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Methods of Nonsmooth Analysis as Appliedto the Problem of Minimizing the Sum of Moduliof Affine Functions 仿射函数模和最小化问题的非光滑分析方法
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040203
G. Sh. Tamasyan, G. S. Shulga
{"title":"Methods of Nonsmooth Analysis as Applied\u0000to the Problem of Minimizing the Sum of Moduli\u0000of Affine Functions","authors":"G. Sh. Tamasyan,&nbsp;G. S. Shulga","doi":"10.1134/S1990478924040203","DOIUrl":"10.1134/S1990478924040203","url":null,"abstract":"<p> An application of constructive nonsmooth analysis methods to the problem of minimizing\u0000a convex piecewise affine function defined as the sum of absolute values of affine functions is\u0000demonstrated. Hypodifferential calculus was used in the general (multidimensional) case, while\u0000subdifferential calculus was employed in the scalar case. Analyzing the optimality criterion, one\u0000can reveal that the point delivering the global minimum can be found by solving the\u0000corresponding linear programming problem. In the scalar case, the solution can also be found in\u0000closed form as the weighted median of the nodes of a broken line.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"875 - 885"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143275","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
Junction Problem for Elastic Timoshenko Inclusionsin Elastic Bodies with a Crack 含裂纹弹性体弹性Timoshenko内含体的连接问题
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040124
N. A. Nikolaeva
{"title":"Junction Problem for Elastic Timoshenko Inclusions\u0000in Elastic Bodies with a Crack","authors":"N. A. Nikolaeva","doi":"10.1134/S1990478924040124","DOIUrl":"10.1134/S1990478924040124","url":null,"abstract":"<p> The paper is concerned with a junction problem for Timoshenko elastic inclusions placed\u0000in an elastic body with a crack. It is assumed that the crack crosses the thin inclusion at some\u0000point. This point is a mutual contact point. Inequality-type boundary conditions are imposed at\u0000the point of contact and on the crack edges to prevent mutual penetration between inclusion parts\u0000and crack edges, respectively. Existence and uniqueness theorems are established. Differential\u0000formulation in the form of a boundary value problem that contains junction boundary conditions\u0000is presented.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"775 - 787"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143115","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
On the Existence of Viscosity Solutionsfor Evolution( p(x) )-Laplace Equationwith One Spatial Variable 演化( p(x) ) -单空间变量拉普拉斯方程黏度解的存在性
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040215
Ar. S. Tersenov
{"title":"On the Existence of Viscosity Solutions\u0000for Evolution\u0000( p(x) )-Laplace Equation\u0000with One Spatial Variable","authors":"Ar. S. Tersenov","doi":"10.1134/S1990478924040215","DOIUrl":"10.1134/S1990478924040215","url":null,"abstract":"<p> In this paper, we study the first boundary value problem for the\u0000<span>( p(x) )</span>-Laplacian with one spatial variable in the presence of gradient terms that do\u0000not satisfy the Bernstein–Nagumo condition. A class of gradient nonlinearities is defined for which\u0000the existence of a viscosity solution that is Lipschitz continuous in\u0000<span>( x )</span> and Hölder continuous in\u0000<span>( t )</span> is proven.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"886 - 904"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143118","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
The Number of Impossible Additive Differentialsfor the Composition of XOR and Bit Rotation 异或和位旋转组合中不可能加性微分的个数
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040094
N. A. Kolomeec
{"title":"The Number of Impossible Additive Differentials\u0000for the Composition of XOR and Bit Rotation","authors":"N. A. Kolomeec","doi":"10.1134/S1990478924040094","DOIUrl":"10.1134/S1990478924040094","url":null,"abstract":"<p> Additive differentials of the function\u0000<span>( (x oplus y) lll r )</span> whose probability is\u0000<span>( 0 )</span> are considered, where\u0000<span>( x, y in mathbb {Z}_2^{n} )</span> and\u0000<span>( 1 leq r &lt; n )</span>. They are called impossible differentials and are interesting in the context of\u0000differential cryptanalysis of ciphers whose schemes consist of additions modulo\u0000<span>( 2^n )</span>, bitwise XORs (\u0000<span>( oplus )</span>), and bit rotations (\u0000<span>( lll r )</span>). The number of all such differentials is calculated for all possible\u0000<span>( r )</span> and\u0000<span>( n )</span>. It is also shown that this number is greater than\u0000<span>( frac {38}{245} 8^n )</span>. Moreover, the estimate is asymptotically tight for\u0000<span>( r, n-r to infty )</span>. For any fixed\u0000<span>( n )</span> the number of all impossible differentials decreases as\u0000<span>( r )</span> goes from\u0000<span>( 1 )</span> to\u0000<span>( lceil n/2 rceil )</span> (to\u0000<span>( lceil n/2 rceil + 1 )</span> in the case of\u0000<span>( n in {4, 5, 6, 8, 10, 12} )</span>) and then increases monotonically as\u0000<span>( r )</span> goes to\u0000<span>( n-1 )</span>. A simplified description of all impossible differentials is obtained up to\u0000known symmetries.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"722 - 743"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143120","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
