Hello,

restart:

N := N0-(1/2)*sqrt(2)*sqrt(Pi*Kc/d)*(sum(erfc((1/2)*(L*n+x)/sqrt(d*t))+erfc((1/2)*((n+1)*L-x)/sqrt(d*t)),

n = 0 .. infinity));

N0:=0.2:L:=0.25:Kc:=2*10^(-12):t:=360000:d:=2.010619298*10^(-10):

When I plot N vs x = 0..0.25 then there is no issue

plot(N,x=0..0.25,axes=box);

but when try to use a loop to get the data, Maple cannot evaluate

for x from 0 to 0.25 by 0.01 do

N[x]:=evalf(N0-sqrt(Pi*Kc/(2*d))*sum(((((erfc((n*L+x)/(2*sqrt(d*t))))+erfc(((n+1)*L-x)/(2*sqrt(d*t))))),n=0..infinity)));
end do;

Thanks

thanks

THE FOLLOWING CODE 

restart;

A:=Matrix([[ a , b ], [ c , d ]]);

a:=1; b:=0; c:=0; d:=1;

A; 

produces differents results under MAPLE 16  linux i386 and under MAPLE 16  linux amd64

in the first case the last evalution has the following printed output:

on the second machine the printed output is

Does anybody has an explication; I thought that the "coorect behaviour was the first one since tables use last-name evalutation. But now I am puzzled.

how to decompose a matrix into time invariant and time variant 

is it possible to make time invariant and time variant template and then decompose into it

i mean decomposition can be 

 time invariant matrix + time variant matrix

or

 time invariant matrix * time variant matrix

 dsolve([Diff(f, t) = f, Diff(f,t) + g = h], f);

 dsolve([Diff(f, t) = f, Diff(f,t)*g = h], f);

where h is orthogonal matrix, f,g,h are matrix

would like to find g and f from h

can dsolve solve differential equation of matrix ? how?

dsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);

dsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);

assume x^2 + 1 is from interpolation of polynomial

pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t)= x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);
pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t) = x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);

these system can not be solved

hope no real number any more after decomposition and only have iinteger in I time invariant function

The matrix:

<3,-2,-1,2,0>;

<11,4,-8,2,7>;

<0,0,2,0,0>;

<3,3,-4,3,3>;

<-8,4,5,-4,-1>;

has eigenvector:

<2,0,-1,0,1>

Find its corresponding eigenvalue.

(Hint: you don't need to find all the eigenvalues and eigenvectors to answer this question.)

Steps and the solution will be greatly appreciated. thanks!

number10:=`466d06ece998b7a2fb1d464fed2ced7641ddaa3cc31c9941cf110abbf409ed39598005b3399ccfafb61d0315fca0a314be138a9f32503bedac8067f03adbf3575c3b8edc9ba7f537530541ab0f9f3cd04ff50d66f1d559ba520e89a2cb2a83`:

number8:=`315c4eeaa8b5f8bffd11155ea506b56041c6a00c8a08854dd21a4bbde54ce56801d943ba708b8a3574f40c00fff9e00fa1439fd0654327a3bfc860b92f89ee04132ecb9298f5fd2d5e4b45e40ecc3b9d59e9417df7c

I first define

f:=x->convert(x, decimal, hex):

with(Bits):
str1:=convert( `Xor(f(number8), f(number10))`, bytes);

now how can I get back the alphabets, since again use of convert with bytes return the inital argument.

Moreover, I would really appreciate if someone could explain the difference between 

convert(`expr`, bytes)

convert( [expr], bytes)

Many regards!!

if kernel is solve(A*x, x);

then , what is cokernel of a numeric matrix ?

I cannot show that the following two sums(A and B) are equal to each other.

How can I simplify the difference(A-B)?

A := sum((-1)^(i-1)*factorial(n0)/(factorial(n1)*(n1+i)^2*factorial(i-1)*factorial(n0-n1-i)), i = 1 .. n0-n1);

B := sum(1/(n1+i), i = 1 .. n0-n1);

`assuming`([simplify(A-B)], [n0::nonnegint, n1::nonnegint, n1 <= n0]);

does not give zero. 

