Journal of Applied and Industrial Mathematics最新文献

{"title":"A Probabilistic Approach to the Game of Guessing in a Random\u0000Environment","authors":"A. P. Kovalevskii","doi":"10.1134/S1990478924010071","DOIUrl":"10.1134/S1990478924010071","url":null,"abstract":"<p> The following game of two persons is formalized and solved in the paper. Player 1 is asked\u0000a question. Player 2 knows the correct answer. Moreover, both players know all possible answers\u0000and their a priori probabilities. Player 2 must choose a subset of the given cardinality of deception\u0000answers. Player 1 chooses one of the proposed answers. Player 1 wins one from Player 2 if he/she\u0000guessed the correct answer and zero otherwise. This game is reduced to a matrix game. However,\u0000the game matrix is of large dimension, so the classical method based on solving a pair of dual\u0000linear programming problems cannot be implemented for each individual problem. Therefore, it is\u0000necessary to develop a method to radically reduce the dimension.\u0000</p><p>The whole set of such games is divided into two classes. The superuniform class of\u0000games is characterized by the condition that the largest of the a priori probabilities is greater than\u0000the probability of choosing an answer at random, and the subuniform class corresponds to the\u0000opposite inequality—each of the a priori probabilities when multiplied by the total number\u0000of answers presented to Player 1 does not exceed one. For each of these two classes, the solving\u0000the extended matrix game is reduced to solving a linear programming problem of a much smaller\u0000dimension. For the subuniform class, the game is reformulated in terms of probability theory. The\u0000condition for the optimality of a mixed strategy is formulated using the Bayes theorem. For the\u0000superuniform class, the solution of the game uses an auxiliary problem related to the subuniform\u0000class. For both classes, we prove results on the probabilities of guessing the correct answer when\u0000using optimal mixed strategies by both players. We present algorithms for obtaining these\u0000strategies. The optimal mixed strategy of Player 1 is to choose an answer at random in the\u0000subuniform class and to choose the most probable answer in the superuniform class. Optimal\u0000mixed strategies of Player 2 have much more complex structure.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 1","pages":"70 - 80"},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804614","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}

{"title":"A Fractional-Differential Approach to Numerical Simulation of\u0000Electron-Induced Charging of Ferroelectrics","authors":"L. I. Moroz,&nbsp;A. G. Maslovskaya","doi":"10.1134/S1990478924010125","DOIUrl":"10.1134/S1990478924010125","url":null,"abstract":"<p> The paper proposes a fractional-differential modification of the mathematical model of the\u0000process of nonstationary charging of polar dielectric materials under conditions of irradiation with\u0000medium-energy electron beams. The mathematical formalization is based on a spherically\u0000symmetric diffusion–drift equation with a fractional time derivative. An implicit finite-difference\u0000scheme is constructed using the Caputo derivative approximation. An application program has\u0000been developed in <span>Matlab</span> software\u0000that implements the designed computational algorithm. Verification of an approximate solution of\u0000the problem is demonstrated using a test example. The results of computational experiments to\u0000evaluate the characteristics of field effects of injected charges in ferroelectrics when varying the\u0000order of fractional differentiation in subdiffusion regimes are presented.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 1","pages":"137 - 149"},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798759","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}

{"title":"A Parallel “Go with the Winners” Algorithm for Some Scheduling Problems","authors":"P. A. Borisovsky","doi":"10.1134/S1990478923040014","DOIUrl":"10.1134/S1990478923040014","url":null,"abstract":"<p> We consider an approach to solving permutation scheduling problems using graphics\u0000accelerators. A parallel evolutionary algorithm based on the iterated random local search and the\u0000“Go with the winners” algorithm is proposed. A computational experiment was carried out on test\u0000instances of the classic Flow Shop problem and one applied production scheduling problem with\u0000time windows. The results show high computing speed and good accuracy of obtained solutions in\u0000comparison with various variants of the genetic algorithm and Gurobi solver. The proposed\u0000approach is easy to implement and convenient for adaptation to particular features of graphics\u0000computing and can be used to solve practical problems.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"687 - 697"},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757376","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}

{"title":"Analysis and Numerical Simulation of the Initial–Boundary Value Problem for Quasilinear Equations of Complex Heat Transfer","authors":"A. Yu. Chebotarev,&nbsp;N. M. Pak,&nbsp;A. E. Kovtanyuk","doi":"10.1134/S1990478923040026","DOIUrl":"10.1134/S1990478923040026","url":null,"abstract":"<p> We consider an initial–boundary value problem for quasilinear equations of complex heat\u0000transfer that model the process of endovenous laser ablation. A priori estimates for the solution\u0000are obtained. Results on the global unique solvability of the problem are presented. An algorithm\u0000for finding a solution of the initial–boundary value problem is proposed. The efficiency of the\u0000algorithm is illustrated by numerical examples. The influence of internal thermal radiation on the\u0000behavior of temperature fields is evaluated.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"698 - 709"},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757380","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}

