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Improved Bounds on the Size of Permutation codes under Kendall τ-metric

IEEE Transactions on Information Theory 2025年第6期71卷 4156-4166页

作者： Parvaresh, Farzad Sobhani, Reza Abdollahi, Alireza Bagherian, Javad Jafari, Fatemeh Khatami, Maryam University of Isfahan Faculty of Engineering Department of Electrical Engineering Isfahan Iran School of Mathematics Tehran19395-5746 Iran University of Isfahan Faculty of Mathematics and Statistics Department of Applied Mathematics and Computer Science Isfahan81746-73441 Iran University of Isfahan Faculty of Mathematics and Statistics Department of Pure Mathematics Isfahan81746-73441 Iran

In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation method has been proposed. In the rank modulation framework, codewords are permutations. In this paper, we study the largest size P(n, d) of permutation codes of length n, i.e., subsets of the set Sn of all permutations on {1, ..., n} with the minimum distance at least (Formula presented) under the Kendall τ-metric. By presenting an algorithm and two theorems, we improve the known lower and upper bounds for P(n, d). In particular, we show that P(n, d) = 4 for all n ≥ 6 and (Formula presented). Additionally, we prove that for any prime number n and integer (Formula presented). This result greatly improves the upper bound of P(n, 3) for all primes n ≥ 37. © 1963-2012 IEEE.

关键词： Flash memory

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Dynamic partition of urban network considering congestion evolution based on random walk

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Chinese Physics B 2025年第1期34卷 530-534页

作者： Zhen-Tong Feng Lele Zhang Yong-Hong Wu Mao-Bin Hu School of Engineering Science University of Science and Technology of ChinaHefei 230026China Department of Mathematics and Statistics University of MelbourneParkville VIC 3010Australia Department of Mathematics and Statistics Curtin UniversityPerth WA 6845Australia

The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted *** intensive studies on the partitioning of urban road networks,the dynamic partitioning of urban regions reflecting the propagation of congestion remains an open *** paper proposes to partition the network into homogeneous sub-regions based on random walk *** from selected random walkers,the road network is partitioned from the early morning when congestion emerges.A modified Akaike information criterion is defined to find the optimal number of *** boundary adjustment algorithms are adopted to optimize the partitioning results to further ensure the correlation of *** traffic data of Melbourne city are used to verify the effectiveness of the proposed partitioning method.

关键词： urban road networks dynamic partitioning random walk Akaike information criterion perimeter control

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Impact of Pollutant Concentration and Particle Deposition on the Radiative Flow of Casson-Micropolar Fluid between Parallel Plates

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Computer Modeling in engineering & Sciences 2025年第1期142卷 665-690页

作者： Ghaliah Alhamzi Badr Saad T.Alkahtani Ravi Shanker Dubey Vinutha Kalleshachar Neelima Nizampatnam Department of Mathematics and Statistics College of ScienceImam Mohammad Ibn Saud Islamic University(IMSIU)Riyadh11564Saudi Arabia Department of Mathematics College of ScienceKing Saud UniversityRiyadh11989Saudi Arabia Department of Mathematics Amity School of Applied SciencesAmity University RajasthanJaipur302002RajasthanIndia Department of Studies in Mathematics Davangere UniversityDavangere577002India Department of Electronics and Communication Engineering Amrita School of EngineeringAmrita Vishwa VidyapeethamBengaluru560035India

Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental *** the effectiveness of treatment methods in reducing pollution scales is made easier by analysing waste discharge *** waste discharge concentration analysis is useful for assessing how effectively wastewater treatment techniques reduce pollution *** study aims to explore the Casson micropolar fluid flow through two parallel plates with the influence of pollutant concentration and thermophoretic particle *** explore the mass and heat transport features,thermophoretic particle deposition and thermal radiation are *** governing equations are transformed into ordinary differential equations with the help of suitable similarity *** Runge-Kutta-Fehlberg’s fourthfifth order technique and shooting procedure are used to solve the reduced set of equations and boundary *** integration of a neural network model based on the Levenberg-Marquardt algorithm serves to improve the accuracy of predictions and optimize the analysis of *** outcomes are displayed to analyze the characteristics of the relevant dimensionless parameters in the current *** reveal that concentration upsurges as the micropolar parameter *** concentration reduces with an upsurge in the thermophoretic *** upsurge in the external pollutant source variation and the local pollutant external source parameters enhances mass *** surface drag force declines for improved values of porosity and micropolar parameters.

