MaplePrimes Questions

how i

Find the length of the curve in interval of x

How do i can find volume of solid of revolution formed when the closed loop of the curve is rotated about the x-axis?

Im trying to solve 12 equations with 12 variables but I can't solve. Please help and advise me to solve this problem. Iproject3.mw
project3.mw

 

 

 

Hi.

I am trying to set up an surface integral in maple. I have been trying with the Student[VectorCalculus] package.

 

I have also tried to use the task template for surface integral over a disk but somehow I mess up huge time.

I want the surface to be the wall of a cylindrical form and i want to integrate a disk that is perpendicular to the surface.

 

I have tried to find help online and in maple help center. If anyone would please take time to explain the syntax of the SurfaceInt command id be happy.

For example should my f be the partial of the surface as it is in the formula? How can i set it up to integrate a circle? I have read at the Student[VectorCalculus][int] help page to get the right synatax but had no luck. Do I for example have to change coors=polar?

and maybe more importantly does that command actually reflect the thing im trying to do? This is the formula for the kind of integral I want:

 

https://i.gyazo.com/f8604b64bf61a94d82a54c1f80cf6aa5.png

 

reference :

Question:Quantile function
Posted:
Mikhail Drugov 88 

 

In the reference above, Mikhail has raised a problem concerning the function Statistics:-Quantile.
A problem of the same kind exists for the function Mode.

In fact  Mode returns the value of the mode only for unimodal distributions ; but for "bimodal" distributions it does not work properly.
Theoritically the mode is the value where the PDF reaches its maximum maximorum. Except in very particular cases this maximum is unique, even if common language speaks of "bimodal distributions" instead of "two bumped distributions".

Here is an example of a two bumped distribution (Z) obtained by mixing two gaussians distributions.
It has two bumps (z=-1, z=2) but only one mode (z=-2).
It could be hopefully acceptable that Mode returns the {-2, 2} (even if only -2 is the true mode), but Mode returns also the value of z that minimizes PDF(Z, z), which is not correct at all.


 

restart:
with(Statistics):

X := RandomVariable(Normal(-2,1)):
Y := RandomVariable(Normal(2,1)):

r    := 0.4:
f__Z := unapply((1-r)*PDF(X,t)+r*PDF(Y,t), t);
Z    := Distribution(PDF=f__Z):

proc (t) options operator, arrow; .1692568750*2^(1/2)*exp(-(1/2)*(t+2)^2)+.1128379167*2^(1/2)*exp(-(1/2)*(t-2)^2) end proc

(1)

plot(PDF(Z,t), t=-4..4);

 

Mode(Z);

{-1.999102417, .1352239093, 1.997971857}

(2)

 


 

Download ProblemWithMode.mw

 

Hi, I have a big system with 27 polynomial equations in 16 unknowns: f_1=...=f_27=0.  I can store these equations but I cannot calculate a Grobner basis of the ideal  J generated by my polynomials (allocation problem) - I use the library "with(FGb)"-  What interests me is whether my system is minimal in the following sense.

If, for example,  I remove f_1, is the ideal generated by (f_2,...f_27)  J again ? That is to say, is f_1 in the ideal generated by f_2,...,f_27 ? I would like to get an answer "yes" or "no" for each removed  f_i.

My question: can we solve the problem above  without calculating a Grobner basis of J?

Thanks in advance.

 

 

 

 

 

I'm trying solve a problem with NLPSolve using procedures like constraints, but it say: Error, (in Optimization: -NLPSolve) constraints must be specified as a set or list of procedures. Theses constraints are inequality and equality.  How i can get procedures as a list or set?. Is there anyone to give a example of it?. Thanks!

I uploaded a test document to my private space in Maple Cloud and I now want to delete it. How does one do that?  Also I just put it in the public space and want to delete it from there.


 

diff(Q(t), t) = k*A*(T__1s(t)-T__2s(t))/d

diff(Q(t), t) = h__1(t)*A*(T__1(t)-T__1s(t))

diff(Q(t), t) = h__2(t)*A*(T__2s(t)-T__2(t))

Q(t) = m__1*c__p*(T__1i-T__1(t))

