Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

I am coding a big module to solving my project : analyze function in math, but when I compile my module maple return "Error," but it doesn't tell me what error happened.

I check the maple help and it said:" If no msgString is given, error raises the most recently occurring exception" but I have no exception before. 

This is the pic of that error.

Thank for your help.

Hi, my dear friend,

i am solving 9 ODE with boundary conditionsNigam.mw

Eq1 := 2.*F1(eta)+diff(H1(eta), eta) = 0

2.*F1(eta)+diff(H1(eta), eta) = 0

(1)

Eq2 := F1(eta)^2-G1(eta)^2+(diff(F1(eta), eta))*H1(eta)-(diff(F1(eta), eta, eta)) = 0

F1(eta)^2-G1(eta)^2+(diff(F1(eta), eta))*H1(eta)-(diff(diff(F1(eta), eta), eta)) = 0

(2)

Eq3 := 2*F1(eta)*G1(eta)+H1(eta)*(diff(G1(eta), eta))-(diff(G1(eta), eta, eta)) = 0

2*F1(eta)*G1(eta)+H1(eta)*(diff(G1(eta), eta))-(diff(diff(G1(eta), eta), eta)) = 0

(3)

Eq4 := 4*F1(eta)*F3(eta)+H3(eta)*(diff(F1(eta), eta))+H1(eta)*(diff(F3(eta), eta))-2*G1(eta)*G3(eta)-2.*F1(eta)^2-1.5*H1(eta)-(diff(F3(eta), eta, eta)) = 0

4*F1(eta)*F3(eta)+H3(eta)*(diff(F1(eta), eta))+H1(eta)*(diff(F3(eta), eta))-2*G1(eta)*G3(eta)-2.*F1(eta)^2-1.5*H1(eta)-(diff(diff(F3(eta), eta), eta)) = 0

(4)

Eq5 := 2*F3(eta)*G1(eta)+4*F1(eta)*G3(eta)+H3(eta)*(diff(G1(eta), eta))-H1(eta)*(diff(G3(eta), eta))-2*F1(eta)*G1(eta)-1.5*H1(eta)*(diff(G1(eta), eta))-(diff(G3(eta), eta, eta)) = 0

2*F3(eta)*G1(eta)+4*F1(eta)*G3(eta)+H3(eta)*(diff(G1(eta), eta))-H1(eta)*(diff(G3(eta), eta))-2*F1(eta)*G1(eta)-1.5*H1(eta)*(diff(G1(eta), eta))-(diff(diff(G3(eta), eta), eta)) = 0

(5)

Eq6 := 4.*F3(eta)+diff(H3(eta), eta) = 0

4.*F3(eta)+diff(H3(eta), eta) = 0

(6)

Eq7 := 6*F1(eta)*F5(eta)-6*F1(eta)*F3(eta)+3.*F3(eta)^2+H1(eta)*(diff(F5(eta), eta))+H3(eta)*(diff(F3(eta), eta))+H5(eta)*(diff(F1(eta), eta))-1.5*(H1(eta)*(diff(F3(eta), eta))+H3(eta)*(diff(F1(eta), eta)))-G3(eta)^2-2*G1(eta)*G5(eta)-(diff(F5(eta), eta, eta)) = 0

6*F1(eta)*F5(eta)-6*F1(eta)*F3(eta)+3.*F3(eta)^2+H1(eta)*(diff(F5(eta), eta))+H3(eta)*(diff(F3(eta), eta))+H5(eta)*(diff(F1(eta), eta))-1.5*H1(eta)*(diff(F3(eta), eta))-1.5*H3(eta)*(diff(F1(eta), eta))-G3(eta)^2-2*G1(eta)*G5(eta)-(diff(diff(F5(eta), eta), eta)) = 0

(7)

Eq8 := 6*G5(eta)*F1(eta)+2*G1(eta)*F5(eta)+4*G3(eta)*F3(eta)-4*F1(eta)*G3(eta)-2*F3(eta)*G1(eta)+H1(eta)*(diff(G5(eta), eta))-1.5*(H1(eta)*(diff(G3(eta), eta))+H3(eta)*(diff(G1(eta), eta)))+H3(eta)*(diff(G3(eta), eta))+H5(eta)*(diff(G1(eta), eta))-(diff(G5(eta), eta, eta)) = 0

