Application Mathematics and Informatics最新文献

BI-HAMILTONIAN STRUCTURE AND EXACTSOLUTIONS OF ONE BURGERS� TYPE NONLINEARDYNAMICAL SYSTEM 一类非线性动力系统的双哈密顿结构与精确解

Application Mathematics and Informatics Pub Date : 2021-03-25 DOI: 10.30970/VAM.2020.28.10948

M. Prytula, I. Mykhailiuk

{"title":"BI-HAMILTONIAN STRUCTURE AND EXACT\u0000SOLUTIONS OF ONE BURGERS� TYPE NONLINEAR\u0000DYNAMICAL SYSTEM","authors":"M. Prytula, I. Mykhailiuk","doi":"10.30970/VAM.2020.28.10948","DOIUrl":"https://doi.org/10.30970/VAM.2020.28.10948","url":null,"abstract":"In the present work, we find the bi-Hamiltonian representation and three classes of exact solutions for the dispersionful (Burgers’ type) nonlinear dynamical system introduced by Szablikowski et al. [13]. In particular, for the above-mentioned system, we construct the infinite hierarchy of functionally independent conservation laws utilizing the gradient holonomic method [3]. Moreover, based on that hierarchy we find the implectic pair of Noetherian operators and corresponding Hamiltonian functionals applying the differentialalgebraic algorithm [8, 12]. Furthermore, we construct three classes of exact traveling wave solutions, in particular, solitary wave and periodic ones, using the –expansion method [18]. It is shown that for the case of the dynamical system under consideration, degrees of the polynomials in cannot be uniquely determined from the system of algebraic equations of the homogeneous balance. Nevertheless, utilizing a more detailed analysis, a general form of the solution is found uniquely. Further, we analyze the obtained results, in particular, the analytical solution is verified by putting it back into original equations. Finally, we anticipate future research objectives, especially finding the standard Lax type representation of the above-mentioned dynamical system.","PeriodicalId":302104,"journal":{"name":"Application Mathematics and Informatics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122702070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

�� '�� I �� , ��

Application Mathematics and Informatics Pub Date : 2020-03-30 DOI: 10.30970/vam.2019.27.10725

O. Zanevych, V. Kukharskyy

{"title":"�� '�� I �� , �� ","authors":"O. Zanevych, V. Kukharskyy","doi":"10.30970/vam.2019.27.10725","DOIUrl":"https://doi.org/10.30970/vam.2019.27.10725","url":null,"abstract":"The timetable problem of classes is an urgent problem in higher education institutions. There are a number of classical methods for solving it: dynamic programming methods, integer programming, nonlinear programming, the branch and bound method, simulation methods, the graph coloring method, assignment problem, and others. The peculiarity of these methods is the mathematical rigor of both the formulation of the timetable problem of classes and algorithms for its solution. They have predetermined convergence time and accuracy of the solution and allow to estimate the inux of dierent factors for time of nding the solution. The disadvantage of all classic methods is that they basically use an iterative search procedure or renement of some initial approximation, whereby the result is searched around that approximation. This means that the result directly depends on some initial approximation and naturally there is a problem of its choice, which leads to the need for a multiple experiment with dierent values of the initial approximation, which signicantly increases the time to nd the nal solution. Also, the classical methods are characterized by the complexity of the mathematical model obtained and the sharp (exponential) increase in time spent nding an acceptable solution as the volume of source information increases. To avoid the above disadvantages of the classical methods, the timetable problem of classes can be solved by applying a genetic algorithm. The paper proposes one variant of setting a objective function for timetable optimization and dening a tness function based on it. The article describes the implementation of classical genetic operators: crossover, mutations, and selection for a population of timetables, and also proposes a correction operator that improves the variants of timetables obtained by calls of classical genetic operators. For the implementation of crossover and correction operators, the concept of a local target function is introduced. The general scheme of the genetic algorithm for solving the timetable problem is presented in the paper, and the results of the numerical experiment are given.","PeriodicalId":302104,"journal":{"name":"Application Mathematics and Informatics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123918996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

�� .NET

Application Mathematics and Informatics Pub Date : 2020-03-05 DOI: 10.30970/vam.2019.27.10137

