Hi,

Please can you give me a hand with numerical solving and visualising the partial differential wave equation with stochastic term eta(t), using methods of stochastic calculus?

diff(u(x, t), t $ 2) - (1+eta(t))*diff(u(x, t), x $ 2) = 0

I had a look at the "stochastic" package by Sasha Cyganowski, but couldn't find an example for stochastic pde.

Look forward to your help.

Thanks,

Dmitrii

Here is a known probability riddle:

A and B are two lists of 100 binary numbers:

A:=[0,1,0,1,0,1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0]:
B:=[0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,1,0]:

One was obtained by tossing a coin (1 for a head, 0 for a tail), and the other by a human, who was asked to simulate tossing a coin.

Question: which one comes from a human brain?
The standard answer: B was produced using a coin, because (among other things) the probabilty of obtaining a "000000" or "111111" is about 80%, but a humain brain tends to avoid such "simulations".

My Question: what (if any) statistical test can be used in Maple for an answer?
(I have tried ChiSquareSuitableModelTest but both lists were accepted).

# I solved the differential equation using a fourier series decomposting method. I found with the help of "Dsolve" the different expressions of the fourier constants and now I will apply the boundary conditions to find the expressions of its constants.

#this my boundary conditions

#this my system of equations

Recently Maple started freezing on me for a few minutes; after that it continues to work and then freezes again and so on (it does not so much freezes as it pauses).  I do not know what changed on my system (which is Windows 10) for this to happen.  I had been using Maple 2019 when this started and then upgraded to Maple 2020 but that did not solve my problem.

It does not seem to have to do with the type of computations I am doing.

I have problem with usage of solve for the solution of the system of six and eight symbolic equations. I need to get expressions for variables: R__xl, R__xs, R__xsi, R__zl, R__zs, R__zsi, dbeta__l(t), dbeta__s(t). I tried to find solution for 8 equations, but I got the message: Warning, solutions may have been lost. I thought that the system is non-linear and tried to solve it for six variables (R__xl, R__xs, R__zl, R__zs, R__zsi, R__xsi), in this case equations are linear, but Maple ignored the solve command and did not give a solution or error. Could someone help me with this problem?

Quasi-static.mw

Hello

I am not sure how to choose between Threads:-Seq and Grid:-Seq.  

The problem:  a procedure, proc1, that calls two other procedures, proc2 and proc3, verifies if a set of parameters fulfills a certain condition. Proc1, proc2 and proc3 are not part of Maple available functions.  

Right now I am using Grid:-Seq to return the result of applying proc1 to chunks of a thousand parameters.  I wonder whether I could use Thread:-Seq instead.   What are the advantages of using one instead of the other?  And when do I choose one over the other?  

I would appreciate if you could provide simple examples to explain the differences.  

Many thanks.

Ed

PS.  There is a problem with Grid:-Seq as reported in one of my previous questions.

Hi,

Maple 2017.3 has these problems which hamper my work with it. I shown three examples.

Example 1: Maple cannot recognize automatically that two complex numbers are equal:

[>eq1:=9*exp((1/9)*(5*I)*Pi)-9*exp((1/9)*(2*I)*Pi) = -8*exp((1/9)*(2*I)*Pi)+7*exp((1/9)*(5*I)*Pi)+exp((1/18)*(13*I)*Pi)*sqrt(3);

Here, lhs(eq1) and rhs(eq1) are in fact equal. Yes, evela(simplify(lhs(eq1)-rhs(eq1)) reduces to zero but not when solving equations (see Example 2).

Example 2:

[>sys1:=[_xx[1]+lhs(eq1),_xx[1]+rhs(eq1)];
[>solve(sys1,[_xx[1],_xx[2]]);

yields no answer.

Example 3:

[>alias(omega=RootOf(_Z^2+_Z+1));
[>rt:=(-1+I*sqrt(3))/2;

Maple fails to substitute the alias and recognize that rt=omega.

Any suggestion on a work-around problems 2 and 3 would be helpful.

Thanks,

Rafal Ablamowicz
www.math.tntech.edu/rafal/


 

I have load the new Physics-Version 678, but it is not active. How can I do this?