6*G5(eta)*F1(eta)+2*G1(eta)*F5(eta)+4*G3(eta)*F3(eta)-4*F1(eta)*G3(eta)-2*F3(eta)*G1(eta)+H1(eta)*(diff(G5(eta), eta))-1.5*H1(eta)*(diff(G3(eta), eta))-1.5*H3(eta)*(diff(G1(eta), eta))+H3(eta)*(diff(G3(eta), eta))+H5(eta)*(diff(G1(eta), eta))-(diff(diff(G5(eta), eta), eta)) = 0

(8)

Eq9 := 6.*F5(eta)+F3(eta)+diff(H5(eta), eta) = 0

6.*F5(eta)+F3(eta)+diff(H5(eta), eta) = 0

(9)

bcs1 := F1(0) = 0, F3(0) = 0, F5(0) = 0

F1(0) = 0, F3(0) = 0, F5(0) = 0

(10)

bcs2 := G1(0) = 1, G3(0) = 0, G5(0) = 0

G1(0) = 1, G3(0) = 0, G5(0) = 0

(11)

bcs3 := H1(0) = 0, H3(0) = 0, H5(0) = 0

H1(0) = 0, H3(0) = 0, H5(0) = 0

(12)

bcs4 := F1(10) = 0, F3(10) = 0, F5(10) = 0

F1(10) = 0, F3(10) = 0, F5(10) = 0

(13)

bcs5 := G1(10) = 0, G3(10) = 0, G5(10) = 0

G1(10) = 0, G3(10) = 0, G5(10) = 0

(14)

R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, Eq7, Eq8, Eq9, bcs1, bcs2, bcs3, bcs4, bcs5}), [F1(eta), F3(eta), F5(eta), G1(eta), G3(eta), G5(eta), H1(eta), H3(eta), H5(eta)], numeric, output = listprocedure)

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

``


Maple Worksheet - Error

Failed to load the worksheet 

Download Nigam.mwNigam.mw

then i got this error

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

i dont know where i need to change.. could you help me..

Dear Maple users,

I have very interesting problem with evaluating of only symbolic equations.

The problem is: (In document mode)
When I try to evaluate all numeric values for example typing 1+2 and press Enter it successfuly evaluates 3.
But when I try to evaluate symbolic values for example x + y nothing happens.

I tried lots of things to solve this, but no luck.
Shortly if the equation contains only numbers it evaluates successfuly.
And if the equation contains one or more symbolic variables like (x, y, z, variable1, test1), it does nothing.

What could be the problem?
 

(Because of this problem I cannot use the document mode, so I'm using the worksheet mode. Worksheet mode works good, but sometimes it is not calculating like document mode)

 

 

System is Windows 7 x64
Maple 2016
8 x 3.50GHz Xeon CPU
128 GB RAM
Windows Language is Turkish, (I tried with also USA English, but no luck either)
Keyboard is Turkish TR, (I tried with also US English, but no luck either)

Hello everyone.

Please can I meet with Computational or/and Numerical anlysts that have worked or working on the algorihms particularly (Runge Kutta Nystrom, Block multistep methods including hybrid and Block Boundaru Value methods) for the solution of both IVP and BVP.

I will appreciante if I can learn from them and possibly collaborate with them. Thank you in anticipation of your positive response.

Find and classify all the critical point(s) for 

f(x,y)=x3 + 3xy2 - 15x + y3 - 15y .

I need a help from someone who knows the GRTensor commands.

If you create a tensor of rank 2 using the grdef ("F {(a) (b)}"). Until then, okay!

However, I would like to define each of the 16 tensor components and I do not know how to do.

Could someone help me?

Thank you very much!

Please I am having problem with this code particularly the last subroutine

#subroutine 1

restart;
Digits:=30:

f:=proc(n)
    -25*y[n]+12*cos(x[n]):
end proc:

#subroutine 2

e1:=y[n+4] = -y[n]+2*y[n+2]+((1/15)*h^2+(2/945)*h^2*u^2+(1/56700)*h^2*u^4-(1/415800)*h^2*u^6-(167/833976000)*h^2*u^8-(2633/245188944000)*h^2*u^10-(2671/5557616064000)*h^2*u^12-(257857/13304932857216000)*h^2*u^14-(3073333/4215002729166028800)*h^2*u^16)*f(n)+((16/15)*h^2-(8/945)*h^2*u^2-(1/14175)*h^2*u^4+(1/103950)*h^2*u^6+(167/208494000)*h^2*u^8+(2633/61297236000)*h^2*u^10+(2671/1389404016000)*h^2*u^12+(257857/3326233214304000)*h^2*u^14+(3073333/1053750682291507200)*h^2*u^16)*f(n+1)+((26/15)*h^2+(4/315)*h^2*u^2+(1/9450)*h^2*u^4-(1/69300)*h^2*u^6-(167/138996000)*h^2*u^8-(2633/40864824000)*h^2*u^10-(2671/926269344000)*h^2*u^12-(257857/2217488809536000)*h^2*u^14-(3073333/702500454861004800)*h^2*u^16)*f(n+2)+((16/15)*h^2-(8/945)*h^2*u^2-(1/14175)*h^2*u^4+(1/103950)*h^2*u^6+(167/208494000)*h^2*u^8+(2633/61297236000)*h^2*u^10+(2671/1389404016000)*h^2*u^12+(257857/3326233214304000)*h^2*u^14+(3073333/1053750682291507200)*h^2*u^16)*f(n+3)+((1/15)*h^2+(2/945)*h^2*u^2+(1/56700)*h^2*u^4-(1/415800)*h^2*u^6-(167/833976000)*h^2*u^8-(2633/245188944000)*h^2*u^10-(2671/5557616064000)*h^2*u^12-(257857/13304932857216000)*h^2*u^14-(3073333/4215002729166028800)*h^2*u^16)*f(n+4):

e2:=y[n+3] = -y[n+1]+2*y[n+2]+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(n)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(n+1)+((97/120)*h^2-(31/10080)*h^2*u^2-(67/302400)*h^2*u^4-(109/8870400)*h^2*u^6-(18127/31135104000)*h^2*u^8-(64931/2615348736000)*h^2*u^10-(9701/9880206336000)*h^2*u^12-(20832397/567677135241216000)*h^2*u^14-(11349439/8646159444443136000)*h^2*u^16)*f(n+2)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(n+3)+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(n+4):

e3:=h*delta[n] = (-149/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[n]+(128/21+(32/245)*u^2+(2648/169785)*u^4+(1118492/695269575)*u^6+(14310311/87603966450)*u^8+(170868550903/10320623287474500)*u^10)*y[n+1]+(-107/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[n+2]+(-(67/1260)*h^2+(1241/198450)*h^2*u^2+(277961/366735600)*h^2*u^4+(26460409/333729396000)*h^2*u^6+(1363374533/168199615584000)*h^2*u^8+(16323847966961/19815596711951040000)*h^2*u^10)*f(n)+((188/105)*h^2+(5078/99225)*h^2*u^2+(556159/91683900)*h^2*u^4+(51834031/83432349000)*h^2*u^6+(67782373/1078202664000)*h^2*u^8+(1854079193287/291405833999280000)*h^2*u^10)*f(n+1)+((31/90)*h^2+(341/33075)*h^2*u^2+(79361/61122600)*h^2*u^4+(23456627/166864698000)*h^2*u^6+(1228061399/84099807792000)*h^2*u^8+(14797833720283/9907798355975520000)*h^2*u^10)*f(n+2)+(-(4/105)*h^2-(46/14175)*h^2*u^2-(809/1871100)*h^2*u^4-(27827/567567000)*h^2*u^6-(637171/122594472000)*h^2*u^8-(33500737/62523180720000)*h^2*u^10)*f(n+3)+((1/252)*h^2+(23/28350)*h^2*u^2+(809/7484400)*h^2*u^4+(27827/2270268000)*h^2*u^6+(637171/490377888000)*h^2*u^8+(33500737/250092722880000)*h^2*u^10)*f(n+4):

e4:=y[3] = -y[1]+2*y[2]+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(0)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(1)+((97/120)*h^2-(31/10080)*h^2*u^2-(67/302400)*h^2*u^4-(109/8870400)*h^2*u^6-(18127/31135104000)*h^2*u^8-(64931/2615348736000)*h^2*u^10-(9701/9880206336000)*h^2*u^12-(20832397/567677135241216000)*h^2*u^14-(11349439/8646159444443136000)*h^2*u^16)*f(2)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(3)+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(4):

