6899

Reputation

25

Badges

These are answers submitted by Markiyan Hirnyk

can be done as follows. We find the rational parametrization in t of the parabola and note that it is enough t=9*n with an arbitrary integer n to this end.

Unfortunately, the command

>isolve({(1/9)*t^2-(1/3)*t+367 = n, (2/27)*t^2-(1/9)*t+244 = k});

produces an incorrect answer

{k = (2/19683)*(4779+(1/1162261467)*_Z1)^2+673/3-(1/282429536481)*_Z1, n = (1/6561)*(4779+(1/1162261467)*_Z1)^2+308-(1/94143178827)*_Z1, t = 177+(1/31381059609)*_Z1}

Mathematica finds the complete answer

(C[1] \[Element] Integers && x == 369 - 9 C[1] + 9 C[1]^2 && y == 246 - 7 C[1] + 6 C[1]^2) || (C[1] \[Element] Integers && x == 367 + 3 C[1] + 9 C[1]^2 && y == 244 + C[1] + 6 C[1]^2)

Download integer_points_on_parabola.mw

See http://www.maplesoft.com/support/help/search.aspx?term=LQR and http://www.maplesoft.com/support/help/Maple/view.aspx?path=applications%2fDCMotor

to this end.

Following Igor Hlivka, the two-dimensional normal distribution is created and its characteristics are found. Specifying the parameters, a sample of the size 1000 is created and plotted. See section

in the Wiki article for math background.

Conditional PDF of

Download _adjusted_sample_1000.mw

It appears there is a lot of such polynomials :

Download polynomials.mw

Look in ?match for info.

Download another_way.mw

PS. The match command works in several dimensions too, whereas the solve,identity command works in one-dimensional case only.

Specifying the parameters, it can be solved with the DirectSearch package which should be downloaded from http://www.maplesoft.com/applications/view.aspx?SID=101333 and installed in your Maple >=13.

restart; A := eval(-(((beta*eta^2-(1/2)*beta+1)*p^2-(1/2)*beta^3)*KummerM(((-beta+2)*p^2-beta^3)/(4*p^2), 1, beta*eta^2)+(1/2)*KummerM(((-beta+6)*p^2-beta^3)/(4*p^2), 1, beta*eta^2)*((beta-2)*p^2+beta^3))*exp(-(1/2)*beta*eta^2)/(p^2*beta) = 0, [p = 1, eta = 1]);

DirectSearch:-SolveEquations([Re(eval(A, beta = a+I*b)), Im(eval(A, beta = a+I*b))], {a = -5 .. 5, b = -5 .. 5}, AllSolutions, number = 300,solutions=10);

Ten roots out of 29 roots in the square are found. In order to get more solutions, one should increase the value of the solutions option.

Download roots.mw

One should exploit the Newton-Leibnitz formula:

Download direct_calculation.mw

In fact, this is an improvement of the sum command: see ?sum for info. There is _EnvFormal option to this end. For example,

Download improvement.mw

Another way is

>restart;sum((1/2)*2^(-k)*(-3)^k*x^k, k = 0 .. infinity)assuming abs(x)<1/ 6;

1/(3*x+2)

The DirectSearch package should be downloaded from http://www.maplesoft.com/applications/view.aspx?SID=101333 and installed in your Maple (>=13). Here is my solution done with the DirectSearch. A more powerful comp is required to obtain more points by increasing the number option.

Download By_DS.mw

Hope this will be useful for you.

This can be done as follows.

Download 5steps.mw

Somewhat extending the Axel's suggestion, one can use

Download parametric=full.mw

J := int(arctan(x)*ln(1+1/x^2), x = 0 .. infinity);IntegrationTools:-Parts(J, ln(1+1/x^2)); (1/6)*Pi^2

This can be directly done by

One can take

N=

Download N.mw

Look in http://www.maplesoft.com/applications/view.aspx?SID=33406

and http://www.mapleprimes.com/posts/89226-WithOrthogonalExpansions

These links can be found by the "fourier" search in MaplePrimes at the top of this page.

You must be logged into your Facebook account in order to share via Facebook.

Click the button below to share this on Google+. A new window will open.

You must be logged in to your Twitter account in order to share. Click the button below to login (a new window will open.)

Please log-in to your MaplePrimes account.

Wrong Email/Password. Please try again.

Error occurred during PDF generation. Please refresh the page and try again