The result of a simple test: 

map(simplify, [seq(eval(A-B, n1 = 10), n0 = 20 .. 30)]);
print(`output redirected...`); 

is

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

I am trying to get a solution to the heat equation with multiple boundary conditions.

Most of them work but I am having trouble with two things: a Robin boundary condition and initial conditions.

First, here are my equations that work:

returns a solution (actually two including u(x,y,z,t)=0).

However, when I try to add:

or

I no longer get a solution.

Any guidance would be appreciated.

Regards.

I have uploaded a worksheet with the equations...

Download heat_equation_pde.mw

Hi everyone

I am currently trying to make my own simple package including a few procedures. So far I have been able to write some "code" that actually works when I open the document and hit "enter". I would, however, like to save the package so it can be accessed during any Maple session using the command "with". I have unsuccesfully tried to comprehend the Maple help pages regarding this question but I definitely don't want to mess things up.

This is what I have written:

mat := module ()
description "useful procedures for mathematics, physics and chemistry";
export AtomicWeight;
option package;

   AtomicWeight := proc (x) description "returns the average atomic mass of the naturally ocurring element";
   Units:-AddSystem(NewSystem, Units:-GetSystem(SI), u);
   return evalf(ScientificConstants:-Element(x, atomicweight, system = NewSystem, units))
   end proc

end module;

What should I do to save it correctly?

Thank in advance,
Mads

Following my previous question

http://www.mapleprimes.com/questions/200627-Lssolve-Midpoint

I wrote the following code

restart:
Phiavg:=0.06;
lambda:=0.05;
Ha:=0;
NBT:=0.5;
Nr:=500;
#N[bt]:=cc*NBT+(1-cc)*4; ## cc between 0 and 1
N[bt]:=cc*NBT+(1-cc^2)*0.75;


                              0.06
                              0.05
                               0
                              0.5
                              500
                                           2
                    0.5 cc + 0.75 - 0.75 cc
eq1:=diff(u(eta),eta,eta)+1/(mu(eta)/mu1[w])*(sigma-Nr*(phi(eta)-phi1[w])-(1-phi(eta))*T(eta)-Ha^2*u(eta))+((1/mu(eta)*(mu_phi*diff(phi(eta),eta)))*diff(u(eta),eta));
eq2:=diff(T(eta),eta)-1/(k(eta)/k1[w]);
eq3:=diff(phi(eta),eta)-phi(eta)/(N[bt]*(1-gama1*T(eta))^2)*diff(T(eta),eta);
 /  d   /  d         \\      1                                 
 |----- |----- u(eta)|| + ------- (mu1[w] (sigma - 500 phi(eta)
 \ deta \ deta       //   mu(eta)                              

    + 500 phi1[w] - (1 - phi(eta)) T(eta)))

             /  d           \ /  d         \
      mu_phi |----- phi(eta)| |----- u(eta)|
             \ deta         / \ deta       /
    + --------------------------------------
                     mu(eta)                
                    /  d         \   k1[w]
                    |----- T(eta)| - ------
                    \ deta       /   k(eta)
                                       /  d         \            
                              phi(eta) |----- T(eta)|            
/  d           \                       \ deta       /            
|----- phi(eta)| - ----------------------------------------------
\ deta         /   /                       2\                   2
                   \0.5 cc + 0.75 - 0.75 cc / (1 - gama1 T(eta))
mu:=unapply(mu1[bf]*(1+a[mu1]*phi(eta)+b[mu1]*phi(eta)^2),eta):
k:=unapply(k1[bf]*(1+a[k1]*phi(eta)+b[k1]*phi(eta)^2),eta):
rhop:=3880:
rhobf:=998.2:
cp:=773:
cbf:=4182:
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):
mu_phi:=mu1[bf]*(a[mu1]+2*b[mu1]*phi(eta)):
gama1:=0.00:
a[mu1]:=39.11:
b[mu1]:=533.9:
mu1[bf]:=9.93/10000:
a[k1]:=7.47:
b[k1]:=0:
k1[bf]:=0.597:
zet:=1:
phi1[w]:=phi0:
mu1[w]:=mu(0):
k1[w]:=k(0):

eq1:=subs(phi(0)=phi0,eq1);
eq2:=subs(phi(0)=phi0,eq2);
eq3:=subs(phi(0)=phi0,eq3);
/  d   /  d         \\   //                                    
|----- |----- u(eta)|| + \\0.0009930000000 + 0.03883623000 phi0
\ deta \ deta       //                                         