e5:=h*delta[0] = (-149/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[0]+(128/21+(32/245)*u^2+(2648/169785)*u^4+(1118492/695269575)*u^6+(14310311/87603966450)*u^8+(170868550903/10320623287474500)*u^10)*y[1]+(-107/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[2]+(-(67/1260)*h^2+(1241/198450)*h^2*u^2+(277961/366735600)*h^2*u^4+(26460409/333729396000)*h^2*u^6+(1363374533/168199615584000)*h^2*u^8+(16323847966961/19815596711951040000)*h^2*u^10)*f(0)+((188/105)*h^2+(5078/99225)*h^2*u^2+(556159/91683900)*h^2*u^4+(51834031/83432349000)*h^2*u^6+(67782373/1078202664000)*h^2*u^8+(1854079193287/291405833999280000)*h^2*u^10)*f(1)+((31/90)*h^2+(341/33075)*h^2*u^2+(79361/61122600)*h^2*u^4+(23456627/166864698000)*h^2*u^6+(1228061399/84099807792000)*h^2*u^8+(14797833720283/9907798355975520000)*h^2*u^10)*f(2)+(-(4/105)*h^2-(46/14175)*h^2*u^2-(809/1871100)*h^2*u^4-(27827/567567000)*h^2*u^6-(637171/122594472000)*h^2*u^8-(33500737/62523180720000)*h^2*u^10)*f(3)+((1/252)*h^2+(23/28350)*h^2*u^2+(809/7484400)*h^2*u^4+(27827/2270268000)*h^2*u^6+(637171/490377888000)*h^2*u^8+(33500737/250092722880000)*h^2*u^10)*f(4):

 

#subroutine 3

 


inx:=0:
ind:=0:
iny:=1:
h:=Pi/4.0:
n:=0:
omega:=5:
u:=omega*h:
N:=solve(h*p = 500*Pi/2, p):

c:=1:
for j from 0 to 5 do
    t[j]:=inx+j*h:
end do:
#e||(1..6);
vars:=y[n+1],y[n+2],y[n+3],delta[n],y[n+4]:

printf("%6s%15s%15s%15s\n",
    "h","Num.y","Ex.y","Error y");
for k from 1 to N do

    par1:=x[0]=t[0],x[1]=t[1],x[2]=t[2],x[3]=t[3],x[4]=t[4],x[5]=t[5]:
    par2:=y[n]=iny,delta[n]=ind:
   

res:=eval(<vars>, fsolve(eval({e||(1..5)},[par1,par2]), {vars}));

    for i from 1 to 5 do
        exy:=eval(0.5*cos(5*c*h)+0.5*cos(c*h)):
        printf("%6.5f%17.9f%15.9f%13.5g\n",
        h*c,res[i],exy,abs(res[i]-exy)):
        
        c:=c+1:
    end do:
    iny:=res[5]:
    inx:=t[5]:
    for j from 0 to 5 do
        t[j]:=inx + j*h:
    end do:
end do:

 

 

 

 

Hi, I am trying to solve two nonlinear simultaneous equations with two unknown variables T & W. The Range of one variable T is from 0 to 0.4

When I use fsolve command to solve it, it gives me a solution in which T value is more than the specified range so it is an invalid solution for me. When I specify the range of T from 0 to 0.4 in fsolve, it doesn't give any solution.

Solve command in maple also doesn't give any solution and just shows evaluating.

My question is how can I get all the roots of unknown variables (T & W), which can solve these two simultaneous equations.

The maple worksheet is attached. 

.maple_simul.equation.mw

Hello

I solved a complex PDE equation in maple but I can not plot the output.

The manner was like bellow:

PDE := [diff(A(z, t), z)+(1/2)*alpha*A(z, t)+(I*beta[2]*(1/2))*(diff(A(z, t), t, t))-(I*beta[3]*(1/6))*(diff(A(z, t), t, t, t))-I*(GAMMA(omega[0]))(abs(A(z, t))^2*A(z, t)) = 0];
IBC := {(D[2](A))(z, 1), A(0, t) = -sin(2*Pi*t), A(z, 0) = sin(2*Pi*z), (D[2](A))(z, 0) = 2*z};
pds := pdsolve(PDE, IBC, type = numeric, time = t, range = 0 .. 1);
pds:-plot3d(A(z, t)*conjugate(A(z, t)), t = 0 .. 1, z = 0 .. 10, shading = zhue, axes = boxed, labels = ["x", "t", "A(z,t)"], labelfont = [TIMES, ROMAN, 20], orientation = [-120, 40]);

It is solved but there is an error like:

Error, (in pdsolve/numeric/plot3d) unable to compute solution for z>INFO["failtime"]:
unable to store 11.2781250000000+4390.00000040000*I when datatype=float[8]

could you please help me?

what is the problem?