Here the output:

                            restart

                           version()

 User Interface: 1455132
         Kernel: 1455132
        Library: 1455132
       MapleIDE: 928330

                            1455132

                      interface(version)

Standard Worksheet Interface, Maple 2020.0, Windows 10, March 4

   2020 Build ID 1455132

                      kernelopts(version)

   Maple 2020.0, X86 64 WINDOWS, Mar 4 2020, Build ID 1455132

                       Physics:-Version()

The "Physics Updates" version in the MapleCloud is 678 and is

   the same as the version installed in this computer, created

   2020, May 20, 10:21 hours, found in the directory

   C:\Users\wgellien\maple\toolbox\Physics Updates\lib\

                            restart

                     Physics:-Version(678)

Warning, this package updates content shipped in a standard Maple install.  Use the 'restart' command to clear your session before using these commands.
Kernel(The "Physics Updates" version "678" is installed but is

   not active. The active version of Physics is within the

   library C:\Users\wgellien\maple\toolbox/Physics Updates/lib\P\

  hysics Updates.maple, created 2020, May 20, 14:46 hours),

  [The "Physics Updates" version "678" is installed but is not

   active. The active version of Physics is within the library

   C:\Users\wgellien\maple\toolbox/Physics Updates/lib\Physics

   Updates.maple, created 2020, May 20, 14:46 hours]

With kind regards

Wolfgang Gellien

Can a second plot be added to a plot generated by a plots[odeplot] command for the case below?

> dsn := dsolve(eval(ddesys, {beta = 4, gamma = 0.0478, sigma = 0.10,tau__1 = 1.1,tau__2 = 8.7}), numeric):

> plots[odeplot](dsn, [[t, S(t), color = green], [t, Ex(t), color = black], [t, Ix(t), color = blue],[t, R(t), color = red]],  0 .. 100, legend = [ S(t), Ex(t), Ix(t), R(t)], labels = [t,""] );
 

Beware!

In Maple 2019 we get the strange value

cos((Pi/2) -1e-12);
                                                  -10
                       -2.051033808 10   

In Maple 2020 we get the correct answer

cos(Pi/2-1e-12);
                                                                      -13
                9.999999999996916397514419 10   

That error in Maple 2019 certainly messed up quite a few of my calcualtions!

POSSIBILITIES OF USING OF COMPUTER IN MATHEMATICS

AND OTHER APPLICATIONS IN INCLUSIVE EDUCATION

Alsu Gibadullina, math teacher, math teacher

Secondary and high school # 57, Kazan, Russia

In recent years Russia actively promoted and implemented the so-called inclusive education (IE). According to the materials of Alliance of human rights organizations “Save the children”: "Inclusive or included education is the term used to describe the process of teaching children with special needs in General (mass) schools. In the base of inclusive education is the ideology that ensures equal treatment for everybody, but creates special conditions for children with special educational needs. Experience shows that any of the rigid educational system some part of the children is eliminated because the system is not ready to meet the individual needs of these children in education. This ratio is 15 % of the total number of children in schools and so retired children become separated and excluded from the overall system. You need to understand that children do not fail but the system excludes children. Inclusive approaches can support such children in learning and achieving success. Inclusive education seeks to develop a methodology that recognizes that all children have different learning needs tries to develop a more flexible approach to teaching. If teaching and learning will become more effective as a result of the changes that introduces Inclusive Education, all children will win (not only children with special needs)."

There are many examples of schools that have developed their strategy implementation of IE, published many theoretical and practical benefits of inclusion today. All of them have common, immaterial character. There is no description of specific techniques implementing the principles of IO in the teaching of certain disciplines, particularly mathematics. In this paper we propose a methodology that can be successfully used as in “mathematical education for everyone", also for the development of scientific creativity of children at all age levels of the school in any discipline.

