Pub Date : 2024-04-26DOI: 10.1134/s1990478924010010
D. N. Barotov
Abstract
A convex continuation of an arbitrary Boolean function to the set ( [0,1]^n ) is constructed. Moreover, it is proved that for any Boolean function ( f(x_1,x_2,dots ,x_n) ) that has no neighboring points on the set ( mathrm{supp} f ), the constructed function ( f_C(x_1,x_2, dots ,x_n) ) is the only totally maximally convex continuation to ( [0,1]^n ). Based on this, in particular, it is constructively stated that the problem of solving an arbitrary system of Boolean equations can be reduced to the problem of minimizing a function any local minimum of which in the desired region is a global minimum, and thus for this problem the problem of local minima is completely resolved.
Abstract A convex continuation of an arbitrary Boolean function to the set( [0,1]^n ) is constructed.此外，还证明了对于任意布尔函数（f(x_1,x_2,dots ,x_n) ）在集合（mathrm{supp} f ）上没有邻接点，所构造的函数（f_C(x_1,x_2,dots ,x_n) ）是到集合（[0,1]^n ）的唯一完全最大凸延续。在此基础上，可以构造性地指出，求解任意布尔方程组的问题可以简化为最小化一个函数的问题，这个函数在所需区域的任何局部最小值都是全局最小值，因此对于这个问题来说，局部最小值的问题是完全可以解决的。
{"title":"Convex Continuation of a Boolean Function and Its Applications","authors":"D. N. Barotov","doi":"10.1134/s1990478924010010","DOIUrl":"https://doi.org/10.1134/s1990478924010010","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A convex continuation of an arbitrary Boolean function to the set\u0000<span>( [0,1]^n )</span> is constructed. Moreover, it is proved that for any Boolean function\u0000<span>( f(x_1,x_2,dots ,x_n) )</span> that has no neighboring points on the set\u0000<span>( mathrm{supp} f )</span>, the constructed function\u0000<span>( f_C(x_1,x_2, dots ,x_n) )</span> is the only totally maximally convex continuation to\u0000<span>( [0,1]^n )</span>. Based on this, in particular, it is constructively stated that the problem of\u0000solving an arbitrary system of Boolean equations can be reduced to the problem of minimizing a\u0000function any local minimum of which in the desired region is a global minimum, and thus for this\u0000problem the problem of local minima is completely resolved.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804662","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}
Pub Date : 2024-04-26DOI: 10.1134/s1990478924010083
I. M. Kulikov
Abstract
Rusanov’s scheme for solving hydrodynamic equations is one of the most robust in the class of Riemann solvers. It was previously shown that Rusanov’s scheme based on piecewise parabolic reconstruction of primitive variables gives a low-dissipative scheme relevant to Roe and Harten–Lax–Van Leer solvers when using a similar reconstruction. Moreover, unlike these solvers, the numerical solution is free from artifacts. In the case of equations of special relativistic magnetohydrodynamics, the spectral decomposition for solving the Riemann problem is quite complex and does not have an analytical solution. The present paper proposes the development of Rusanov’s scheme using a piecewise parabolic reconstruction of primitive variables to use in the equations of special relativistic magnetohydrodynamics. The developed scheme was verified using eight classical problems on the decay of an arbitrary discontinuity that describe the main features of relativistic magnetized flows.