 

 

I have tried to compile a simple program looking for counterexamples to a conjecture by Goldbach that every odd number is a sum of a prime and twice a square. Stern gave the counterexamples 5777 and 5993 a long time ago, so this is mainly for instruction purposes.

My program

othergoldbachFCi:=proc(sieve::Array(1..10000,datatype=integer[4]))
   local i,j,M; 
   M:=10000;
   for i from 1 to M do
      if(sieve[i] mod 2=0) then 
         for j from 1 to iquo(M-i,2*i+1) do 
            sieve[i+j*(2*i+1)]:=2*iquo(sieve[i+j*(2*i+1)],2)+1;
         end do; 
         for j from 1 to floor(sqrt(M-i)) do 
            sieve[i+j*j]:=2+sieve[i+j*j] mod 2;  
         end do;
      else 
         if(sieve[i]<2) then 
            printf("%d is a counterexample\n",2*i+1); 
         end if; 
      end if; 
   end do; 
end proc;

works fine and compiles without problems. (I have to pass the array for the sieve because compiled program cannot declare memory, and it has to be 4 bytes even though I only need to use the lower 2 bit).  But the compiled version breaks with

   Error, (in compiledOGi) array index out of bounds

 

already in the first instance of the for loop. After a lot of trial and error I found out that if I replaced the line 

   sieve[i+j*j]:=2+sieve[i+j*j] mod 2;  

by

   temp:=iquo(sieve[i+j*j],2);
   sieve[i+j*j]:=2+(sieve[i+j*j]-2*temp);  

 

then the problem goes away and the compiled version works beautifully. It is not enough to do the mod 2 computation in temp, and not enough to replace mod by iquo in one line. 

This makes very little sense to me. Can anybody explain? I'm still using Maple 2016 and do not know if the issue has been resolved in Maple 2017.

 

Best,

Soren

 

Since I am a very recent Maple user, I do not know why I obtained a wrong answer with the following two comands:

Exp:= Psi(rho(x,t),theta(x,t));
                  Psi(rho(x, t), theta(x, t))
Exp1:= diff(Exp,t);
     / d           \                                  
     |--- rho(x, t)| D[1](Psi)(rho(x, t), theta(x, t))
     \ dt          /                                  

          / d             \                                
    + |--- theta(x, t)| Psi(rho(x, t) + 1, theta(x, t))
          \ dt            /                                
 

Can someone, please, help me?

Thank you.

 

In the below calculations, I get some solutions after solving the system. I am not sure if this is done assuming that all the values that are under the radicals are positive or indeed they are positive without further assumptions. I mean can I be sure that each given set of solution is a feasible solution? I suspect that Maple may ignore the assumptions sometimes.  

The following are the equation and plot3d of the minimal surface named Catalan:

Catalan := [alpha-sin(alpha)*cosh(beta), 1-cos(alpha)*cosh(beta), 4*sin((1/2)*alpha)*sinh((1/2)*beta)]
plot3d(Catalan, alpha = 0 .. 2*Pi, beta = -3 .. 3, scaling = constrained, title = "Catalan's surface", titlefont = [Courier, bold, 14])

I would like to color and thicken the edge of this surface to emphasize what I presume is the wire which frames the soap film which forms the surface.

Contourplot3d only shows contours at constant values of the z coordinate, however the plot3d display with style option "surface with line" clearly shows the surface's edge contour, among others.

Given the surface equation, is there any way to display the surface edge programmatically e.g. as a spacecurve? 

Without my knowingly changing any Maple parameters, the execution time values of variables appearing in the window displayed when a DEBUG statement is executed have recently started to be listed at the end of my worksheet.

If I have been doing extensive debugging this list can be quite lengthy and a nuisance to erase.

Why did this listing suddenly begin and how can I stop it?

 I'm thinking upload a technical paper into maple cloud, and i would like to keep the intellectual property of this paper or have a mention from the reader if they use it. Is it possible?. Thanks!

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