How should linearization a nonlinear equation with maple?

I'm trying to use the ExpectedValue function to get the next close value of a stock.

restart; with(Finance)

W := WienerProcess()

T := 1.0

S := SamplePath(W(t), t = 0 .. T, timesteps = 100, replications = 10^4)

A := S[1 .. 10^4, 50]

TI := 1

AN := 100 (Start Value)

sigma := 3.5 (volatility)

r := 0.5e-1    (interest)

ANF := AN*exp((r-(1/2)*sigma^2)*TI+sigma*W(TI))       (ANF: is the forecasting Value)

ExpectedValue(ANF, timesteps = 100, replications = 10^3)

Is this approach right?

Why it be like that and how to solve it ?

>restart;
> ODEtools[declare]((S, L, B)(t), prime = t);
         ODEtools[declare](S(t), L(t), B(t), prime = t)
> DE1 := diff(S(t), t) = -L*S*beta-`μS`+mu;
                    d                               
            DE1 := --- S(t) = -L S beta - μS + mu
                    dt                              
> DE2 := diff(L(t), t) = L*S*beta-(gamma+mu)*S;
                  d                                  
          DE2 := --- L(t) = beta S L - (gamma + mu) S
                  dt                                 
> DE3 := diff(B(t), t) = L*gamma-gamma*mu;
                      d                           
              DE3 := --- B(t) = L gamma - gamma mu
                      dt                          
> init_conds := S(0) >= 0, L(0) >= 0, B(0) >= 0;
         init_conds := 0 <= S(0), 0 <= L(0), 0 <= B(0)
> sys := {init_conds, diff(B(t), t) = L*gamma-gamma*mu, diff(L(t), t) = L*S*beta-(gamma+mu)*S, diff(S(t), t) = -L*S*beta-`&mu;S`+mu};

> sol := dsolve(sys, numeric, parameters = [mu, beta, gamma, S(t), L(t), B(t)], method = rkf45);

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

> sol(parameters = [mu = .234, beta = 2.345, gamma = 5.678, S(t) = 6.678, L(t) = 6.789, B(t) = 7.123]);
           sol(parameters = [mu = 0.234, beta = 2.345, gamma = 5.678, S(t) = 6.678, L(t) = 6.789, B(t) = 7.123])

Is the following a bug? I am using Maple 2019  64 bit with latest Physics package 357 on windows 10.

Download bug2.mw

I want to find following NxN matrix P                                           (N=2^k.M where k and M are a positive integers)  

My Code Try: question.mw

restart:
with(LinearAlgebra):
interface(rtablesize=20):
k:=2:
M:=4:
N:=2^k*M: 
for i from 1 to M do
S:= (sqrt(2)/2^k)*Matrix(M,M, (i,j)-> `if`(`and`(i::odd,j=1) ,-1/(i*(i-2)),0)):   
end do:
C:= (1/2^k)*BandMatrix( [ [ seq(-1/(2*sqrt(2)*(i-1)*(i-3)), i=4..M)], [ 1, seq(0*i,i=1..M-1) ],[ seq(4/2*(i-3),i=2..M)]
                ]
              ); #I think the matrix C is not same in the question
     
Gen:=proc(K::posint,A,B)
  Matrix(scan=triangular[upper],[seq([A,seq(B,i=j..2^(K)-1)],j=1..2^(K))]);
end proc: 
P:=Gen(k,C,S);

question.mw

Hello,

Is there any way to make this kind of problem in Maple?

I have to find the intersection of subsets, and if there is no intersection then to multiply elements of the subsets. For example,

A={x6,x4,x2,x7,x8,x9,x10},  B={x2,x3,x5,x8} and C={x4,x9,x11,x12,x13}.

Now, the intersection of A and B is {x2}, after that, I don't have the intersection with C, so the solution is x2x4, x2x9, x2x11, x2x11 and x2x13.

Another solution is to make the intersection of A and C and it will be {x4,x9} and after that, I don't have the intersection with B so I have to multiply x4 and x9 with elements in B (obviously, the first solution is better because it has fewer terms)

Is something like this is possible to do in Maple and how?

Thanks in advance! 