Variable Neighborhood Descent for Finding the ThresholdStability Radius in the Facility Location and Discriminatory Pricing Problem 设施选址与歧视性定价问题中求阈值稳定半径的变邻域下降算法
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040136
A. A. Panin, D. A. Piskeeva, A. V. Plyasunov
{"title":"Variable Neighborhood Descent for Finding the Threshold\u0000Stability Radius in the Facility Location and Discriminatory Pricing Problem","authors":"A. A. Panin,&nbsp;D. A. Piskeeva,&nbsp;A. V. Plyasunov","doi":"10.1134/S1990478924040136","DOIUrl":"10.1134/S1990478924040136","url":null,"abstract":"<p> A new threshold stability problem in the context of facility location and discriminatory\u0000pricing is considered. In the statement of facility location and pricing problem, the company\u0000decides to open facilities and assign prices to each customer at each facility. The implementation\u0000of discriminatory pricing leads to a scenario where each customer is compelled to expend the\u0000maximum amount of their available financial resources, thereby ensuring the maximum revenue\u0000for the company. In the threshold stability problem, the available financial resources or budget of\u0000each consumer is a parameter with a known expected value. The objective is to maximize the\u0000deviation of the parameters from the expected value, provided that the company’s income remains\u0000above a given threshold.\u0000</p><p>An algorithm based on variable neighborhood descent (VND) is proposed to solve\u0000the threshold stability problem. Numerical investigation of the algorithm is carried out on known\u0000instances and randomly generated ones. Various ways of constructing the starting facility location\u0000and different criteria for comparing the location vectors are analyzed.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"788 - 799"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143024","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
On the Complexity of Fanout-Bounded ParallelPrefix Circuits 扇出界并行前缀电路的复杂度
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040185
I. S. Sergeev
{"title":"On the Complexity of Fanout-Bounded Parallel\u0000Prefix Circuits","authors":"I. S. Sergeev","doi":"10.1134/S1990478924040185","DOIUrl":"10.1134/S1990478924040185","url":null,"abstract":"<p> We prove that the complexity of a universal depth-\u0000<span>( n )</span> parallel prefix circuit on\u0000<span>( 2^n )</span> inputs with fanout bounded by\u0000<span>( 2 )</span> is at least\u0000<span>( 0.75(n-1)2^{n} )</span>. We also propose a number of simple constructions and upper complexity\u0000bounds on fanout-\u0000<span>( 2 )</span> prefix circuits of depth\u0000<span>( n+k )</span>.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"850 - 859"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143053","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
The( ell )-Rauzy Graphs on Infinite Words ( ell ) -无限词的模糊图
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040161
M. Rajavel Praveen, R. Rama
{"title":"The\u0000( ell )-Rauzy Graphs on Infinite Words","authors":"M. Rajavel Praveen,&nbsp;R. Rama","doi":"10.1134/S1990478924040161","DOIUrl":"10.1134/S1990478924040161","url":null,"abstract":"<p> Word-representable graphs are vital in the Combinatorics of Words and Graph Theory.\u0000We define one such graph, the\u0000<span>( ell )</span>-Rauzy graph, and study its structural properties for a few infinite words. The\u0000<span>( ell )</span>-Rauzy graph of order\u0000<span>( k )</span> for an infinite word\u0000<span>( w )</span> is a directed graph in which each vertex is a subword of length\u0000<span>( k )</span> of\u0000<span>( w )</span>, where any two vertices\u0000<span>( u,v )</span> form an arc\u0000<span>( uv )</span> iff the prefix of\u0000<span>( v )</span> of length\u0000<span>( ell )</span> is the same as the suffix of\u0000<span>( u )</span> of length\u0000<span>( ell )</span> and the concatenated word formed by the arc\u0000<span>( uv )</span> of length\u0000<span>( 2k-ell )</span> is a subword of\u0000<span>( w )</span>. As main results, we show that the\u0000<span>( ell )</span>-Rauzy graph of order\u0000<span>( k )</span> for the infinite Fibonacci word\u0000<span>( f )</span> is strongly connected, and we explicitly find the graph structure of the\u0000<span>( ell )</span>-Rauzy graph of order\u0000<span>( k )</span> for an infinite periodic word, by knowing the locations of subwords of\u0000<span>( f )</span> and infinite periodic words. As locating the subwords in an infinite word is\u0000not easy, we show that the\u0000<span>( ell )</span>-Rauzy graph of order\u0000<span>( k )</span> for an Arnoux-Rauzy word is strongly connected using a different approach.