According to the author, one of the most effective methodological tools for education is a computer mathematics (SCM, SSM). Despite the fact that the SCM were created for solving problems of higher mathematics, their ability can successfully implement them in the school system. This opinion is confirmed by more than 10–year-old author's experience of using the package Maple in teaching mathematics. At first it was just learning the system and primitive using its. Then author’s interactive demonstrations, e-books, programs of analytical testing were created by the tools packages. The experience of using the system Maple in teaching inevitably led to the necessity to teach children to work with it. At first worked a club who has studied  the principles of the package’s work, which eventually turned into a research laboratory for the use of computer technology. Later on its basis there was created the scientific student society (SSS) “GEODROMhic" which operates to this day. The main idea and the ultimate goal of SSS – individual research activities on their interests with the creation of the author electronic scientific journals through the use of computer mathematics Maple. The field of application of the package was very diverse: from mathematics to psychology and cultural phenomena. SSS’s activity is very high: they are constantly and successfully participate in intellectual high-level activities (up to international). Obviously, not every SSS’s member reaches high end result. However, even basic experience in scientific analysis, modeling, intelligent  using of the computer teaches the critical thinking skills, evokes interest to new knowledge, allows you to experience their practical value, gives rise to the development of creative abilities. As a result, the research activity improves intellectual culture, self-esteem and confidence, resistance to external negative influence. It should be noted, however, that members of the scientific societies are not largely the so-called "gifted", than ordinary teenagers with different level of intellectual development and mathematical training. With all this especially valuable is that the student is dealing with mathematical signs and mathematical models, which contributes to the development of mathematical thinking.

From 2007 to 2012. our school (№. 57 of Kazan) was the experimental platform of the Republican study SKM (Maple) and other application software in the system of school mathematical education under the scientific management of Professor Yu. G. Ignatyev of Kazan state University (KF(P)U).

Practical adaptation of computer mathematics and other useful information technologies to the educational process of secondary schools passed and continues to work in the following areas:

1. The creation of a demonstration support of different types of the lessons;
2. The embedding of computing to the structure of practical trainings;
3. In the form of additional courses - studying of computer applications through which you can conduct a research of the mathematical model and create animated presentation videos, web-pages, auto-run menu;
4. Students’ working on individual creative projects:
   • construction of computer mathematical models;
   • creating author's programs with elements of scientific researches;
   • students create interactive computer-based tutorials;
   • creation of an electronic library of creative projects;
5. The participation of students  in the annual competitions and scientific conferences for students;
6. The accumulation and dissemination of new methodological experience.

Traditionally, the training system has the structure: explanation of a new →  the solution of tasks→ check, self-test and control → planning of the new unit  with using analysis. However, the main task types: 1) elementary, 2) basic, 3) combined, 4) integrated, 5) custom. With the increasing the level of training a number of basic tasks are growing and some integrated tasks become a class of basic. Thus, the library for basic operations is generated. The decision of the educational task occurs on the way of mastering the theoretical knowledge of mathematical modeling: 1) analysis of conditions (and construction drawing), 2) the search for methods of solution, 3) computation, 4) the researching.

To introduce computer mathematics in this training system, you can:

• At demonstrations. For example, with Maplе facilities you can create a step-by-step interactive and animated images, which are essentially the exact graphic interpretation of mathematical models.
• If we have centralized collective control.
• If students have individual self-control.
• In the analysis of the conditions of the problem, for the construction and visualization of its model, the study of this model.
• In the computations.
• In practical training of different forms.
• In individual projects with elements of research.

In the learning process with the use of computer mathematics in the school a library of themed demonstrations, tasks of different levels and purpose, programs, analytical testing, research projects is generated. With all this especially valuable is that the student is dealing with mathematical signs and mathematical models. Addiction to them processed in the course of working with them it’s unobtrusive, naturally, organically.

Mathematical modelling (MM) is increasingly becoming an important component of scientific research. Today's powerful engineering tools allow to carry out numerous computer experiments, deep and full enough of exploring the object, without significant cost painless. Thus provided the advantages of theoretical approach, and experiment. The integration of information technology and MM method is effective, safe and economical. This explains its wide distribution and makes unavoidable component of scientific and technical progress.