Q(t) = m__2*c__p*(T__2(t)-T__2i)

h__1(t) = k(T__1(t), T__1s(t))*(.825+.387*(g*h^3*c__p*beta(T__1(t), T__1s(t))*rho(T__1(t), T__1s(t))^2*(T__1(t)-T__1s(t))/(k(T__1(t), T__1s(t))*mu(T__1(t), T__1s(t))))^(1/6)/(1+(.492*k(T__1(t), T__1s(t))/(c__p*mu(T__1(t), T__1s(t))))^(9/16))^(8/27))^2/h

h__2(t) = k(T__2(t), T__2s(t))*(.825+.387*(g*h^3*c__p*beta(T__2(t), T__2s(t))*rho(T__2(t), T__2s(t))^2*(T__2s(t)-T__2(t))/(k(T__2(t), T__2s(t))*mu(T__2(t), T__2s(t))))^(1/6)/(1+(.492*k(T__2(t), T__2s(t))/(c__p*mu(T__2(t), T__2s(t))))^(9/16))^(8/27))^2/h

 

 

rho(T__1(t), T__1s(t)) = 999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4

beta(T__1(t), T__1s(t)) = -(4.216485*10^(-2)-7.097451*10^(-3)*(T__1(t)+T__1s(t))+2.63217825*10^(-5)*(T__1(t)+T__1s(t))^2-4.9518879*10^(-8)*(T__1(t)+T__1s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4)
mu(T__1(t), T__1s(t)) = 2.414*10^(247.8/(.5*(T__1(t)+T__1s(t))+133)-5)

k(T__1(t), T__1s(t)) = -9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949

 

 

rho(T__2(t), T__2s(t)) = 999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4

beta(T__2(t), T__2s(t)) = -(4.216485*10^(-2)-7.097451*10^(-3)*(T__2(t)+T__2s(t))+2.63217825*10^(-5)*(T__2(t)+T__2s(t))^2-4.9518879*10^(-8)*(T__2(t)+T__2s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4)
mu(T__2(t), T__2s(t)) = 2.414*10^(247.8/(.5*(T__2(t)+T__2s(t))+133)-5)

k(T__2(t), T__2s(t)) = -9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949

 

"`h__1`(t)=(-9.481411*10^(-6) (`T__1`(t)+`T__1s`(t))^(2)+2.1356735*10^(-3) (`T__1`(t)+`T__1s`(t))+0.5599920949)/(h) (0.825+(0.387 ((g h^(3) `c__p` (-(4.216485*10^(-2)-7.097451*10^(-3) (`T__1`(t)+`T__1s`(t))+2.63217825*10^(-5) (`T__1`(t)+`T__1s`(t))^(2)-4.9518879*10^(-8) (`T__1`(t)+`T__1s`(t))^(3))/(999.9399+2.1082425*10^(-2) (`T__1`(t)+`T__1s`(t))-1.77436275*10^(-3) (`T__1`(t)+`T__1s`(t))^(2)+0.438696375*10^(-5) (`T__1`(t)+`T__1s`(t))^(3)  -0.6189861563*10^(-8) (`T__1`(t)+`T__1s`(t))^(4))) (999.9399+2.1082425*10^(-2) (`T__1`(t)+`T__1s`(t))-1.77436275*10^(-3) (`T__1`(t)+`T__1s`(t))^(2)+0.438696375*10^(-5) (`T__1`(t)+`T__1s`(t))^(3)  -0.6189861563*10^(-8) (`T__1`(t)+`T__1s`(t))^(4))^(2) (`T__1`(t)-`T__1s`(t)))/((-9.481411*10^(-6) (`T__1`(t)+`T__1s`(t))^(2)+2.1356735*10^(-3) (`T__1`(t)+`T__1s`(t))+0.5599920949) 2.414*10^((247.8)/(0.5 (`T__1`(t)+`T__1s`(t))+133)-5)))^((1)/(6)))/((1+((0.492 (-9.481411*10^(-6) (`T__1`(t)+`T__1s`(t))^(2)+2.1356735*10^(-3) (`T__1`(t)+`T__1s`(t))+0.5599920949))/(`c__p` 2.414*10^((247.8)/(0.5 (`T__1`(t)+`T__1s`(t))+133)-5)))^((9)/(16)))^((8)/(27))))^(2)"