{"title":"Using Piecewise Parabolic Reconstruction of Physical Variables in Rusanov’s Solver. II. Special Relativistic Magnetohydrodynamics Equations","authors":"I. M. Kulikov","doi":"10.1134/s1990478924010083","DOIUrl":"https://doi.org/10.1134/s1990478924010083","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Rusanov’s scheme for solving hydrodynamic equations is one of the most robust in the\u0000class of Riemann solvers. It was previously shown that Rusanov’s scheme based on piecewise\u0000parabolic reconstruction of primitive variables gives a low-dissipative scheme relevant to Roe and\u0000Harten–Lax–Van Leer solvers when using a similar reconstruction. Moreover, unlike these solvers,\u0000the numerical solution is free from artifacts. In the case of equations of special relativistic\u0000magnetohydrodynamics, the spectral decomposition for solving the Riemann problem is quite\u0000complex and does not have an analytical solution. The present paper proposes the development of\u0000Rusanov’s scheme using a piecewise parabolic reconstruction of primitive variables to use in the\u0000equations of special relativistic magnetohydrodynamics. The developed scheme was verified using\u0000eight classical problems on the decay of an arbitrary discontinuity that describe the main features\u0000of relativistic magnetized flows.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798787","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}
Pub Date : 2024-04-26DOI: 10.1134/s1990478924010058
V. N. Khmelev, A. V. Shalunov, R. N. Golykh
Abstract
We propose a method for calculating the kinetics of ultrasonic coagulation of PM2.5 during fine gas cleaning that provides an order of magnitude higher calculation performance. Increased productivity is achieved through the proposed and justified method of reducing the original three-dimensional problem to a two-dimensional one. The proposed reduction method is based on the fact that the time of complete rotation of vortex acoustic flows turns out to be much shorter than the characteristic coagulation time during fine gas cleaning. This makes it possible to present the fractional composition of aerosol particles as a function of two stream functions instead of three coordinates. Calculations carried out using the proposed method make it possible to identify the possibility of increasing the efficiency of coagulation in three-dimensional flows due to the following mechanisms: a local increase in concentration caused by the inertial transfer of particles to the periphery of three-dimensional vortices in the gas phase, increasing the frequency of particle collisions due to three-dimensional turbulent disturbances in ultrasonic fields with a high amplitude of oscillatory velocity (more than 10 m/s), and increasing productivity and ensuring the possibility of continuous implementation of the process in flow mode due to the transfer of particles between the streamlines of the main vortices initiated by ultrasonic vibrations as well as due to external flows perpendicular to the plane of the vortices in three-dimensional space. The developed set of programs for implementing calculations can be used in the design of gas cleaning equipment.
{"title":"A Method for Calculating Ultrasonic Coagulation of PM2.5 Particles in Vortex and Turbulent Acoustic Flows","authors":"V. N. Khmelev, A. V. Shalunov, R. N. Golykh","doi":"10.1134/s1990478924010058","DOIUrl":"https://doi.org/10.1134/s1990478924010058","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We propose a method for calculating the kinetics of ultrasonic coagulation of PM2.5\u0000during fine gas cleaning that provides an order of magnitude higher calculation performance.\u0000Increased productivity is achieved through the proposed and justified method of reducing the\u0000original three-dimensional problem to a two-dimensional one. The proposed reduction method is\u0000based on the fact that the time of complete rotation of vortex acoustic flows turns out to be much\u0000shorter than the characteristic coagulation time during fine gas cleaning. This makes it possible to\u0000present the fractional composition of aerosol particles as a function of two stream functions\u0000instead of three coordinates. Calculations carried out using the proposed method make it possible\u0000to identify the possibility of increasing the efficiency of coagulation in three-dimensional flows due\u0000to the following mechanisms: a local increase in concentration caused by the inertial transfer of\u0000particles to the periphery of three-dimensional vortices in the gas phase, increasing the frequency\u0000of particle collisions due to three-dimensional turbulent disturbances in ultrasonic fields with a\u0000high amplitude of oscillatory velocity (more than 10 m/s), and increasing productivity and\u0000ensuring the possibility of continuous implementation of the process in flow mode due to the\u0000transfer of particles between the streamlines of the main vortices initiated by ultrasonic vibrations\u0000as well as due to external flows perpendicular to the plane of the vortices in three-dimensional\u0000space. The developed set of programs for implementing calculations can be used in the design of\u0000gas cleaning equipment.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798785","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}
Pub Date : 2024-04-26DOI: 10.1134/s1990478924010101
E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva
Abstract
This paper is a survey of modern post-quantum cryptographic schemes based on codes and isogenies. Special attention is paid to cryptanalysis of these schemes. In particular, for code-based cryptosystems we describe the information set decoding and the support splitting algorithm as main attacks, and for cryptosystems based on isogenies we describe in detail the Castryck–Decru attack on SIDH/SIKE.
