Journal of Applied and Industrial Mathematics最新文献

{"title":"On Graphs with Small Number of Edges Having Extremal\u0000Number of Open Triangles","authors":"A. V. Pyatkin","doi":"10.1134/S1990478925020103","DOIUrl":"10.1134/S1990478925020103","url":null,"abstract":"<p> In an undirected graph, a 3-vertex induced subgraph having exactly 2 edges is called\u0000an open triangle (OT). We consider the class of graphs where the difference between the numbers\u0000of edges and vertices is a fixed constant\u0000<span>( c )</span>. The complete characterization of graphs on at least\u0000<span>( c+7 )</span> vertices with the maximum number of OTs is obtained for this class.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"313 - 321"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579346","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 Relation between two Classes of Extremal Trees\u0000with Prescribed Degree Sequence","authors":"S. A. Krupoderova,&nbsp;A. D. Kurnosov","doi":"10.1134/S1990478925020061","DOIUrl":"10.1134/S1990478925020061","url":null,"abstract":"<p> A nonpendant vertex of a graph is called a <i>support\u0000vertex</i> if it is adjacent to any leaf. This paper examines how two classes of extremal\u0000trees among all trees with a prescribed degree sequence can relate to each other: the class of trees\u0000minimizing the number of support vertices and the class of trees minimizing the domination\u0000number. Two specially defined values play important role here: the Slater number, proposed by\u0000Slater as a lower bound on domination number, and the lower bound on the number of the\u0000support vertices of a tree proposed by Kurnosov. In the paper, the problem of comparing the\u0000classes is completely solved in the case where the maximum of two values is the latter.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"268 - 277"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579351","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":"Numerical Model of the Influence of Ultrasonic Crossed Fields on\u0000the Formation of Smoke Particle Agglomerates","authors":"R. N. Golykh,&nbsp;A. V. Shalunov,&nbsp;V. N. Khmelev,&nbsp;P. D. Danilov","doi":"10.1134/S199047892502005X","DOIUrl":"10.1134/S199047892502005X","url":null,"abstract":"<p> A method for calculating the behavior and formation of smoke particle agglomerates in\u0000crossed ultrasonic fields is proposed. The proposed method takes into account: the convergence of\u0000agglomerates with allowance for the moments of flow forces from the gas flow, the rotation of\u0000agglomerates due to the moments of forces from the flow around the gas flow, and a phase shift\u0000between ultrasonic cross fields, leading to the rotation of the resulting vibrational velocity vector\u0000and, consequently, to an increase in the effective collision cross-sectional area due to the rotation\u0000of the agglomerates. A description of the morphology and position of agglomerates is constructed\u0000when representing the agglomerate as a solid body, typical for solid-phase aerosols in the form of\u0000smoke. An equation for the dynamics of translational and rotational motion of an agglomerate is\u0000obtained taking into account the interaction of particles. The statement about the presence of\u0000rotational motion with a limited angular velocity proportional to the sound pressure level is\u0000proven, with a phase shift of cross fields equal to 90 deg. By means of numerical experiments a\u0000critical value of the phase shift angle is established at which the pseudo-rotational motion (change\u0000in the rotation angle in a limited range the width of which is less than 180 deg) transforms into\u0000rotational motion (the agglomerate makes a full revolution through 360 deg). The critical phase\u0000shift depends (weakly) on the sound pressure level and ranges from 82 to 85 deg. The transition to\u0000rotational motion increases the efficiency of forming larger agglomerates due to an increase in the\u0000average cross section during particle collisions, caused by the difference in the sizes of agglomerates\u0000along different axes. It was established that for the practical implementation of increasing the\u0000efficiency of smoke deposition, the most appropriate and feasible is ultrasonic action in cross fields\u0000with a frequency difference much lower than the fundamental frequency (from approximaterly 100\u0000to 200 Hz). Such action is much easier to implement compared to maintaining a constant phase\u0000shift between the cross fields and increases the collision cross-sectional area up to several times.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"255 - 267"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579350","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":"Solvability and Controllability\u0000of Differential-Algebraic Equations with Hysteresis","authors":"P. S. Petrenko","doi":"10.1134/S1990478925020097","DOIUrl":"10.1134/S1990478925020097","url":null,"abstract":"<p> In this note, we single out some promising classes of differential-algebraic equations\u0000(DAEs) with nonlinearity of hysteresis type modeled by a sweeping process. DAEs is a well\u0000recognized and extensively studied area of the modern applied mathematics, arisen as a natural\u0000generalization of the concept of ordinary differential equations (ODEs). The unsolvability measure\u0000with respect to the derivatives for some DAE is an integer that is called the index of the DAE.