"`h__2`(t)=(-9.481411*10^(-6) (`T__2`(t)+`T__2s`(t))^(2)+2.1356735*10^(-3) (`T__2`(t)+`T__2s`(t))+0.5599920949)/(h) (0.825+(0.387 ((g h^(3) `c__p` (-(4.216485*10^(-2)-7.097451*10^(-3) (`T__2`(t)+`T__2s`(t))+2.63217825*10^(-5) (`T__2`(t)+`T__2s`(t))^(2)-4.9518879*10^(-8) (`T__2`(t)+`T__2s`(t))^(3))/(999.9399+2.1082425*10^(-2) (`T__2`(t)+`T__2s`(t))-1.77436275*10^(-3) (`T__2`(t)+`T__2s`(t))^(2)+0.438696375*10^(-5) (`T__2`(t)+`T__2s`(t))^(3)  -0.6189861563*10^(-8) (`T__2`(t)+`T__2s`(t))^(4))) (999.9399+2.1082425*10^(-2) (`T__2`(t)+`T__2s`(t))-1.77436275*10^(-3) (`T__2`(t)+`T__2s`(t))^(2)+0.438696375*10^(-5) (`T__2`(t)+`T__2s`(t))^(3)  -0.6189861563*10^(-8) (`T__2`(t)+`T__2s`(t))^(4))^(2) (`T__2s`(t)-`T__2`(t)))/((-9.481411*10^(-6) (`T__2`(t)+`T__2s`(t))^(2)+2.1356735*10^(-3) (`T__2`(t)+`T__2s`(t))+0.5599920949) 2.414*10^((247.8)/(0.5 (`T__2`(t)+`T__2s`(t))+133)-5)))^((1)/(6)))/((1+((0.492 (-9.481411*10^(-6) (`T__2`(t)+`T__2s`(t))^(2)+2.1356735*10^(-3) (`T__2`(t)+`T__2s`(t))+0.5599920949))/(`c__p` 2.414*10^((247.8)/(0.5 (`T__2`(t)+`T__2s`(t))+133)-5)))^((9)/(16)))^((8)/(27))))^(2)"

diff(Q(t), t) = k*A*(T__1s(t)-T__2s(t))/d, diff(Q(t), t) = A*(T__1(t)-T__1s(t))*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949)*(.825+.387*(((-g*h^3*c__p*(4.216485*10^(-2)-7.097451*10^(-3)*(T__1(t)+T__1s(t))+2.63217825*10^(-5)*(T__1(t)+T__1s(t))^2-4.9518879*10^(-8)*(T__1(t)+T__1s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4))*((999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4)^2))*(T__1(t)-T__1s(t))/(2.414*10^(247.8/(.5*(T__1(t)+T__1s(t))+133)-5)*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949)))^(1/6)/(1+((.492*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949))/(2.414*c__p*10^(247.8/(.5*(T__1(t)+T__1s(t))+133)-5)))^(9/16))^(8/27))^2/h, diff(Q(t), t) = A*(T__2s(t)-T__2(t))*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949)*(.825+.387*(((-g*h^3*c__p*(4.216485*10^(-2)-7.097451*10^(-3)*(T__2(t)+T__2s(t))+2.63217825*10^(-5)*(T__2(t)+T__2s(t))^2-4.9518879*10^(-8)*(T__2(t)+T__2s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4))*((999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4)^2))*(T__2s(t)-T__2(t))/(2.414*10^(247.8/(.5*(T__2(t)+T__2s(t))+133)-5)*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949)))^(1/6)/(1+((.492*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949))/(2.414*c__p*10^(247.8/(.5*(T__2(t)+T__2s(t))+133)-5)))^(9/16))^(8/27))^2/h, Q(t) = m__1*c__p*(T__1i-T__1(t)), Q(t) = m__2*c__p*(T__2(t)-T__2i)