关键词： Micropolar fluid thermal radiation porous medium thermophoretic particle deposition waste discharge concentration

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Ultrametric spaces generated by labeled star graphs

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Journal of Mathematical Sciences (United States) 2025年第2期288卷 182-198页

作者： Dovgoshey, Oleksiy Rovenska, Olga Institute of Applied Mathematics and Mechanics of the NAS of Ukraine Slov’yans’k Ukraine Department of Mathematics and Statistics University of Turku Turku Finland Department of Mathematics and Modelling Donbas State Engineering Academy Kramators’k Ukraine

For an arbitrary star graph S with a non-degenerate vertex labeling l: V (S) → ℝ+, we denote by dl the corresponding ultrametric on the vertex set V (S) of S. We characterize the class US of all ultrametric spaces (V... 详细信息

For an arbitrary star graph S with a non-degenerate vertex labeling l: V (S) → ℝ⁺, we denote by d_l the corresponding ultrametric on the vertex set V (S) of S. We characterize the class US of all ultrametric spaces (V (S), d_l) up to isometry. We also find the necessary and sufficient conditions under which the group of all self-isometries of ultrametric space (V (S), d_l) coincides with the group of all selfisomorphisms of the labeled star graph S(l). © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

关键词： graph isomorphism isometry of metric spaces Labeled tree Primary 54E35 Secondary 54E4 star graph ultrametric space

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Formulation and Solution Approach for Uncertain Multi-Objective Material Requirement Planning Problem with Multi-Mode Demand, Overtime Production, and Outsourcing Possibilities

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Journal of Systems Science and Systems engineering 2025年第1期34卷 1-28页

作者： Sadegh Niroomand Dragan Pamucar Ali Mahmoodirad Department of Industrial Engineering Firouzabad Higher Education CenterShiraz University of TechnologyShirazIran Department of Operations Research and Statistics Faculty of Organizational SciencesUniversity of BelgradeBelgradeSerbia Department of Industrial Engineering and Management Yuan Ze UniversityTaoyuan CityTaiwanChina Department of Mechanics and Mathematics Western Caspian UniversityBakuAzerbaijan Department of Mathematics Babol BranchIslamic Azad UniversityBabolIran

Material requirement planning is a type of production planning problems that is used to plan about a final product, its sub-assemblies, and its raw parts simultaneously by considering time phased demands of the final product. In this study a multi-product material requirement planning problem with limited manufacturing resources is considered. As an important novelty, a multi-mode demand strategy is considered in this problem where the total customers’ satisfaction degrees of the selected demand modes is maximized. Furthermore, three types of capacities such as regular, over time, and outsourcing capacities are considered for such system as another novelty. The problem is formulated as a bi-objective model to maximize total profit and total satisfaction degree of the customers simultaneously. To respect the uncertain nature of the problem, it is formulated in a belief-degree based uncertain form. This is for the first time in the literature of material requirement planning that this type of uncertainty is considered. The uncertain problem is converted to a crisp form using some techniques such as expected value model and chance constrained model. Then, a new hybrid form of the fuzzy programming approach is developed to solve the bi-objective crisp formulations. A case study from the petroleum industries of Iran is used to perform the required computational experiments. The required experiments are done, and possible comparisons are made on the obtained results. Furthermore, some managerial insights are given in order to be used in the production system of the case study. According to the obtained results, the proposed hybrid fuzzy programming approach is superior to existing approaches in at least 38 percent of the experiments.

关键词： Material requirement planning multi-mode demand belief-degree based uncertainty multi-objective optimization fuzzy programming approach

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Combinatorial Alphabet-Dependent Bounds for Insdel Codes

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IEEE Transactions on Information Theory 2025年第5期71卷 3544-3559页

作者： Kong, Xiangliang Tamo, Itzhak Wei, Hengjia Tel Aviv University Department of Electrical Engineering-Systems Tel Aviv-Yafo6997801 Israel Xi’an Jiaotong University School of Mathematics and Statistics Xi’an710049 China

Error-correcting codes resilient to synchronization errors such as insertions and deletions are known as insdel codes. In this paper, we present several new combinatorial upper and lower bounds on the maximum size of q-ary insdel codes. Our main upper bound is a sphere-packing bound obtained by solving a linear programming (LP) problem. It improves upon previous results for cases when the distance d or the alphabet size q is large. Our first lower bound is derived from a connection between insdel codes and matchings in special hypergraphs. This lower bound, together with our upper bound, shows that for fixed block length n and edit distance d, when q is sufficiently large, the maximum size of insdel codes is (Formula presented). The second lower bound refines Alon et al.’s recent logarithmic improvement on Levenshtein’s GV-type bound and extends its applicability to large q and d. © 1963-2012 IEEE.