{"title":"Post-Quantum Cryptosystems: Open Problems and Current Solutions. Isogeny-Based and Code-Based Cryptosystems","authors":"E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva","doi":"10.1134/s1990478924010101","DOIUrl":"https://doi.org/10.1134/s1990478924010101","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> This paper is a survey of modern post-quantum cryptographic schemes based on codes\u0000and isogenies. Special attention is paid to cryptanalysis of these schemes. In particular, for\u0000code-based cryptosystems we describe the information set decoding and the support splitting\u0000algorithm as main attacks, and for cryptosystems based on isogenies we describe in detail the\u0000Castryck–Decru attack on SIDH/SIKE.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804578","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}
Pub Date : 2024-04-26DOI: 10.1134/s1990478924010034
G. A. Chumakov, N. A. Chumakova
Abstract
In this paper, we study a nonlinear dynamical system of autonomous ordinary differential equations with a small parameter ( mu ) such that two variables ( x ) and ( y ) are fast and another one ( z ) is slow. If we take the limit as ( mu to 0 ), then this becomes a “degenerate system” included in the one-parameter family of two-dimensional subsystems of fast motions with the parameter ( z ) in some interval. It is assumed that in each subsystem there exists a structurally stable limit cycle ( l_z ). In addition, in the complete dynamical system there is some structurally stable periodic orbit ( L ) that tends to a limit cycle ( l_{z_0} ) for some ( z=z_0 ) as ( mu ) tends to zero. We can define the first return map, or the Poincaré map, on a local cross section in the hyperplane ( (y,z) ) orthogonal to ( L ) at some point. We prove that the Poincaré map has an invariant manifold for the fixed point corresponding to the periodic orbit ( L ) on a guaranteed interval over the variable ( y ), and the interval length is separated from zero as ( mu ) tends to zero. The proved theorem allows one to formulate some sufficient conditions for the existence and/or absence of multipeak oscillations in the complete dynamical system. As an example of application of the obtained results, we consider some kinetic model of the catalytic reaction of hydrogen oxidation on nickel.
Abstract 在本文中，我们研究了一个具有一个小参数的非线性自主常微分方程动力系统，这个小参数使得两个变量（x）和（y）是快速的，而另一个变量（z）是慢速的。如果我们把这个极限取为0，那么它就变成了一个 "退化系统"，包含在参数（ z ）在某个区间内的二维非快速运动子系统的一参数族中。假设在每个子系统中都存在一个结构稳定的极限周期（ l_z ）。此外，在完整的动力系统中，存在一些结构上稳定的周期轨道（L），当（mu）趋向于零时，对于某些（z=z_0）趋向于极限循环（l_{z_0}）。我们可以在超平面（（y,z））中与（L）正交的某一点上的局部截面上定义第一个返回图，或称Poincaré图。我们证明，Poincaré映射在变量（y）的保证区间上与周期轨道（L）相对应的定点有一个无变量manifold，当（mu ）趋向于零时，区间长度与零分离。所证明的定理允许我们为完整动力系统中多峰振荡的存在和/或不存在提出一些充分条件。作为应用所获结果的一个例子，我们考虑了镍上氢氧化催化反应的一些动力学模型。
{"title":"Differential Equations with a Small Parameter and Multipeak Oscillations","authors":"G. A. Chumakov, N. A. Chumakova","doi":"10.1134/s1990478924010034","DOIUrl":"https://doi.org/10.1134/s1990478924010034","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, we study a nonlinear dynamical system of autonomous ordinary differential\u0000equations with a small parameter\u0000<span>( mu )</span> such that two variables\u0000<span>( x )</span> and\u0000<span>( y )</span> are fast and another one\u0000<span>( z )</span> is slow. If we take the limit as\u0000<span>( mu to 0 )</span>, then this becomes a “<i>degenerate\u0000system</i>” included in the one-parameter family of two-dimensional subsystems of\u0000<i>fast motions</i> with the parameter\u0000<span>( z )</span> in some interval. It is assumed that in each subsystem there exists\u0000a <i>structurally stable</i> limit cycle\u0000<span>( l_z )</span>. In addition, in the <i>complete</i>\u0000dynamical system there is some structurally stable periodic orbit\u0000<span>( L )</span> that tends to a limit cycle\u0000<span>( l_{z_0} )</span> for