MaplePrimes Questions

In dark matter cosmology the following integral in x  does not yet have an analytical solution. I report the integral in

Maple 2018 notation

int(1/sqrt((1+x)^3*a+(1-a)*(1+x)^(3+3*b)), x)

If someone has some smart idea is welcome

Dear Community,

I run a MapleSim model from Maple. The simulation runs fine giving me the correct graphical plots, but I wonder how could I obtain also the numerical values of the probes vs. time? Sorry I could not figure it out. A matrix format would be perfect: 1st column time, the other columns probe 1 .. n values vs. time. (Files attached)

Tx for the kind help in advance,

best regards

Andras

RunMapleSim.mw , RCNetwork.msim


 

with(Physics)

Setup(mathematicalnotation = true)

Setup(Coordinatesystem = (X = [x1, x2, x3, x4]), metric = -dx3^2*u22+2*dx3*dx4*u12-dx4^2*u11+dx1*dx3+dx2*dx4)

`* Partial match of  'Coordinatesystem' against keyword 'coordinatesystems'`

 

`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (x1, x2, x3, x4)}

 

`Systems of spacetime Coordinates are: `*{X = (x1, x2, x3, x4)}

 

[coordinatesystems = {X}, metric = {(1, 3) = 1/2, (2, 4) = 1/2, (3, 3) = -(diff(diff(u(X), x2), x2)), (3, 4) = Physics:-diff(diff(u(X), x1), x2), (4, 4) = -(diff(diff(u(X), x1), x1))}]

(1)

Setup(spacetimeindices = lowercaselatin)

u22 := diff(u(x1, x2, x3, x4), x2, x2)

Physics:-diff(Physics:-diff(u(X), x2), x2)

(2)

u12 := diff(u(x1, x2, x3, x4), x1, x2)

Physics:-diff(Physics:-diff(u(X), x1), x2)

(3)

u11 := diff(u(x1, x2, x3, x4), x1, x1)

Physics:-diff(Physics:-diff(u(X), x1), x1)

(4)

u24 := diff(u(x1, x2, x3, x4), x2, x4)

Physics:-diff(Physics:-diff(u(X), x2), x4)

(5)

u13 := diff(u(x1, x2, x3, x4), x1, x3)

Physics:-diff(Physics:-diff(u(X), x1), x3)

(6)

g_[]

Physics:-g_[a, b] = Matrix(%id = 18446745064427858870)

(7)

Define(W, quiet)

"W[~i,j,k,l]=1/(2)sqrt('g_[determinant]')g_[~i,~a]g_[~b,~c]LeviCivita[a,j,b,d]Weyl[~d,c,k,l]"

W[`~i`, j, k, l] = (1/2)*Physics:-g_[determinant]^(1/2)*Physics:-g_[`~a`, `~i`]*Physics:-g_[`~b`, `~c`]*Physics:-LeviCivita[a, b, d, j]*Physics:-Weyl[`~d`, c, k, l]

(8)

Define(W[`~i`, j, k, l] = (1/2)*Physics[g_][determinant]^(1/2)*Physics[g_][`~a`, `~i`]*Physics[g_][`~b`, `~c`]*Physics[LeviCivita][a, b, d, j]*Physics[Weyl][`~d`, c, k, l])

`Defined objects with tensor properties`

 

{Physics:-D_[a], Physics:-Dgamma[a], Physics:-Psigma[a], Physics:-Ricci[a, b], Physics:-Riemann[a, b, c, d], W[`~i`, j, k, l], Physics:-Weyl[a, b, c, d], Physics:-d_[a], Physics:-g_[a, b], Physics:-Christoffel[a, b, c], Physics:-Einstein[a, b], Physics:-KroneckerDelta[a, b], Physics:-LeviCivita[a, b, c, d], Physics:-SpaceTimeVector[a](X)}

(9)

W[definition]

W[`~e`, f, g, h] = (1/32)*16^(1/2)*Physics:-g_[`~a`, `~e`]*Physics:-g_[`~b`, `~c`]*Physics:-LeviCivita[a, b, d, f]*Physics:-Weyl[`~d`, c, g, h]

(10)

u11*u22-u12^2+u13+u24 = 0

diff(diff(u(X), x1), x3)+diff(diff(u(X), x2), x4)+(diff(diff(u(X), x2), x2))*(diff(diff(u(X), x1), x1))-(diff(diff(u(X), x1), x2))^2 = 0

(11)

u113 := diff(-u11*u22+u12^2-u24, x1)