关键词： Coding errors

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Lump and new interaction solutions of the (3+1)-dimensional generalized Shallow Water-like equation along with chaotic analysis

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Alexandria engineering Journal 2025年 126卷 160-169页

作者： Gu, Yongyi Zhang, Xiaoting Peng, Liudi Huang, Zhishang Lai, Yongkang School of Statistics and Mathematics Guangdong University of Finance and Economics Guangzhou510320 China Department of Basic Courses Teaching Software Engineering Institute of Guangzhou Guangzhou510990 China

In recent years, interest in nonlinear evolution equations has surged, underscoring their critical role in understanding complex dynamic systems. This work focuses on the (3+1)-dimensional generalized shallow water-like equation, especially for its relevance to nonlinear wave phenomena. Using Hirota bilinear method, we derive lump solutions for this equation and innovatively explore the interaction dynamics between these lumps and the Weierstrass elliptic function. Additionally, we analyze chaotic solutions for lumps derived from the Duffing chaotic system, examining their chaotic structures in detail. The physical characteristics of these solutions are illustrated via three-dimensional profiles and their corresponding two-dimensional plots. Our findings reveal that the methods employed are both efficient and effective, providing valuable insights into the dynamics of mathematical physics equations. © 2025 The Authors

关键词： Nonlinear equations

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Length-Minimizing LED Trees

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Operations Research Forum 2025年第1期6卷 1-38页

作者： Sarkociová Remešíková, Mariana Sarkoci, Peter Trnovská, Mária Department of Mathematics and Constructive Geometry Faculty of Civil Engineering Slovak University of Technology in Bratislava Radlinského 11 Bratislava 81005 Slovakia Department of Applied Mathematics and Statistics Faculty of Mathematics Physics and Informatics Mlynská Dolina F1 Bratislava 84248 Slovakia

In this paper, we introduce a previously not studied type of Euclidean tree called LED (Leaves of Equal Depth) tree. LED trees can be used, for example, in computational phylogeny, since they are a natural representative of the time evolution of a set of species in a feature space. This work is focused on LED trees that are length minimizers for a given set of leaves and a given isomorphism type. The underlying minimization problem can be seen as a variant of the classical Euclidean Steiner tree problem. Even though it has a convex objective function, it is rather non-trivial, since it has a non-convex feasible set. The main contribution of this paper is that we prove the uniqueness of a stationary point of the length function on the feasible set. Moreover, we prove several geometrical characteristics of the length minimizers that are analogous to the properties of Steiner minimal trees. We also explore some geometrical and topological properties of the feasible set. At the end, to demonstrate the applicability of our theoretical results, we show an example of an application in historical linguistics. © The Author(s) 2025.

关键词： Computational phylogeny Euclidean graph Euclidean tree Language evolution LED tree Length-minimizing tree Phylogenetic tree Steiner tree

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On Dissipativity-Preserving for Switched Positive Takagi–Sugeno Fuzzy Delayed Systems via Switching

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IEEE Transactions on Fuzzy Systems 2025年第5期33卷 1605-1616页

作者： Wang, Peng Sang, Hong Huang, Chuangxia Cao, Jinde Abdel-Aty, Mahmoud Fuzhou University School of Mathematics and Statistics Fuzhou350108 China Dalian Maritime University College of Marine Electrical Engineering Dalian116026 China Changsha University of Science and Technology School of Mathematics and Statistics Changsha410114 China Southeast University School of Mathematics Nanjing211189 China Purple Mountain Laboratories Nanjing211111 China Ahlia University Deanship of Graduate Studies and Scientific Research Manama10878 Bahrain Sohag University Mathematics Department Faculty of Science Sohag82524 Egypt

In this article, we tackle the problem of analyzing dissipativity, via devising switching mechanisms, for switched positive Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. To leverage the positivity properties of state, input, and output variables, a novel concept of dissipativity is developed, focusing on linear supply rates and linear copositive storage functionals. When state information is available, the state dependent switching mechanism satisfying a dwell time constraint is introduced dependent on the constructed time-varying multiple linear copositive storage functionals. This mechanism allows for solving the dissipativity issue for the entire system without imposing any solvability requirements on subsystems and reduces the switching frequency. In cases, where state information is unavailable, dissipativity is ensured by a dwell-time dependent switching mechanism. Further, all conditions guaranteeing the solvability of the problem are presented in the form of linear vector inequalities. Two simulation examples are finally offered, demonstrating that the proposed techniques are effective and superior. © 1993-2012 IEEE.

关键词： Fuzzy systems

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Breathers and multi wave solutions of three different space-time fractional nonlinear coupled waves dynamical models and their applications

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Applied mathematics(A Journal of Chinese Universities) 2025年第1期40卷 33-52页

作者： Ambreen Sarwar GANG Tao Muhammad Arshad Iftikhar Ahmed LU Dian-chen School of Energy and Power Engineering Nanjing University of Science and TechnologyNanjing 210094China Department of Mathematics&Statistics University of AgricultureFaisalabadPakistan Faculty of Science Jiangsu UniversityZhenjiang 212013China

In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation *** we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean ***,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal ***,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a *** obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic ***,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related *** hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.

关键词： conformable fractional derivative solitons breather waves jacobi elliptic function solutions

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