diff(Q(t), t) = k*A*(T__1s(t)-T__2s(t))/d, diff(Q(t), t) = A*(T__1(t)-T__1s(t))*(-0.9481411000e-5*(T__1(t)+T__1s(t))^2+0.2135673500e-2*T__1(t)+0.2135673500e-2*T__1s(t)+.5599920949)*(.825+.387*(-.4142502071*g*h^3*c__p*(0.4216485000e-1-0.7097451000e-2*T__1(t)-0.7097451000e-2*T__1s(t)+0.2632178250e-4*(T__1(t)+T__1s(t))^2-0.4951887900e-7*(T__1(t)+T__1s(t))^3)*(999.9399+0.2108242500e-1*T__1(t)+0.2108242500e-1*T__1s(t)-0.1774362750e-2*(T__1(t)+T__1s(t))^2+0.4386963750e-5*(T__1(t)+T__1s(t))^3-0.6189861563e-8*(T__1(t)+T__1s(t))^4)*(T__1(t)-T__1s(t))/(10^(247.8/(.5*T__1(t)+.5*T__1s(t)+133)-5)*(-0.9481411000e-5*(T__1(t)+T__1s(t))^2+0.2135673500e-2*T__1(t)+0.2135673500e-2*T__1s(t)+.5599920949)))^(1/6)/(1+.4087338992*((-0.9481411000e-5*(T__1(t)+T__1s(t))^2+0.2135673500e-2*T__1(t)+0.2135673500e-2*T__1s(t)+.5599920949)/(c__p*10^(247.8/(.5*T__1(t)+.5*T__1s(t)+133)-5)))^(9/16))^(8/27))^2/h, diff(Q(t), t) = A*(T__2s(t)-T__2(t))*(-0.9481411000e-5*(T__2(t)+T__2s(t))^2+0.2135673500e-2*T__2(t)+0.2135673500e-2*T__2s(t)+.5599920949)*(.825+.387*(-.4142502071*g*h^3*c__p*(0.4216485000e-1-0.7097451000e-2*T__2(t)-0.7097451000e-2*T__2s(t)+0.2632178250e-4*(T__2(t)+T__2s(t))^2-0.4951887900e-7*(T__2(t)+T__2s(t))^3)*(999.9399+0.2108242500e-1*T__2(t)+0.2108242500e-1*T__2s(t)-0.1774362750e-2*(T__2(t)+T__2s(t))^2+0.4386963750e-5*(T__2(t)+T__2s(t))^3-0.6189861563e-8*(T__2(t)+T__2s(t))^4)*(T__2s(t)-T__2(t))/(10^(247.8/(.5*T__2(t)+.5*T__2s(t)+133)-5)*(-0.9481411000e-5*(T__2(t)+T__2s(t))^2+0.2135673500e-2*T__2(t)+0.2135673500e-2*T__2s(t)+.5599920949)))^(1/6)/(1+.4087338992*((-0.9481411000e-5*(T__2(t)+T__2s(t))^2+0.2135673500e-2*T__2(t)+0.2135673500e-2*T__2s(t)+.5599920949)/(c__p*10^(247.8/(.5*T__2(t)+.5*T__2s(t)+133)-5)))^(9/16))^(8/27))^2/h, Q(t) = m__1*c__p*(T__1i-T__1(t)), Q(t) = m__2*c__p*(T__2(t)-T__2i)

(1)

"(->)"

``

``

``

i have a system with 5 dif equations and five unknows. i have told to maple to solve it numerically with interactively solve comand (right cilck button). the window open like it normally does and i put values to my parameters, with an initial condition for the system (Q(0)=0). then i press numerically solve and that's all, the program just keep evaluating with no answer. i wait for 15 min, which i think is too much time, and got any answer yet.

hope you can help with this

thanks.. 
 

Download propuesta_transfer.mw

Hello

I have a procedure that builds an ideal from a specific set of polynomials and then calls the Groebner basis package to eliminate some of the variables.  Even though the procedure is running on a machine with 2 processors, 24 cores and 72 GB of ram, only one core has been used (and is always on a 100% usage).  Would the Grid Computing Toolbox be of some hope in this case?  If so,  how to insert the Grid commands so that Maple sends the calculations to the other cores (I find the document rather confusing)?   If I am talking non sense,  please let me know.

Many thanks

Ed

 

 

 

Hi guys,

I would like to compute the complex roots of the following equations

u*(BesselJ(0,u)^2 + BesselJ(1,u)^2) = 2 BesselJ(0,u)*BesselJ(1,u)

The function fsolve in Maple gives only 0. I was wondering whether other complex solutions could be obtained as well.

Your help is highly appreciated.

Thanks

Federiko

with(DifferentialGeometry):with(JetCalculus):
DGsetup([x],[u],E,5);
vars≔x,u,u[1],u[1,1],u[1,1,1];
PDEtools[declare](Q(vars));
TotalDiff(Q(vars),x);
TotalDiff(u[1,1],x);

 

Hi everyone,

Recently I came across the total differentiation command in the PDEtools. For its

documentation, I used the following link

http://www.maplesoft.com/support/help/Maple/view.aspx?path=DifferentialGeometry/JetCalculus/TotalDiff

Unfortunately, when I try to replicate this it did not work as expected. I am getting the total derivative of the expression to be zero. I do not understand where I am going wrong.

You can find my code above. I am also attaching the screen shot of my maple file.

I would really appreciate if someone could help me out. Thanks for your help.


 

is there a possibility to display the partial derivative of f(x,y) wrt. y as

and second order / cross-partials accordingly?

 

thx

jo

 

 

I have created several animated 3-d figures using Maple.  Exporting an animation as a gif file I find that with, for example, Quicktime, I can run the animation. However I cannot rotate the 3-d figures using Quicktime.  Is there some other way to make such animations available to people not having Maple, so they can rotate the figure as well as run the animation? I would appreciate any ideas about this.

The following program hangs on the last command and a hard restart is required. The computation of a 2 x 2 matrix times a 2-vector is not that hard. Any ideas as to what is happening?

Another question: if v is a vector that depends on x and y say why does
>solve(v=0,{x,y})
not work?

It should only take a few lines of code to change v=0 to the system {components of v = 0}

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