-(diff(diff(diff(u(X), x1), x2), x4))-(diff(diff(u(X), x1), x1))*(diff(diff(diff(u(X), x1), x2), x2))-(diff(diff(u(X), x2), x2))*(diff(diff(diff(u(X), x1), x1), x1))+2*(diff(diff(u(X), x1), x2))*(diff(diff(diff(u(X), x1), x1), x2))

(12)

u123 := diff(-u11*u22+u12^2-u24, x2)

-(diff(diff(diff(u(X), x2), x2), x4))-(diff(diff(u(X), x1), x1))*(diff(diff(diff(u(X), x2), x2), x2))-(diff(diff(u(X), x2), x2))*(diff(diff(diff(u(X), x1), x1), x2))+2*(diff(diff(u(X), x1), x2))*(diff(diff(diff(u(X), x1), x2), x2))

(13)

u133 := diff(-u11*u22+u12^2-u24, x3)

-(diff(diff(diff(u(X), x2), x3), x4))-(diff(diff(diff(u(X), x2), x2), x3))*(diff(diff(u(X), x1), x1))-(diff(diff(u(X), x2), x2))*(diff(diff(diff(u(X), x1), x1), x3))+2*(diff(diff(u(X), x1), x2))*(diff(diff(diff(u(X), x1), x2), x3))

(14)

u134 := diff(-u11*u22+u12^2-u24, x4)

-(diff(diff(diff(u(X), x2), x4), x4))-(diff(diff(diff(u(X), x2), x2), x4))*(diff(diff(u(X), x1), x1))-(diff(diff(u(X), x2), x2))*(diff(diff(diff(u(X), x1), x1), x4))+2*(diff(diff(u(X), x1), x2))*(diff(diff(diff(u(X), x1), x2), x4))

(15)

u234 := diff(u(x1, x2, x3, x4), x2, x3, x4)

Physics:-diff(Physics:-diff(Physics:-diff(u(X), x2), x3), x4)

(16)

u223 := diff(u(x1, x2, x3, x4), x2, x2, x3)

Physics:-diff(Physics:-diff(Physics:-diff(u(X), x2), x2), x3)

(17)

u133 = -u11*u223-u113*u22+2*u12*u123-u234

-(diff(diff(diff(u(X), x2), x3), x4))-(diff(diff(diff(u(X), x2), x2), x3))*(diff(diff(u(X), x1), x1))-(diff(diff(u(X), x2), x2))*(diff(diff(diff(u(X), x1), x1), x3))+2*(diff(diff(u(X), x1), x2))*(diff(diff(diff(u(X), x1), x2), x3)) = -(diff(diff(diff(u(X), x2), x3), x4))-(-(diff(diff(diff(u(X), x1), x2), x4))-(diff(diff(u(X), x1), x1))*(diff(diff(diff(u(X), x1), x2), x2))-(diff(diff(u(X), x2), x2))*(diff(diff(diff(u(X), x1), x1), x1))+2*(diff(diff(u(X), x1), x2))*(diff(diff(diff(u(X), x1), x1), x2)))*(diff(diff(u(X), x2), x2))-(diff(diff(diff(u(X), x2), x2), x3))*(diff(diff(u(X), x1), x1))+2*(diff(diff(u(X), x1), x2))*(-(diff(diff(diff(u(X), x2), x2), x4))-(diff(diff(u(X), x1), x1))*(diff(diff(diff(u(X), x2), x2), x2))-(diff(diff(u(X), x2), x2))*(diff(diff(diff(u(X), x1), x1), x2))+2*(diff(diff(u(X), x1), x2))*(diff(diff(diff(u(X), x1), x2), x2)))

(18)

Weyl[`~i`, j, k, l, nonzero]+W[`~i`, j, k, l, nonzero]

Weyl[`~i`, j, k, l, nonzero]-W[`~i`, j, k, l, nonzero]

``

(19)

`in`(half*flat*metrics, 4*D)

``

NULL

NULL

 

I require one of these Weyl + W or Weyl - W (where W is Weyl tensor with hodge star operator, the equation may be found in my code) to be identically equal to zero. The computer will not recognise that it is identally equal unless i input the original p.d.e which I have, and I have also added some partial differentials up to the third order, maybe I need to include up to the fourth order? I am unsure what to add can someone please help me make this identically equal to zero! Thanks in advance for any help!

(I have put colon's after the equations Weyl+W and Weyl-W as the output was too long, but rest assured its not looking identically equal to zero!)
 