Modeling is a natural process for people, it is present in any activity. The introduction with nature by man occurs through constant  modeling of situation, comparing with the basic models and past experience by them. Method for modeling, abstraction as a method of understanding the world is therefore  an effective method of learning. Training activities associated with the creative transformation of the subject. The main feature of educational training activities is the systematic solution of the educational problems. The connection of the principles of developmental education, mathematical modeling, neurophysiological mechanisms of the brain and experience with Maple leads to the following conclusions: the method of mathematical modeling is not only scientific research but also the way of development of thinking in general; computer and mathematical environment (Maple), which is a powerful tool for scientific simulation can be considered as the elementary analogue of the brain. These qualities of computer mathematics led to the idea of using it not only as an effective methodological tool but as a means of nurturing the thinking and development of mental functions of the brain. To study this effect the school psychologist conducted a test, which confirm the observations: the dynamics of intellectual options students  who working with Maple compares favorably with peers. In the process of doing computer math, in particular Maple, are involved in complex different mental functions. It is in the inclusion of all mental functions is the essence of integration of learning, its educational character. And this, in turn, contributes to the solution of moral problems.

Long-term work with computer mathematics led to the idea to use it as a tool for psychological testing. One of the projects focuses on the psychology and contains authors Maple–tests to identify the degree of development of different mental functions. Interactive mathematical environment  gives a wide variability and creative testing capabilities. Moreover, Maple–test can be used not only as diagnostic but also as educational, and corrective. This technology was tested in one of psycho neurological dispensaries a few years ago.

Currently, one of the author's students, the so-called "homeworkers", the second year is a young man with a diagnosis, categories F20, who does not speak and does not write independently. It was impossible to get feedback from him and have basic training until then author have begun to apply computer-based tools, including system Maple. Working with the computer tests and mathematical objects helps to see not only the mental and even the simplest thinking movement, but also emotional movement!

In general, the effectiveness of the implementation in the structure of educational process of secondary school of new organizational forms of the use of computers, based on the application of the symbolic mathematics package Maple, computer modeling and information technology, has many aspects, here are some of them:

• goals of education and math in particular;
• additional education;
• methodical and professional opportunities;
• theoretical education;
• modeling;
• scientific creativity;
• logical language;
• spatial thinking, the development of the imagination;
• programming skills;
• the specificity of technical translation;
• differentiation and individualization of educational process;
• prospective teaching, the continuity of higher and secondary mathematics education;
• development of creative abilities, research skills;
• analytical thinking;
• mathematical thinking;
• mental diagnosis;
• mental correction.

       According to the author, the unique experience of the Kazan 57–th school suggests that computer mathematics (Maple) is the most effective also universal tool of new methods of inclusion. In recent decades, there are more children with a specific behavior, with a specific perception, not able to focus, with a poor memory, poor thinking processes. There are children, emotionally and intellectually healthy, or even ahead of their peers in one team together with them. High school should provide all the common core learning standards. It needed a variety of programs and techniques, as well as specialists who use them. Due to its remarkable features, computer mathematics, in particular Maple, can be used or be the basis of the variation of methods of physico-mathematical disciplines of inclusive education.

I'm trying to create a graph using a matrix that has numbers and text values, how can I specify that some values of the matrix are strings and others are numbers? I'd like to create something like this

Here is the simplest example of the problem. If I type

assume(j, integer, j>0); assume(k, integer, k > 0);

followed by

int(cos(j*t)*cos(k*t), t = -Pi..Pi);

Maple gives the answer 0, not, as I would have expected, Pi*KroneckerDelta[j,k].

Is there a way to force Maple to alllow for both the possibilities that j = k and j <> k, and thereby to give the general result using the Kronecker delta (or equivalent)?

Bought this book way back in 2000 to learn programming in Maple for procedures.

Problem was that i could not test myself with the exercises, because there were no answers included 

Has someone answers in Maple from these exercises ? 

That is the only way to learn from this book and check my knowledge about programming.

Jan 

The following spreadsheet contains an integral to be done

in the framework of the Maxwell–Jüttner distribution and therefore date back to 1911

integrale_juttner_primes.mw
 

Download integrale_juttner_primes.mw