These are Posts that have been published by Markiyan Hirnyk
The purpose of this post is the investigation of the connection between the connectivity of an undirected graph and the numbers of its vertices and edges with help of the GraphTheory package.
The reader is referred to http://en.wikipedia.org/wiki/Graph_theory and to ?GraphTheory for info.
This is an effective method of solving systems of N nonlinear and nonalgebraic equations in N+1 real-valued variables:
F(x)=0, where F=(f1,f2,..., fN) and x=(x1,x2,...,xN+1). (1)
The Maple dsolver is very powerful, but everything has advantages and disadvantages. I was recently asked the following question.
Let us consider the system of ODEs
>restart; sys := [diff(y(x), x) = -(4*cos(x)*y(x)+z(x)*cos(x)^2+3*z(x))/(sin(x)*(cos(x)^2-9)),
>diff(z(x), x) = -(y(x)*cos(x)^2+3*y(x)+4*z(x)*cos(x))/(sin(x)*(cos(x)^2-9))]:
>y1 := C*(cos(x)+1)^(1/2)/(cos(x)+3)^(1/2)+C*(1-cos(x))^(1/2)/(3-cos(x))^(1/2):
>z1 := -C[1...
It is the first time I post a Maple bug in MaplePrimes because I use to submit an SCR.
There is a serious reason to do so. Let us look at the output of
> implicitplot(sqrt(x^2+y^2)-sqrt((x-4)^2+(y-3)^2) = 5, x = -20 .. 20, y = -20 .. 20,
numpoints = 10^6, thickness = 5, scaling = constrained);
(both in Maple 13 and in Maple 16)
Starting from Maple 15, the useful ?plottools/getdata command is added. It tansforms a Maple plot to a Matrix. Unfortunately, the getdata command deals only with Maple plots. The question arises: "How to get a data from bmp, jpg, tiff, pcx, gif, png and wmf formats?" This is used in medicine and engineering. Such question was asked here
This is one of rank tests.
Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars).
The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.
In terms of levels of measurement, non-parametric methods result in "ordinal" data.
After the introduction to the topic let's turn to an example.
The following is the matter of so-called central limit theorems. We have the sum of random variables S:= ksi + ksi + .. ksi[n]. We know only that the number n is large, the variables are independent or weakly dependent, and each ksi[j] is small with respect to S in a certain sense.
By the central limit theorems it implies that S is close to the normal distribution.
Here is the procedure which illustrates the Lindeberg-Levi theorem ( see
I would like to pay attention to the article "Exploratory Experimentation and Computation" by David H. Bailey and Jonathan M. Borwein just published in Notices of AMS, 2011, V. 58, N 10, 1410-1419
( http://www.ams.org/notices/201110/rtx111001410p.pdf ) . It should be noted that Maple is one of the leading characters of this article.
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