{"title":"On Relations Associated with the Euler Function","authors":"V. K. Leontiev,&nbsp;E. N. Gordeev","doi":"10.1134/S1990478923040075","DOIUrl":"10.1134/S1990478923040075","url":null,"abstract":"<p> The paper studies the properties of the set of numbers smaller than and coprime to\u0000<span>( n )</span> with the modulo\u0000<span>( n )</span> multiplication operation introduced on it (this object is sometimes called the\u0000Euler group). The cardinality of such a set is the well-known Euler function\u0000<span>( varphi (n) )</span>, which is one of the classical functions in the number theory. The fields of its\u0000application are quite wide and include, for example, various branches of discrete mathematics, and\u0000it also has significant applications in cryptography. The paper considers various combinatorial\u0000problems arising in the study of the Euler group and the Euler function. Relations between\u0000theoretical and numerical parameters associated with the Euler group and Euler function are\u0000derived. The combinatorial relations obtained in the paper can be used when solving applied\u0000combinatorial problems and in cryptography.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"760 - 766"},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757446","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}

{"title":"A Complete Complexity Dichotomy of the Edge-Coloring Problem for All Sets of (8)-Edge Forbidden Subgraphs","authors":"D. S. Malyshev,&nbsp;O. I. Duginov","doi":"10.1134/S1990478923040099","DOIUrl":"10.1134/S1990478923040099","url":null,"abstract":"<p> For a given graph, the edge-coloring problem is to minimize the number of colors sufficient\u0000to color all the graph edges so that any adjacent edges receive different colors. For all classes\u0000defined by sets of forbidden subgraphs, each with 7 edges, the complexity status of this problem is\u0000known. In this paper, we obtain a similar result for all sets of 8-edge prohibitions.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"791 - 801"},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881904","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}

{"title":"Interaction of Plane Strain Waves in a Heteromodular Elastic Half-Space at the Stage of Forced Stopping of Its Boundary after Uniaxial Tension–Compression","authors":"O. V. Dudko,&nbsp;A. A. Lapteva,&nbsp;V. E. Ragozina","doi":"10.1134/S1990478923040038","DOIUrl":"10.1134/S1990478923040038","url":null,"abstract":"<p> The evolution of the wave pattern in a multimodulus elastic half-space with a boundary\u0000moving in nonstationary uniaxial piecewise linear “tension–compression–stop” mode is studied.\u0000The solution of the boundary value problem includes all cases of interaction between plane\u0000one-dimensional strain waves, including reflected weak-intensity fronts. A number of new features\u0000of one-dimensional elastic deformation dynamics in a multimodulus medium are revealed, some of\u0000which (e.g., the appearance of a reflected shock wave at a distance from the loaded boundary,\u0000cyclic transitions of a narrow moving zone from a compressed to rigid state and back, and a\u0000stepwise decrease in the tensile strain level in the near-boundary zone after the boundary is\u0000stopped) can be obtained with a given boundary loading only taking into account reflection\u0000effects.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"710 - 723"},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881791","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}

{"title":"Existence of Solutions of the Boundary Value Problem for the Equations of Barotropic Flows of a Multicomponent Medium. I. Statement of the Main Problem. Solvability of an Auxiliary Problem","authors":"A. E. Mamontov,&nbsp;D. A. Prokudin","doi":"10.1134/S1990478923040105","DOIUrl":"10.1134/S1990478923040105","url":null,"abstract":"<p> The problem of steady barotropic motion of a multicomponent medium consisting of\u0000viscous compressible fluids in a bounded domain of three-dimensional space is formulated. The\u0000viscosity matrices are assumed to be arbitrary (nondiagonal). The solvability of a regularized\u0000(approximate) problem is proved.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"802 - 814"},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881799","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}

{"title":"Influence of Mathematical Model Parameters on Plasma Transfer in a Helical Magnetic Field","authors":"G. G. Lazareva,&nbsp;I. P. Oksogoeva,&nbsp;A. V. Sudnikov","doi":"10.1134/S1990478923040063","DOIUrl":"10.1134/S1990478923040063","url":null,"abstract":"<p> The paper presents the results of mathematical modeling of plasma transfer in a helical\u0000magnetic field using new experimental data obtained at the SMOLA trap created at the Budker\u0000Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences. Plasma is\u0000confined in the trap by transmitting a pulse of magnetic field with helical symmetry to the\u0000rotating plasma. The mathematical model is based on a stationary plasma transfer equation in\u0000the axially symmetric formulation. The distribution of the concentration of the substance\u0000obtained by numerical simulation confirmed the confinement effect obtained in the experiment.\u0000The dependences of the integral characteristics of the substance on the depth of magnetic field\u0000corrugation and on plasma diffusion and potential are obtained. The numerical implementations\u0000of the model by the relaxation method and by the Seidel method are compared.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"750 - 759"},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757382","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}

{"title":"Bäcklund Transformations of the Relativistic Schrödinger Equation","authors":"M. V. Neshchadim,&nbsp;A. A. Simonov","doi":"10.1134/S1990478923040129","DOIUrl":"10.1134/S1990478923040129","url":null,"abstract":"<p> We study the system of equations obtained on the basis of the relativistic\u0000Schrödinger equation and relating the potential, amplitude, and phase functions. Using\u0000the methods of the theory of consistency of systems of partial differential equations, we obtain\u0000completely integrable systems that relate only two functions of the above three. The systems\u0000found are related by Bäcklund transformations.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"828 - 841"},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881897","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}