some\u0000<span>( z=z_0 )</span> as\u0000<span>( mu )</span> tends to zero. We can define the first return map, or the Poincaré\u0000map, on a local cross section in the hyperplane\u0000<span>( (y,z) )</span> orthogonal to\u0000<span>( L )</span> at some point. We prove that the Poincaré map has an invariant\u0000manifold for the fixed point corresponding to the periodic orbit\u0000<span>( L )</span> on a guaranteed interval over the variable\u0000<span>( y )</span>, and the interval length is separated from zero as\u0000<span>( mu )</span> tends to zero. The proved theorem allows one to formulate some sufficient\u0000conditions for the existence and/or absence of multipeak oscillations in the complete dynamical\u0000system. As an example of application of the obtained results, we consider some kinetic model of\u0000the catalytic reaction of hydrogen oxidation on nickel.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798781","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}
Pub Date : 2024-04-26DOI: 10.1134/s1990478924010137
N. N. Shilov, A. A. Duchkov
Abstract
Seismic images of subsurface structures are the most valuable outcome of seismic data processing. The image quality is strongly affected by the accuracy of background velocity model. In this paper, we develop a gradient-descent velocity update algorithm based on our original high-frequency asymptotics of the Double Square Root equation, i.e., a special one-way approximation of the wave equation describing single-scattered wave field only. We propose a loss function consistent with widely adopted imaging condition and derive equations for its gradient computation. We test our method on noise-free synthetic datasets in 2D settings.
{"title":"Migration Velocity Analysis Using a Ray Method Asymptotics of the Double Square Root Equation","authors":"N. N. Shilov, A. A. Duchkov","doi":"10.1134/s1990478924010137","DOIUrl":"https://doi.org/10.1134/s1990478924010137","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Seismic images of subsurface structures are the most valuable outcome of seismic data\u0000processing. The image quality is strongly affected by the accuracy of background velocity model.\u0000In this paper, we develop a gradient-descent velocity update algorithm based on our original\u0000high-frequency asymptotics of the Double Square Root equation, i.e., a special one-way\u0000approximation of the wave equation describing single-scattered wave field only. We propose a loss\u0000function consistent with widely adopted imaging condition and derive equations for its gradient\u0000computation. We test our method on noise-free synthetic datasets in 2D settings.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798780","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}
Pub Date : 2024-04-26DOI: 10.1134/s199047892401006x
A. A. Klyushin, I. B. Kozhukhov, D. Yu. Manilov, A. V. Reshetnikov
Abstract
In 1961, L.M. Gluskin proved that a given set ( X ) with an arbitrary nontrivial quasiorder ( rho ) is determined up to isomorphism or anti-isomorphism by the semigroup ( T_rho (X) ) of all isotone transformations of ( (X,rho ) ), i.e., the transformations of ( X ) preserving ( rho ). Subsequently, L.M. Popova proved a similar statement for the semigroup ( P_rho (X) ) of all partial isotone transformations of ( (X,rho ) ); here the relation ( rho ) does not have to be a quasiorder but can be an arbitrary nontrivial reflexive or antireflexive binary relation on the set ( X ). In the present paper, under the same constraints on the relation ( rho ), we prove that the semigroup ( B_rho (X) ) of all isotone binary relations (set-valued mappings) of ( (X,rho ) ) determines ( rho ) up to an isomorphism or anti-isomorphism as well. In addition, for each of the conditions ( T_rho (X)=T(X) ), ( P_rho (X)=P(X) ), and ( B_rho (X)=B(X) ), we enumerate all ( n )-ary relations ( rho ) satisfying the given condition.