Serhiy Yaroshko, S. Yaroshko

{"title":"�� .NET","authors":"Serhiy Yaroshko, S. Yaroshko","doi":"10.30970/vam.2019.27.10137","DOIUrl":"https://doi.org/10.30970/vam.2019.27.10137","url":null,"abstract":"The majority of modern software applications make use of several execution threads. For example, in the text editor, one thread is responsible for the spell cheking, another for autosaving, one more thread for handling the user input. The mechanism of multiple threads provides the software developer with a convenient way of structuring the functional possibilities: the software application architecture will be more stable, if it's various possibilities are programmed separately from each other. The ability to use multiple threads will be useful even for a specialist of numerical computing. The iteration methods usually need to execute a large amount of computations in order to receive an approximate solution of a certain problem. This circumstance should be taken into account at the stage of software design architecture so, that a user could follow the computational process and not worry about the responsiveness of the application. In order to launch a separate execution thread, the .Net framework provides a developer with an eective template of task-based asynchronous programming [3] that uses some new keywords async, await and classes Task, Task from the namespace System.Threading.Tasks. The instances of this class are created very fast, they need only a little amount of system resources and they eectively use the processors time. That's why it is convenient to move the computations to a separate thread, which on its turn can also launch dierent parallel computational threads. This approach signicantly accelerates a software performance on a multiprocessor (or multi-core) computer. The keyword async in the name of an asynchronous method changes the way of how the result of this method is handled, and gives a possibility to use the instruction await for launching any awaitable object. For this purpose, in the .Net framework there are usually used the instances of the classes Task and Task . The task, launched with the instruction await, does not block the user interface thread during the computation. Before launching an synchronous task, there are dierent preparation steps: create a stop-marker CancellationToken token, an object Progress progress in order to be able to send the data to the main thread, and nally a set of local variables to correctly catch the execution context. Then the asynchronous method in the right moment calls progress.Report(data), for a \"soft\" termination of an asynchronous algorithm. In a convenient point in time, this algorithm should check the property token.IsCancellationRequested and terminate the execution on request. The cancellation request can be initiated from the main thread by calling the method token.Cancel(). In order to synchronize the nishing of the array of asynchronous tasks, the static method Task.WhenAll(tasks).Wait() is used. For the demonstration of the described approaches an application has been created. It demonstrates how to apply the genetic algorithm in order to solve the traveling sales-man pr","PeriodicalId":302104,"journal":{"name":"Application Mathematics and Informatics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131914283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

�� '�� -�� в�� ʲ��

Application Mathematics and Informatics Pub Date : 2020-03-05 DOI: 10.30970/vam.2019.27.10410

A. Hlova, Svyatoslav Litynskyy, Yu. Muzychuk, A. Muzychuk

{"title":"�� '�� -�� в�� ʲ�� ","authors":"A. Hlova, Svyatoslav Litynskyy, Yu. Muzychuk, A. Muzychuk","doi":"10.30970/vam.2019.27.10410","DOIUrl":"https://doi.org/10.30970/vam.2019.27.10410","url":null,"abstract":"Exterior Dirichlet and Robin initial boundary-value problems for the homogeneous wave equation with homogeneous initial conditions are considered in domains which are three-dimensional in spatial variables. Using a solution representation by the Kirchho formula these problems are reduced to time-domain boundary integral equations (TDBIEs) with unknown Cauchy data on a boundary surface. We have one nonstationary integral equation with an unknown normal derivative of the solution of the problem in the case of the Dirichlet problem and a system of two TDBIEs for both Cauchy data for the Robin problem. As a result of applying the Laguerre transform in the time variable to that TDBIEs and regrouping the corresponding Fourier-Laguerre coecients, we obtained innite sequences of boundary integral equations (BIEs), which depend only on the coordinates at boundary surfaces. All BIEs obtained from the Dirichlet problem are represented by the same elliptic boundary operator in the left-hand side of the equations and by recurrently dependent expressions in the right-hand sides. In the case of Robin problem, the structure of the resulting sequence is similar, but now we are dealing with a matrix operator, which is composed of four boundary operators and is elliptic in some Sobolev space. For the numerical solution of obtained BIEs, a fast boundary element method was developed as an implementation of the Galerkin method. The unknown traces and normal derivatives of the solutions are approximated by linear and piece-wise constant basis functions, respectively. To reduce the required storage and computational costs, an adaptive cross-approximation of the discretized boundary operators was implemented. A series of computational experiments on the numerical solution of the Dirichlet and Robin model problems were carried out. Their results demonstrate the high accuracy and estimated order of convergence of the proposed method.","PeriodicalId":302104,"journal":{"name":"Application Mathematics and Informatics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126934706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

�� I�� I� �I��

Application Mathematics and Informatics Pub Date : 2020-03-05 DOI: 10.30970/vam.2019.27.10271