\u0000The analysis is carried out under the assumption of the existence of a structural form with\u0000separated “differential” and “algebraic” subsystems. This structural form is equivalent to the initial\u0000system in the sense of solution, and the operator that transformes the DAE into the structural\u0000form possesses the left inverse operator. Finding the structural form is constructive and does not\u0000use a change of variables. In addition, the problem of consistency of initial data is solved\u0000automatically. Systems of DAEs are attracting more and more attention due to mathematical\u0000modeling problems in many applied domains: automated control theory, optimal control with\u0000mixed constraints, mechanics, chemical kinetics, hydrodynamics, thermal engineering, etc. The\u0000systems under investigation arise in modeling various physical processes, in particular, in electrical\u0000circuits with hysteresis phenomena. For such a DAE, we design an equivalent structural form (in\u0000the sense of solutions). Necessary and sufficient conditions for the existence and uniqueness of a\u0000solution to an initial value problem and controllability are proved. Illustrative examples are given\u0000in the conclusions.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"302 - 312"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579353","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":"Local Control of In-Flows in Regular Resource Networks with\u0000Low Resource","authors":"A. V. Evseenko,&nbsp;V. A. Skorokhodov","doi":"10.1134/S1990478925020048","DOIUrl":"10.1134/S1990478925020048","url":null,"abstract":"<p> The paper is devoted to solving the problem of local control of in-flows in regular resource\u0000networks with low resource. For such networks, a set of controlled vertices is specified. The local\u0000control problem is to determine such capacities of arcs entering the controlled vertices that the\u0000unique limit state\u0000<span>( Q^* )</span> of regular resource network is the closest to a given state\u0000<span>( Q^{prime } )</span>. Conditions for the unreachability of the limit state that coincides with the\u0000state\u0000<span>( Q^{prime } )</span> are obtained. Various configurations of resource networks with respect to the\u0000distribution of controlled vertices in them are considered. It is shown that if the conditions for the\u0000unreachability of the limit state are not satisfied, then there exists a set of capacities of arcs\u0000entering the controlled vertices for which the limit state\u0000<span>( Q^* )</span> is equal to the given state\u0000<span>( Q^{prime } )</span>.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"240 - 254"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579360","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":"Interior Nonlocal Problem for a Third-Order Mixed\u0000Parabolic-Hyperbolic Type Equation","authors":"Yu. P. Apakov,&nbsp;A. A. Sopuev","doi":"10.1134/S1990478925020012","DOIUrl":"10.1134/S1990478925020012","url":null,"abstract":"<p> The existence of a unique solution to a nonlocal conjugation problem for a third-order\u0000partial differential equation of mixed parabolic-hyperbolic type is established. In the upper\u0000half-plane, the characteristic equation has a triple root, while in the lower half-plane, it has one\u0000simple root and two multiple ones. By applying the order reduction method, Green’s and\u0000Riemann’s functions, and the method of integral equations, the problem is equivalently reduced to\u0000a nonlocal problem with an integral condition imposed on the trace of the unknown function along\u0000the type-change line of the equation. This, in turn, is reduced to solving a Fredholm integral\u0000equation of the second kind, the solvability of which is proven using the method of successive\u0000approximations. The solution in the parabolic part of the domain is constructed using Green’s\u0000function, whereas in the hyperbolic part, the Riemann function method is employed, reducing the\u0000problem to a two-dimensional Volterra integral equation of the second kind. Examples are\u0000provided.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"197 - 211"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579283","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 Scalable Approach to Codesign of Topologies\u0000and Routing Algorithms for Families of Optimal\u0000Degree-Four Circulant Networks","authors":"O. G. Monakhov,&nbsp;E. A. Monakhova","doi":"10.1134/S1990478925020085","DOIUrl":"10.1134/S1990478925020085","url":null,"abstract":"<p> This paper presents a new approach to the joint construction of topologies of\u0000diameter-optimal circulant networks\u0000<span>( C(N; pm 1, pm s_2) )</span> and optimal routing algorithms of complexity\u0000<span>( O(1) )</span> implemented for them. New routing algorithms are based on the use of\u0000scalable parameters of\u0000<span>( L )</span>-shaped patterns in a dense packing of graphs on the plane for families of\u0000optimal