to get the differences between two sequences directly? (instead of using a list)

I don't quit understand why the second method would collapse the 0s into just a single value. It's not a set.

Thanks,

casper

Suppose i am trying to do a sequential if command as follows:

seq(`if`(a[i] < b[i], c[i], d[i]), i = 1 .. 10);

now this doesnot evaluate the i's in c[i] and d[i].

please help me with complete evaluation of this statement.

I want to sum over several variables at once.

For example, something like

add(add(add(f(k1,k2,k3),k1=range1),k2=range2),k3=range3);

sums over 3 variables. But this can only be done if I know the number of variables in advance. I want to write a code that will sum over m variables, with m being supplied on demand.

Maple can do this for integrals. If I write

int(f(seq(k[i],i=1..m)),[seq(k[i]=range[i],i=1..m)]);

the integral is computed over m variables, for any m.

How can something like this be implemented for summation?

As am trying to solve this integration:

A(c,n,m):=evalf(int(1/(y)*exp(-c*y^(2)),y=n..m))

B(c,n,m):=evalf(int(exp(-c*y^(2)),y=n..m))

C(c,n,m):=evalf(int(y*exp(-c*y^(2)),y=n..m))

d(c,n,m):=evalf(int(y^(2)*exp(-c*y^(2)),y=n..m))

E(c,n,m):=evalf(int(y^(3)*exp(-c*y^(2)),y=n..m))

F0 := exp(beta*s1)*exp(gamma0^2*exp(beta*s1)/(2*gamma1))*A((1/2)*gamma1*exp(beta*s1), gamma0/gamma1,gamma0/gamma1+tau1)/gamma1+exp(beta*s2)*exp(gamma0^2*exp(beta*s2)/(2*gamma1))*A((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)/gamma1+exp(beta*s3)*exp(gamma0^2*exp(beta*s3)/(2*gamma1))*A((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)/gamma1

F1 := exp(beta*s1)*exp(gamma0^2*exp(beta*s1)/(2*gamma1))*(gamma0^2*A((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1)/gamma1^2-2*gamma0*B((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1)/gamma1+C((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1))/gamma1+exp(beta*s2)*exp(gamma0^2*exp(beta*s2)/(2*gamma1))*(gamma0^2*A((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)/gamma1^2-2*gamma0*B((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)/gamma1+C((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a))/gamma1+exp(beta*s3)*exp(gamma0^2*exp(beta*s3)/(2*gamma1))*(gamma0^2*A((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)/gamma1^2-2*gamma0*B((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)/gamma1+C((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b))/gamma1

F01 := exp(beta*s1)*exp(gamma0^2*exp(beta*s1)/(2*gamma1))*(B((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1)-gamma0*A((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1)/gamma1)/gamma1+exp(beta*s2)*exp(gamma0^2*exp(beta*s2)/(2*gamma1))*(B((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)-gamma0*A((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)/gamma1)/gamma1+exp(beta*s3)*exp(gamma0^2*exp(beta*s3)/(2*gamma1))*(B((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)-gamma0*A((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)/gamma1)/gamma1

`F&beta;` := int((s1^2*(gamma0*t+(1/2)*gamma1*t^2)*exp(beta*s1)*(gamma1*t+gamma0)*exp(beta*s1))*exp(-(gamma0*t+(1/2)*gamma1*t^2)*exp(beta*s1)), t = 0 .. tau1)+int((s2^2*(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2)*exp(beta*s2)*(gamma0+gamma1*(a+t-tau1))*exp(beta*s2))*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2)*exp(beta*s2)), t = tau1 .. tau2)+int((s3^2*(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2)*exp(beta*s3)*(gamma0+gamma1*(b+t-tau2))*exp(beta*s3))*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2)*exp(beta*s3)), t = tau2 .. c)+int((s3^2*(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2)*exp(beta*s3)*(gamma0+gamma1*(b+t-tau2))*exp(beta*s3))*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2)*exp(beta*s3)), t = c .. infinity)

I need to have tau2 as varibles to get there optimal values ..

Minimize(1/((F0*F1-F01^2)*n^3*`F&beta;`), tau2 = 237..273})

But this error keeps coming :

Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got HFloat(1.0) = 121.0828419 .. HFloat(193.0828419)

Please Help ..

I have 3 column vectors:

phi contains the number of radians from the North Pole

theta contains the number of radians from the Greenwich meridian

D contains number data corresponding to the point (phi,theta) on the sphere.

How do I plot:

a) a contour plot on the surface of the sphere where each point at (phi, theta) has a corresponding data value D?

b) a plot where the height above the surface at (phi, theta) is some linear function of D such as radius*D*constant?

I have a Matrix of data points I am plotting using plots:-listdensityplot. That works fine.

However, the axes are labeled by row and column number of the Matrix (e.g. 1..20 or whatever). In reality, these are of course some parameters the range of which has been mapped onto the rows and columns of the Matrix.

How can I display the axes using the values of the original parameters? I know the transformation from Matrix row or column to the actual parameters (and in this case it is linear).

TIA,

Mac Dude

Hi experts,

the standard resolution for maple contourplots is 72 dpi wich is not suitable for publication purposes. I need at least a resolution between 500 - 1000 dpi. How do I get better resolutions for my contourplots when exporting them to .bmp or .jpg-files?
Somebody any ideas?