{"title":"Definability of Relations by Semigroups of Isotone Transformations","authors":"A. A. Klyushin, I. B. Kozhukhov, D. Yu. Manilov, A. V. Reshetnikov","doi":"10.1134/s199047892401006x","DOIUrl":"https://doi.org/10.1134/s199047892401006x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In 1961, L.M. Gluskin proved that a given set\u0000<span>( X )</span> with an arbitrary nontrivial quasiorder\u0000<span>( rho )</span> is determined up to isomorphism or anti-isomorphism by the semigroup\u0000<span>( T_rho (X) )</span> of all isotone transformations of\u0000<span>( (X,rho ) )</span>, i.e., the transformations of\u0000<span>( X )</span> preserving\u0000<span>( rho )</span>. Subsequently, L.M. Popova proved a similar statement for the semigroup\u0000<span>( P_rho (X) )</span> of all partial isotone transformations of\u0000<span>( (X,rho ) )</span>; here the relation\u0000<span>( rho )</span> does not have to be a quasiorder but can be an arbitrary nontrivial reflexive\u0000or antireflexive binary relation on the set\u0000<span>( X )</span>. In the present paper, under the same constraints on the relation\u0000<span>( rho )</span>, we prove that the semigroup\u0000<span>( B_rho (X) )</span> of all isotone binary relations (set-valued mappings) of\u0000<span>( (X,rho ) )</span> determines\u0000<span>( rho )</span> up to an isomorphism or anti-isomorphism as well. In addition, for each of\u0000the conditions\u0000<span>( T_rho (X)=T(X) )</span>,\u0000<span>( P_rho (X)=P(X) )</span>, and\u0000<span>( B_rho (X)=B(X) )</span>, we enumerate all\u0000<span>( n )</span>-ary relations\u0000<span>( rho )</span> satisfying the given condition.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806653","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}
Pub Date : 2024-04-26DOI: 10.1134/s1990478924010046
V. N. Grebenev, A. G. Demenkov, G. G. Chernykh
Abstract
To study the flow in a far plane turbulent wake in a passively stratified medium, we use a mathematical model that includes differential equations for the balance of turbulence energy, the transfer of its dissipation rate, shear turbulent stress, a defect of the density of the liquid, and the vertical component of the mass flux vector. Algebraic truncation of the last equation leads to a well-known gradient relation for the vertical component of the mass flux vector. It is established that under a certain constraint on the values of empirical constants in the mathematical model and the law of time scale growth consistent with the mathematical model, this relation is a differential constraint for the model. The equivalence of the local equilibrium approach for the vertical component of the mass flux vector and the zero Poisson bracket for the dimensionless turbulent diffusion coefficient and the averaged density is shown. The results of numerical experiments illustrating the theoretical results are presented.
{"title":"Local Equilibrium Approach in the Problem of the Dynamics of a Plane Turbulent Wake in a Passively Stratified Medium","authors":"V. N. Grebenev, A. G. Demenkov, G. G. Chernykh","doi":"10.1134/s1990478924010046","DOIUrl":"https://doi.org/10.1134/s1990478924010046","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> To study the flow in a far plane turbulent wake in a passively stratified medium, we use a\u0000mathematical model that includes differential equations for the balance of turbulence energy, the\u0000transfer of its dissipation rate, shear turbulent stress, a defect of the density of the liquid, and the\u0000vertical component of the mass flux vector. Algebraic truncation of the last equation leads to a\u0000well-known gradient relation for the vertical component of the mass flux vector. It is established\u0000that under a certain constraint on the values of empirical constants in the mathematical model\u0000and the law of time scale growth consistent with the mathematical model, this relation is a\u0000differential constraint for the model. The equivalence of the local equilibrium approach for the\u0000vertical component of the mass flux vector and the zero Poisson bracket for the dimensionless\u0000turbulent diffusion coefficient and the averaged density is shown. The results of numerical\u0000experiments illustrating the theoretical results are presented.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798761","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}
Pub Date : 2024-04-26DOI: 10.1134/s1990478924010149
D. S. Taletskii
Abstract
A set ( J_k ) of graph vertices is said to be ( k )-dominating independent ( ( k geq 1 )) if its vertices are pairwise adjacent and every vertex not in ( J_k ) is adjacent to at least ( k ) vertices in ( J_k ). In the present paper, we obtain new upper bounds for the number of ( k )-dominating independent sets for ( k geq 2 ) in some planar graph classes.