V. Chernyakhivskyy

{"title":"�� I�� I� �I�� ","authors":"V. Chernyakhivskyy","doi":"10.30970/vam.2019.27.10271","DOIUrl":"https://doi.org/10.30970/vam.2019.27.10271","url":null,"abstract":"The analysis of problem-solving tasks and construction of graphs have been leading to the development of new algorithms and software implementations. To verify the algorithm, it is necessary to make test data in such a way, that all values for the test are predetermined. The values for testing algorithms via graphs are: the number of vertices in the graph; the vertex degree; connectivity of the graph; permissibility of multiple edges and loops; the weight of the graph edges. If the values are known for the test graph then we can calculate the expected results of the designed algorithm and match them with the actual ones in a well-posed manner. The algorithm and some elements of software implementation of generating nite undirected graphs, with such values as the number of vertices n and the degree of the vertices k = const, which correspond to correctness of additional conditional statements, are presented in the article. The general scheme of the algorithm is as follows. Create two lists of vertices L1 and L2. The list L1 is initially empty; in the list L2 we have all vertices of the graph from 1 to n. We take the rst vertex in L2, we build all k edges to it and transfer it to the list L1. Repeat the same for each next vertex of the L2 list, except the last one. The last vertex L2 is just transferred to L1. The algorithm immediately builds the adjacency matrix by modeling list operations with L1 and L2. According to the algorithm, the adjacency matrix will always be the same for xed n and k when the algorithm is repeated. To obtain dierent matrices, the rule of graph isomorphism is used: perform the permutations of the rows and columns of the resulting matrix.","PeriodicalId":302104,"journal":{"name":"Application Mathematics and Informatics","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116267991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

�� в� �� PYTHON

Application Mathematics and Informatics Pub Date : 2020-03-05 DOI: 10.30970/vam.2019.27.10293

B. Hoshko, V. Chernyakhivskyy

{"title":"�� в� �� PYTHON","authors":"B. Hoshko, V. Chernyakhivskyy","doi":"10.30970/vam.2019.27.10293","DOIUrl":"https://doi.org/10.30970/vam.2019.27.10293","url":null,"abstract":"The semantic denitions of compound Python programming language operators, for which we have expanding applications in application projects, are explained in the article. The denitions are written in the basic initial form, which is primary for the study of programming and for the construction of algorithms for data processing. On the basis of semantic denitions, syntax denitions are formed, which form the correct subset of the general Python syntax, and can be supplemented by extension operations without modication of the base part. The method of operational-functional denition of semantics is presented, which allows to rebuild syntax denitions so as to preserve the basic semantics of individual constructions of the language and to minimize the length of output by grammatical denitions startdef=>+\"example\". For this purpose we use basically three methods: reduction of complete grammatical rules; substitution of denitions of non-terminals on the right side of the syntax; adding non-strictly dened terminals with reference to previously dened non-terminals. Semantics models are built on the classication of operations and data conversion functions. Models are treated as universal algebras U(A) = , where M is a nonempty set (quantities, memory cells, structures, operators), and Ω is a set of operations (possibly partial) on the set M, including the signature. We dene semantics models in two groups: 1)models based on valid Python operations; 2)models based on Python operators and control structures. For each group of models of algebra semantics has its own peculiarities. Semantics models are dened for the following objects: numeric types, assignment, data system, print, input; conditional expressions, conditional operator if; loop operators while, for; try exception control operator; operator with context managers.","PeriodicalId":302104,"journal":{"name":"Application Mathematics and Informatics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121498507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

�� '�� I �I�I�� I�� I�� I��

Application Mathematics and Informatics Pub Date : 1900-01-01 DOI: 10.30970/vam.2019.27.10447

H. Yarmola, A. Dudykevych

引用次数: 0

Версія алгоритму виявлення завершення, що придатна до налаштування у фреймворку InDiGO

Application Mathematics and Informatics Pub Date : 1900-01-01 DOI: 10.30970/vam.2021.29.11304

B. Колесніков

引用次数: 0

��I �� I�I�I��I� ��I� � ��I��I��

Application Mathematics and Informatics Pub Date : 1900-01-01 DOI: 10.30970/vam.2022.30.11635

�� ³��볿�� , �� , ��

引用次数: 0

Розробка прототипу системи оптичного розпізнавання тексту для зображень низької якості

Application Mathematics and Informatics Pub Date : 1900-01-01 DOI: 10.30970/vam.2021.29.11344

M. Баранов, C. Іванов, Ярослав Соколовський, Юрій Валерійович Юрченко

引用次数: 0