Hello

I am using Maple to solve a couple of differential equations.  Here is what I did so far

k := 141/10000;
yB0 := 296/1000;
e := -148/1000;
Ff0 := 67844/1000;
Far0 := 323066/1000;
FB0 := 135688/1000;
P0 := 10;
x0 := 0;
a := 38/1000;
dsys:={diff(x(w),w)=(k*((yB0*p(w)*(1 - x(w)))/(1 + e*x(w)))^(1/3)*(Ff0/(Far0 + FB0)*p(w)*((Ff0/FB0 - 1/2*x(w))/(1 + e*x(w))))^(2/3))/FB0,
diff(p(w),w)=P0*(-a)/(2*p(w)/P0)*(1 + e*x(w)),x(0)=x0,p(0)=P0}:
dsn1:≔dsolve(dsys,numeric,[x(w),p(w)],stiff=true);

Maple returns neither an error message or a solution.   I am sure I have mistyped something or did not understand how dsolve works at all.  

Can you help me out?

Many thanks

Ed

PS. How to plot the solution?  

On CBS tv show Survivor S38E4, an interesting scenario arose. There was initially 2 teams comprising 6 persons (blue team) and 9 persons (yellow team). Then they decided to mix it up, and split it into 3 teams. Each player was randomly assigned a buff, (red, green or orange =3 colored buffs *5).= 3 teams of 5.

What was interesting was 5 out of the original 6 blue team are now in the new red team. 5 of the original yellow team are in the new green team and 4 of the original yellow team are in the new orange team. 

What is the chances of that happening?
A couple of attempts:

survivor_rand.mw

How i can generate P_r matrix when P_r = -x and x₀=-1 , x₁=-2/3 , x₂=-1/3 , and x₃=0 with the help loop?

Hi everybody:

I have one equation:

EQ := V^3-R*T*V^2/P-(B^2+P*B*R*T*sqrt(T)/(P-A))*V-A*B/(P*sqrt(T)) = 0;
how can I obtain these derivatives:

macros can be made to work like subs, you just need to know a few tricks to get it to work the same way.  macros just works in a slightly different manner and we can make it useful.

The difference is with subs, one has to keep specifying the substitution with each equation you want subbed, whereas macro will already have it defined.  As an example:

a := v^2*z^3 - 34/(5*x^2*sin(y*v^2)) + 36*v^2 - b*v^2 + 3^(v^2 - cos(v^2 + g))
                            

If we want to substitute h for v^2, then we would normally do this using subs

subs(v^2=h,a)
                          

however, we can also use macro

macro(v^2=h)
                                    

now it doesn't just automatically substitute those values so we need to coax maple a little bit.  We can do that by converting the equation to a string and parsing it.

parse(convert(a,string))
                     

so as you see we arrive at the same result.  Now there is a caveat using macro, if you've already defined a variable in a macro, subs will not work using the same variable sustitution - you first need to reset the variable in the macro back to itself. 

subs(v^2=h,a)
                      #doesn't work since the variable is defined in a macro

macro(v^2=v^2) #reset the variable in the macro

subs(v^2=h,a)
                         # now it works

we could also define a little procedure to simplify our typing, to have the macro variable work on our equation.

mvs:=proc(a) #macro variable substitution
  parse(convert(a,string));
end proc:

macro(v^2=h)
mvs(a)
            

now if we had some other existing equation before defining the macro
aa:=exp(v^2-sin(theta))+v^2*cos(theta)-1/x^sin(v^2-g)
                                   

we just have to simply apply our proc on the equation to apply the variable substitution
mvs(aa)
              

I just noticed with chagrin that one of my favorite menu commands, Edit -> Remove output -> From worksheet, is missing from Maple 2019's Standard GUI. Is there a keyboard command or toolbar item to replace it?

How can I plot Y in terms of X (Y is the vertical axis and X is the horizontal axis) in below equation with Maple?

X^3-24.478115*X^2/Y-(0.2038793409e-2+19.08455282*Y/(Y-97.539))*X-.2550630228/Y = 0

X:=0..50

Y:=0..1

How we can get matrix M with the help of loop?