{"title":"On the Number of $$ k $$ -Dominating Independent Sets in Planar Graphs","authors":"D. S. Taletskii","doi":"10.1134/s1990478924010149","DOIUrl":"https://doi.org/10.1134/s1990478924010149","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A set\u0000<span>( J_k )</span> of graph vertices is said to be\u0000<span>( k )</span>-dominating independent (\u0000<span>( k geq 1 )</span>) if its vertices are pairwise adjacent and every vertex not in\u0000<span>( J_k )</span> is adjacent to at least\u0000<span>( k )</span> vertices in\u0000<span>( J_k )</span>. In the present paper, we obtain new upper bounds for the number of\u0000<span>( k )</span>-dominating independent sets for\u0000<span>( k geq 2 )</span> in some planar graph classes.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804561","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}
Pub Date : 2024-04-26DOI: 10.1134/s1990478924010113
E. A. Monakhova, O. G. Monakhov
Abstract
Arden and Lee proposed a class of chordal ring networks of degree three as communication networks for multicomputer systems, derived a formula for the diameter, and produced an algorithm for finding the shortest paths for them. In this paper, it is shown that the formula for the diameter and the routing algorithm presented by them are inaccurate. We have obtained a large dataset containing parameters for describing optimal diameter chord rings for all the numbers of nodes up to 60 000 and found the exact lower bound for the diameter of chordal ring networks. A new method is proposed and the algorithms for automatic search for analytical descriptions of families of optimal chordal rings are realized based on an analysis of the database. Using the latter, analytical descriptions of over 500 new families of optimal chordal ring networks for many values of the number of nodes are found (only six families have been known until now in the literature).
摘要 Arden 和 Lee 提出了一类阶数为三的弦环网络作为多计算机系统的通信网络，推导出了直径公式，并提出了为其寻找最短路径的分析方法。本文证明，他们提出的直径公式和路由算法是不准确的。我们获得了一个庞大的数据集，其中包含描述所有节点数（最高达 60 000 个）的最佳弦环直径的参数，并找到了弦环网络直径的精确下限。在对数据库进行分析的基础上，我们提出了一种新方法，并实现了自动搜索最优弦环分析描述族的算法。利用该算法，我们找到了 500 多个新的最优弦环网络族的分析描述，适用于多种节点数（迄今为止，文献中只知道六个族）。
{"title":"A Method for Automatic Search for Families of Optimal Chordal Ring Networks","authors":"E. A. Monakhova, O. G. Monakhov","doi":"10.1134/s1990478924010113","DOIUrl":"https://doi.org/10.1134/s1990478924010113","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Arden and Lee proposed a class of chordal ring networks of degree three as communication\u0000networks for multicomputer systems, derived a formula for the diameter, and produced an\u0000algorithm for finding the shortest paths for them. In this paper, it is shown that the formula for\u0000the diameter and the routing algorithm presented by them are inaccurate. We have obtained a\u0000large dataset containing parameters for describing optimal diameter chord rings for all the\u0000numbers of nodes up to 60 000 and found the exact lower bound for the diameter of chordal ring\u0000networks. A new method is proposed and the algorithms for automatic search for analytical\u0000descriptions of families of optimal chordal rings are realized based on an analysis of the database.\u0000Using the latter, analytical descriptions of over 500 new families of optimal chordal ring networks\u0000for many values of the number of nodes are found (only six families have been known until now in\u0000the literature).\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806557","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}
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