Download NEED_11.mw

restart;
ddesys := {diff(pred(t), t) = pred(t)*[prey(t)/(prey(t)+10)-2/3], diff(prey(t), t) = prey(t)*[2-(1/20)*prey(t-tau)]-prey(t)*[pred(t)/(prey(t)+10)]-10, pred(0) = 1, prey(0) = 1};
 

dsn := dsolve[eval(ddesys, tau = 0)];
plots[odeplot](dsn, [[t, prey(t), color = red], [t, pred(t), color = blue]], 0 .. 300, legend = [prey, pred], labels = [t, ""]);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution 

I do not understand what i mistake, please help me regarding this issue, thanks in advance

This is a question out of curiosity only ...

I can easily import a matrix from an Excel spreadsheet / source. Maple then displays matrix dimensions, data type, storage and order ... which is fine. Now - suppose I wished to import the standard matrix in question, with all entries displayed - can this be done?

 

I am working on a problem in geometry where I have ended up with a system of nonlinear ODEs in F and G where F and G are functions of a coordinate y, and A and B are both real constants.  I have included the worksheet where I am working on the equations.


Ric_Equations.mw
 

dsolve((2*d^2*F(Y)*F(y)*G(y)/dy^2-(d*F(y)/dy*(d*G(y)/dy))*F(y)+(n-3)*(d*F(y)/dy)^2*G(y))/(4*F(y)*G(y)^2) = A, -(3*(2*d^2*F(y)/dy^2-(d*F(y)/dy)^2*G(y)-(d*F(y)/dy*(d*G(y)/dy))*F(y)))/(F(y)^2*G(y)) = B)

Error, (in dsolve) expecting an ODE or a set or list of ODEs. Received (1/4)*(2*d^2*F(Y)*F(y)*G(y)/dy^2-d^2*F(y)^2*G(y)/dy^2+(n-3)*d^2*F(y)^2*G(y)/dy^2)/(F(y)*G(y)^2) = A

 

NULL

 

 I would like to solve these in as explicit a way as possible by obtaining expressions for F and G and was wondering how best to do this with Maple (it doesn't really matter if the explicit solutions are messy, as I just need to know that they exist and can be written down in some form).  I have tried using the dsolve command directly but I receive the error message which you can see above.

 

 

 

 

 

Consider A is an nxn binary matrix where n>1000. Assume that there is an integer k<100 such that the entries of the kth power of A, denoted A^k, are all positive integer numbers.  

My problem is that the computation of A^k takes too times and I want to ask: Is there some techniques in Maple for obtaining the matrix A^k. 

One technique that I am used is based on the boolean semiring with 1+1=1. In fact, I evaluate A^k until I reach the full-1 matrix. But the mentioned technique dose not effect the time of computation. 

For example consider the 1024*1024 binary matrix which is given as an attachment. It takes 2278 seconds to find out the entries of the 20th power of this matrix are all positive integer numbers.

I am used the following version of Maple 15. 
Thanks for any suggestions.

 Matrix.txt

Edition(1): The following command maybe useful. From the next command you can upload the given matrix in your worksheet and test it for my claim.

input := FileTools:-Text:-ReadFile("C:/Users/Desktop/Matrix.txt")

Sam := Sample(('Uniform')(10, 20), 30)

My question has two steps:

STEP 1:  The multiplication  of is defined as follows

 

if n<>l, then

.

if n=l and m<=s,

Question 1: I wrote a code for calculating the multiplication  of. Is it right?

The code for Step 1  

restart;

multiply:=proc(n,m,l,s) local g,a: 
a:=unapply(doublefactorial(2*j-1)/factorial(j),j):
g:=unapply((a(m-j)*a(j)*a(s-j)/a(m+s-j))*(2*m+2*s-4*j+1)/(2*m+2*s-2*j+1),j):

if n<>l then 0 else
sqrt((2*m+1)*(2*s+1))*2^(K/2-1).add((g(j)/sqrt(m+s-2*j+1/2))*phi[n, m+s-2*j],j=0..m) 
end if
end proc:
 
n:=2:
l:=2:
m:=1:
s:=1:
multiply(n,m,l,s);

when I compared the results which I got and the results which is given in the book as follows, I think it is right.

Step 2:

We know that the outer product matrix is calculated as follows 

  

We found the elements of the outer product matrix in Step 1. 

Question 2 : I want to write the elements which are derived in step 1 to the outer product matrix in step 2. In here, the outer product matrix is NxN matrix. N=(M+1).2^(K-1) where K, M are any integers.