networks. The scalability of the parameters of\u0000<span>( L )</span>-shaped templates for many families of optimal networks\u0000<span>( C(N; pm 1, pm s_2) )</span> has been proven, analytical formulas for the dependence of these parameters\u0000on the diameter of the graphs have been obtained, reducing the time for setting up the routing\u0000algorithm at the preliminary stage from\u0000<span>( O (log N) )</span> to\u0000<span>( O(1) )</span>. A comparison of the new routing algorithm with the optimal routing\u0000algorithm known in the literature showed its greater efficiency by an average of 10 percent in\u0000terms of time spent on routing in families of optimal graphs. Due to their good scalability and\u0000ease of routing, optimal degree-four circulant networks are of interest as efficient and reliable\u0000communication networks for networks-on-chip, multiprocessor supercomputer systems,\u0000telecommunications network structures, and neural communication networks.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"291 - 301"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579352","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":"Optimal Control in Thermo-Electro-Elasticity: Addressing\u0000Signorini’s Problem\u0000with Tresca’s Friction Law","authors":"L. Essafi,&nbsp;R. Fakhar,&nbsp;M. A. Faqihi,&nbsp;L. Oumouacha","doi":"10.1134/S1990478925020139","DOIUrl":"10.1134/S1990478925020139","url":null,"abstract":"<p> This study focuses on investigating an optimal control problem that represents the\u0000unilateral frictional contact between a thermo-electro-elastic body and a foundation with electrical\u0000and thermal conductivity. The problem is considered in a static setting, and the material behavior\u0000is described using linear thermo-piezoelectric constitutive laws. Tresca’s friction law is used to\u0000model the contact, along with regularized conditions for electrical and thermal conductivity. The\u0000mathematical properties of the problem, including its variational formulation, existence, and\u0000uniqueness of weak solutions, are discussed. Additionally, an optimal control problem is\u0000formulated, and the existence of at least one solution is established. A regularized version of the\u0000unilateral contact and Tresca’s law is then incorporated into the model. The existence of a weak\u0000solution to the regularized control problem is proven, and its convergence to the solution of the\u0000original optimal control problem is verified. Finally, an optimality condition is presented for this\u0000type of problem.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"356 - 373"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579348","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 an Asymptotic Method for Solving Homogeneous\u0000Integro-Differential Equations Describing Vibrations\u0000of Objects with Moving Boundaries","authors":"V. L. Litvinov,&nbsp;M. V. Shamolin","doi":"10.1134/S1990478925020073","DOIUrl":"10.1134/S1990478925020073","url":null,"abstract":"<p> The problem of vibrations of objects with moving boundaries is presented as a differential\u0000equation with boundary and initial conditions and is a nonclassical generalization of a hyperbolic\u0000problem. In the present paper, equivalent integro-differential equations with symmetric and\u0000time-dependent kernels and time-varying integration limits are constructed. An expansion of the\u0000integro-differential equation of motion of variable-length objects into an infinite system of ordinary\u0000differential equations with variable coefficients is given. The concept of eigenfunctions and\u0000eigenvalues is defined for a boundary value problem in a domain bounded by time-varying\u0000integration limits. Solutions to homogeneous integro-differential equations describing vibrations of\u0000variable-length objects and systems of ordinary differential equations with changing parameters\u0000are constructed using asymptotic methods. Expressions for the amplitudes and phases of\u0000vibrations are obtained. This approach is especially useful in studying complex dynamical systems\u0000with lumped masses that oscillate under the influence of moving loads.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"278 - 290"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579323","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":"An Inverse Problem for the Equation of Electrodynamics\u0000with Nonlinear Absorption","authors":"V. G. Romanov,&nbsp;T. V. Bugueva","doi":"10.1134/S1990478925020115","DOIUrl":"10.1134/S1990478925020115","url":null,"abstract":"<p> The inverse problem of determining two unknown functions\u0000<span>( sigma _0(x) )</span> and\u0000<span>( sigma _1(x) )</span> included in the absorption coefficient\u0000<span>( sigma (x,u)=sigma _0(x)+sigma _1(x)u )</span> in the equation of electrodynamics is considered. An a priori estimate of the\u0000solution to the direct problem is obtained, and the existence and uniqueness theorems of solutions\u0000to the direct and inverse problems are proved.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"322 - 347"},"PeriodicalIF":0.58,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579290","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}