                      2\                                 
   + 0.5301627000 phi0 / (sigma - 500 phi(eta) + 500 phi0

                           \//               
   - (1 - phi(eta)) T(eta))/ \0.0009930000000

                                                   2\   
   + 0.03883623000 phi(eta) + 0.5301627000 phi(eta) / +

  /                                       /  d           \ /  d  
  |(0.03883623000 + 1.060325400 phi(eta)) |----- phi(eta)| |-----
  \                                       \ deta         / \ deta

         \\//                                        
   u(eta)|| \0.0009930000000 + 0.03883623000 phi(eta)
         //                                          

                          2\
   + 0.5301627000 phi(eta) /
           /  d         \     0.597 + 4.45959 phi0  
           |----- T(eta)| - ------------------------
           \ deta       /   0.597 + 4.45959 phi(eta)
                                        /  d         \
                            1. phi(eta) |----- T(eta)|
         /  d           \               \ deta       /
         |----- phi(eta)| - --------------------------
         \ deta         /                           2
                             0.5 cc + 0.75 - 0.75 cc  
Q:=proc(pp2,fi0) option remember; local res,F0,F1,F2,a,INT0,INT10,B;
print(pp2,fi0);
if not type([pp2,fi0],list(numeric)) then return 'procname(_passed)' end if;
res := dsolve(subs(sigma=pp2,phi0=fi0,{eq1=0,eq2=0,eq3=0,u(1)=-lambda*D(u)(1),u(0)=lambda*D(u)(0),phi(0)=phi0,T(0)=0}), numeric,output=listprocedure,initmesh=10, continuation=cc);
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)]));
INT0:=evalf(Int((abs(F0(eta)),eta=0..1)));
INT10:=evalf(Int(abs(F0(eta))*F1(eta),eta=0..1));
a[1]:=evalf(Int(F0(eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf),eta=0..1));
#a[1]:=evalf(Int((F0(eta),eta=0..1)));
a[2]:=(INT10/INT0-Phiavg)/Phiavg; #relative
[a[1],a[2]]
end proc:
Q1:=proc(pp2,fi0) Q(_passed)[1] end proc;
Q2:=proc(pp2,fi0) Q(_passed)[2] end proc;
proc(pp2, fi0)  ...  end;
proc(pp2, fi0)  ...  end;
#Q(116,0.0041);
#tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[130,0.01]);
#tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[43.55,0.39]);
tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[5.65,0.00036]);
#tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[12,0.003]); # khoob ba 1
#tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[5,0.01]);
                  HFloat(5.65), HFloat(3.6e-4)
           HFloat(5.650000070103341), HFloat(3.6e-4)
           HFloat(5.65), HFloat(3.600105456508193e-4)
     HFloat(29.63242379055208), HFloat(0.0205927592420527)
    HFloat(12.803902258015825), HFloat(0.006395385884750864)
    HFloat(12.803902403534572), HFloat(0.006395385884750864)
    HFloat(12.803902258015825), HFloat(0.00639539649402585)
   HFloat(12.804004931505949), HFloat(0.0063954867657199386)
    HFloat(12.804107604996073), HFloat(0.006395587646689013)
    HFloat(12.80400483062498), HFloat(0.006498160255844027)
    HFloat(12.803902157134855), HFloat(0.006498059374874952)
   HFloat(-1.0206939292143726), HFloat(-3.32764179807047e-4)
   HFloat(-1.0206939079125088), HFloat(-3.32764179807047e-4)
   HFloat(-1.0206939292143726), HFloat(-3.327536344433438e-4)
    HFloat(18.749500943683863), HFloat(0.01993840615828979)
    HFloat(3.9953780262640484), HFloat(0.00481041471606933)
     HFloat(6.166152606930136), HFloat(0.00703619658484674)
    HFloat(7.3193201827812295), HFloat(0.008218585352824569)
Error, (in Optimization:-LSSolve) complex value encountered
sigma:=tempe[2](1);
                          tempe[2](1)
phi0:=tempe[2](2);
                          tempe[2](2)
with(plots):