\u0000<span>( ell )</span>\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"824 - 838"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143114","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
Approximation Algorithms for Graph Clustering Problems withClusters of Bounded Size 具有有限大小聚类的图聚类问题的逼近算法
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040069
V. P. Il’ev, S. D. Il’eva, A. V. Kononov
{"title":"Approximation Algorithms for Graph Clustering Problems with\u0000Clusters of Bounded Size","authors":"V. P. Il’ev,&nbsp;S. D. Il’eva,&nbsp;A. V. Kononov","doi":"10.1134/S1990478924040069","DOIUrl":"10.1134/S1990478924040069","url":null,"abstract":"<p> In the cluster editing problem, one has to partition the set of vertices of a graph into\u0000pairwise disjoint subsets (called clusters) minimizing the number of edges between clusters and the\u0000number of missing edges within clusters. We consider a version of the problem in which cluster\u0000sizes are bounded from above by a positive integer\u0000<span>( s )</span>. This problem is NP-hard for any fixed\u0000<span>( s geqslant 3 )</span>. We propose polynomial-time approximation algorithms for this version of\u0000the problem. Their performance guarantees equal\u0000<span>( 5/3 )</span> for the case\u0000<span>( s = 3 )</span> and\u0000<span>( 2 )</span> for\u0000<span>( s = 4 )</span>. We also show that the cluster editing problem is APX-hard for the case of\u0000<span>( s = 3 )</span>.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"686 - 696"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143113","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
Updated Estimates for Algorithms for Packing2-Bar Charts in a Strip 条形图包装算法的更新估计
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040112
S. A. Nazarenko
{"title":"Updated Estimates for Algorithms for Packing\u00002-Bar Charts in a Strip","authors":"S. A. Nazarenko","doi":"10.1134/S1990478924040112","DOIUrl":"10.1134/S1990478924040112","url":null,"abstract":"<p> We consider a two-bar charts packing problem in which it is necessary to pack bar charts\u0000consisting of two bars in a unit-height strip of minimum length. Each bar has a height of at most\u00001 and unit length. The problem under consideration is NP-hard and generalizes the bin packing\u0000problem and two-dimensional vector packing problem. This paper proves updated accuracy\u0000estimates and time complexity for several previously developed polynomial approximation\u0000algorithms for the two-bar charts packing problem and particular cases of the problem. We show\u0000the attainability of the estimates. Furthermore, we consider a problem of packing an unlimited\u0000number of bar charts belonging to\u0000<span>( k )</span> different types and propose a polynomial algorithm to solve the problem in\u0000case\u0000<span>( k = text {const} )</span>.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"759 - 774"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143121","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
Uniform Attractors for the Kelvin–Voigt Model Taking intoAccount Memory along Fluid Motion Trajectories 考虑沿流体运动轨迹记忆的Kelvin-Voigt模型的均匀吸引子
IF 0.58
Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI: 10.1134/S1990478924040227
M. V. Turbin, A. S. Ustiuzhaninova
{"title":"Uniform Attractors for the Kelvin–Voigt Model Taking into\u0000Account Memory along Fluid Motion Trajectories","authors":"M. V. Turbin,&nbsp;A. S. Ustiuzhaninova","doi":"10.1134/S1990478924040227","DOIUrl":"10.1134/S1990478924040227","url":null,"abstract":"<p> The paper is devoted to the study of the qualitative behavior of solutions for the\u0000Kelvin–Voigt model taking into account memory along fluid motion trajectories. Namely, based\u0000on the theory of attractors of noninvariant trajectory spaces, for the model under consideration in\u0000the nonautonomous case the existence of a uniform trajectory and a uniform global attractor is\u0000proved under certain conditions on the coefficients.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"905 - 917"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143119","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
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