Hello,

How I can take variation from left-hand side of  5, and reach to right-hand side of  5. After by using integral by part obtained  7?

Thank you

I use Maple 2015, is it possible to animate a standing wave as shown below?

 

 A working animation can be found on https://oceanservice.noaa.gov/facts/seiche.html

inequal({F__i*(1-e__0/k__b)/A__c+M__min__B/Z__t >= sigma__ti, .8*F__i*(1-e__0/k__t)/A__c-M__max__B/Z__b >= sigma__ts, .8*F__i*(1-e__0/k__b)/A__c+M__max__B/Z__t <= sigma__cs, F__i*(1-e__0/k__t)/A__c-M__min__B/Z__b <= sigma__ci, abs(e__0) <= `(e__0)__mp`}, 1/F__i = 0 .. 10, e__0 = -5 .. 5, color = "Niagara 2")
Error, (in plots:-inequal) invalid input: Plot:-Inequality expects its 2nd argument, r1, to be of type name = range(And(realcons, Not(infinity))), but received `1__`/F__i = 0 .. 10
 


 

restart

Loading Statistics

Sam := Sample(('Uniform')(10, 20), 10)

Sam := Vector[row](10, {(1) = 18.147236863931788, (2) = 19.057919370756192, (3) = 11.26986816293506, (4) = 19.133758561390195, (5) = 16.323592462254094, (6) = 10.975404049994095, (7) = 12.784982188670483, (8) = 15.468815192049838, (9) = 19.575068354342974, (10) = 19.648885351992767}, datatype = float[8])

(1)

``

a := min(Sam)

10.9754040499940952

(2)

b := max(Sam)

19.6488853519927673

(3)

M := int((Q-x)*f(x), x = 0 .. Q)

int((Q-x)*f(x), x = 0 .. Q)

(4)

N := int((x-Q)*f(x), x = Q .. b)

int((x-Q)*f(x), x = Q .. 19.6488853519927673)

(5)

Ecost := M*co+N*cs

(int((Q-x)*f(x), x = 0 .. Q))*co+(int((x-Q)*f(x), x = Q .. 19.6488853519927673))*cs

(6)

DCost := diff(Ecost, Q)

(int(f(x), x = 0 .. Q))*co+(int(-f(x), x = Q .. 19.6488853519927673))*cs

(7)

``

Df := max(Sam)-min(Sam)

8.67348130

(8)

NULL

Val := eval(DCost, [f(x) = 1/Df, co = 20, cs = 25])

5.188228168*Q-56.63494470

(9)

QStar := fsolve(Val, Q)

10.91604742

(10)

NULL

``

NULL

``


 

Download dummy_1.mw

I want to write a procedure P such that the input of P is a positive integer number n and the output of P is a random permutation of the numbers {1,2,..,n}. 

I know that there is a command in Maple 2017 such that the command produces the mentioned request (random permutation in the combinatoric package), but I should work with Maple 15 and there is no the random permutation command in Maple 15. 

One of the solutions that I am used is based on the random number and check that if the produced numbers are pairwise distinct or not. The problem of this method  is that for n>128, it takes too time to generate a random permutation of the length n.

Thanks for any suggestions. 

I'm trying to better understand the Black and Scholes model; which is a scalar function on (positive reals)^5.
a maplesoft worksheet defines it as

BS_Price=exp(-r*T)*(-(1/2)*erf((1/4)*sqrt(2)*(sigma^2*T-2*r*T+2*ln(K)-2*ln(S[0]))/(sigma*sqrt(T)))+1/2)

I am trying to understand the parameter vectors (r ,T,K,S[0],sigma) that give the same values of BS_Price - and particularly whether these form curves, closed curves, surfaces or similar.

Right now, I am not sure how to procede.

EDIT
I've just put together  a procedure that evaluates BS at points in R^5 - and i think i can move forward by using the curry or rcurry functions to get a 5d tensor of the values of BS, that i can start to look for patterns within.

BS_Price := proc (InterestRate, StockPrice, StrikePrice, Duration, Volatility) evalf(subs([r = InterestRate, S[0] = StockPrice, K = StrikePrice, T = Duration, sigma = Volatility], exp(-r*T)*(-(1/2)*erf((1/4)*sqrt(2)*(sigma^2*T-2*r*T+2*ln(K)-2*ln(S[0]))/(sigma*sqrt(T)))+1/2))) end proc

could anyone give me advice on doing this?
 

First 399 400 401 402 403 404 405 Last Page 401 of 2119