res2 := dsolve({eq1=0,eq2=0,eq3=0,u(1)=-lambda*D(u)(1),u(0)=lambda*D(u)(0),phi(0)=phi0,T(0)=0}, numeric,output=listprocedure,continuation=cc);
Error, (in dsolve/numeric/process_input) boundary conditions specified at too many points: {0, 1, 2}, can only solve two-point boundary value problems
G0,G1,G2:=op(subs(res2,[u(eta),phi(eta),T(eta)])):
ruu:=evalf((Int(abs(G0(eta))*(G1(eta)*rhop+(1-G1(eta))*rhobf ),eta=0..zet)))/(Phiavg*rhop+(1-Phiavg)*rhobf);
phb:=evalf((Int(abs(G0(eta))*G1(eta),eta=0..1))) / evalf((Int(abs(G0(eta)),eta=0..1))) ;
TTb:=evalf(Int(abs(G0(eta))*G2(eta)*(G1(eta)*rhop*cp+(1-G1(eta))*rhobf*cbf ),eta=0..1))/evalf(Int(abs(G0(eta))*(G1(eta)*rhop*cp+(1-G1(eta))*rhobf*cbf ),eta=0..1));
Error, invalid input: subs received res2, which is not valid for its 1st argument
                /  /1.                                        \
                | |                                           |
0.0008538922115 | |    |G0(eta)| (2881.8 G1(eta) + 998.2) deta|
                | |                                           |
                \/0.                                          /
                    /1.                       
                   |                          
                   |    |G0(eta)| G1(eta) deta
                   |                          
                  /0.                         
                  ----------------------------
                        /1.                   
                       |                      
                       |                      
                       |    |G0(eta)| deta    
                      /                       
                       0.                     
                                                              /Int(
                              1                               |     
------------------------------------------------------------- |     
  /1.                                                         |     
 |                                                            \     
 |              /             6                       6\            
 |    |G0(eta)| \-1.1752324 10  G1(eta) + 4.1744724 10 / deta       
/                                                                   
 0.                                                                 

                    /             6                       6\ , eta = 0. .. 1.)
  |G0(eta)| G2(eta) \-1.1752324 10  G1(eta) + 4.1744724 10 /                  

  \
  |
  |
  |
  /
#rhouu:=evalf((Int((G1(eta)*rhop+(1-G1(eta))*rhobf)*G0(eta),eta=0..1)));

odeplot(res2,[[eta,u(eta)/ruu],[eta,phi(eta)/phb],[eta,T(eta)/TTb]],0..1);
#odeplot(res2,[[eta,u(eta)],[eta,phi(eta)],[eta,T(eta)]],0..1);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
rhou:=evalf((Int(abs(G0(eta))*(G1(eta)*rhop+(1-G1(eta))*rhobf ),eta=0..zet))):

Nub:=(1/G2(1))*(((1+a[k1]*abs(G1(0))+b[k1]*abs(G1(0))^2)/(1+a[k1]*Phiavg+b[k1]*Phiavg^2)));
                0.6905123602 (1 + 7.47 |G1(0)|)
                -------------------------------
                             G2(1)             
(rhs(res2(0.0000000000001)[3])-rhs(res2(0)[3]))/0.0000000000001;
Error, invalid input: rhs received res2(0.1e-12)[3], which is not valid for its 1st argument, expr
sigma;
                          tempe[2](1)
NBT;
                              0.5
>

the above code has been worked for NBT=0.6 and higher, whereas as NBT decreases, the code doesnt converge easily.

How can I fix this problem?

Thanks for your attention in advance

Amir

Good afternoon sir.

I request your kind suggestion to the above cited question.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

I have two matrices.How to find matrix "x". Equation of x is given. I can evaluate the value of 'x' at a point. 

This is a Windows specific question. If I currently have the worksheet named "myworksheet.mw" in the directory "C:\projects" open in Maple, is there a command I can execute to retreive the path "C:/projects" as a string? 

assume f:= x^2*y^3/z^7

would like to get [x^2, y^3, z^(-7)]