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Dative B–N bonds weaven toward two-dimensional purely organic materials for single crystals

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Science China Chemistry 2025年第01期 12-14页

作者： Wei-Lei Zhou Siwei Wang Yong Chen College of Chemistry and Materials Science Inner Mongolia Key Laboratory of Chemistry for Nature Products and Synthesis for Functional Molecules Innovation Team of Optical Functional Molecular Devices Inner Mongolia Minzu University College of Chemistry Nankai University

Molecular topology is one of the important topics to study and understand the relationship between molecular structure and properties [1]. Particularly, two-dimensional (2D) materials with extremely high surface area and ultra-thin morphology have attracted considerable attention due to their unexpected properties in materials and chemistry [2,3].

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Gray codes over certain run-length sequences for local rank modulation

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Science China(Information Sciences) 2018年第10期61卷 98-113页

作者： Xiang WANG Fang-Wei FU National Computer Network Emergency Response Technical team The Chern Institute of mathematics and LPMC Nankai University

In the local rank modulation(LRM) scheme, a sliding window produces a sequence of permutations by moving over a sequence of variables. LRM has been presented as a method of storing data in flash memory, which represents a natural generalization of the classical rank modulation scheme. In this paper, we present a study on Gray codes over certain run-length sequences for the(1, 2, n)-LRM scheme to simulate virtual multilevel flash memory cells while maintaining the advantages of LRM. Unlike previous studies on the LRM scheme, we present Gray codes over certain run-length sequences in the(1, 2, n)-LRM scheme. This class of Gray codes can overcome the drawback of the many distinct charge levels required in the rank modulation scheme and in certain Gray codes for LRM. Furthermore, we demonstrate that the proposed codes have an asymptotically optimal rate.

关键词： flash memory local rank modulation Gray codes rank modulation run-length sequences

Sharp large deviations for sums of bounded from above random variables

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Science China mathematics 2017年第12期60卷 2465-2480页

作者： FAN XieQuan Center for Applied mathematics Tianjin University Tianjin 300072 China Regularity team INRIA Saclay Palaiseau 91120 France

We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.

关键词： sharp large deviations Cram′er large deviations Talagrand’s inequality Hoeffding’s inequality sums of independent random variables

Exact and Approximation Algorithms for the Multi-Depot Capacitated Arc Routing Problems

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Tsinghua Science and Technology 2023年第5期28卷 916-928页

作者： Wei Yu Yujie Liao Yichen Yang School of mathematics East China University of Science and TechnologyShanghai 200237China Sabre Lab Research team Sabre Inc.SouthlakeTX 76092USA

In this work,we investigate a generalization of the classical capacitated arc routing problem,called the Multi-depot Capacitated Arc Routing Problem(MCARP).We give exact and approximation algorithms for different variants of the ***,we obtain the first constant-ratio approximation algorithms for the MCARP and its nonfixed destination ***,for the multi-depot rural postman problem,i.e.,a special case of the MCARP where the vehicles have infinite capacity,we develop a(2-1/2k+1)-approximation algorithm(k denotes the number of depots).Third,we show the polynomial solvability of the equal-demand MCARP on a line and devise a 2-approximation algorithm for the multi-depot capacitated vehicle routing problem on a ***,we conduct extensive numerical experiments on the algorithms for the multi-depot rural postman problem to show their effectiveness.

关键词： approximation algorithm multi-depot vehicle routing problem arc routing problem rural postman problem

SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON'S EQUATION

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Acta Mathematica Scientia 2016年第3期36卷 791-801页

作者： Bouikhalene BELAID Elqorachi ELHOUCIEN Bouikhalene Belaid Polydisciplinary FacultyUniversity Sultan Moulay Slimane Elqorachi Elhoucien Functional Equations and Applications TeamDepartment of MathematicsFaculty of SciencesUniversity Ibn Zohr

In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t）＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t）＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy）＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.

关键词： d'Alembert's functional equation locally compact group involution character complex measure Wilson's functional equation Hyers-Ulam stability

Predefined-Time Constrained Optimization of Multi-Agent Systems Under Impulsive Effects

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IEEE/CAA Journal of Automatica Sinica 2025年第1期 255-257页

作者： Zhuyan Jiang Xiaoyang Liu Xiang Jiang Jinde Cao the School of Computer Science and Technology Jiangsu Normal University IEEE the School of mathematics Southeast University

Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for impulse effects. Firstly, to address the inequality constraints,the penalty method is introduced. Then, a novel optimization strategy is developed, which only requires that the team objective function be strongly convex.

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Continuity of Solution Mappings for Parametric Generalized Set-Valued Weak Vector Equilibrium Problems

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Journal of Systems Science & Complexity 2017年第2期30卷 378-391页

作者： PENG Zaiyun ZHAO Yong YANG Xinmin College of mathematics and Statistics Chongqing JiaoTong University Department of mathematics Sichuan University Department of mathematics Chongqing Normal University

This paper obtains some stability results for parametric generalized set-valued weak vector equilibrium problem. Under new assumptions, which do not contain any information about solution mappings, the authors establish the continuity of the solution mapping to a parametric generalized set-valued weak vector equilibrium problem without monotonicity. These results extend and improve some results in the literature. Some examples are given to illustrate the results.

关键词： Continuity parametric generalized set-valued weak vector equilibrium problems solution mapping stability.

Solution of N-S equations based on the quadtree cut cell method

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Science China(Physics,Mechanics & Astronomy) 2009年第6期52卷 877-884页

作者： KASE Kiwamu Volume CAD Modeling team RIKEN Institute

With the characteristic of the quadtree data structure, a new mesh generation method, which adopts square meshes to decompose a background domain and a cut cell approach to express arbitrary boundaries, is proposed to keep the grids generated with a good orthogonality easily. The solution of N-S equations via finite volume method for this kind of unstructured meshes is derived. The mesh generator and N-S solver are implemented to study two benchmark cases, i.e. a lid driven flow within an inclined square and a natural convection heat transfer flow in a square duct with an inner hot circular face. The simulation results are in agreement with the benchmark values, verifying that the present methodology is valid and will be a strong tool for two-dimensional flow and heat transfer simulations, especially in the case of complex boundaries.

关键词： quadtree cut cell N-S equations finite volume method

Weak and strong stabilization of linear systems

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控制理论与应用（英文版） 2009年第4期7卷 359-366页

作者： Mohamed OUZAHRA Hamid BOURRAY Asmae KAMAL Rachid El AYADI Departement of mathematics and Informatics Ecole Normale Supérieure University Sidi Mohamed Ben Abdellah Fès Morocco I2R team AFACSI Laboratory Faculty of Sciences Departement of Mathematics and Computer Sciences Moulay Ismail University Meknes Morocco

We study the problem of stabilizing a distributed linear system on a subregion of its geometrical domain. We are concerned with two methods： the first approach enables us to characterize a stabilizing control via the steady state Riccati equation, and the second one is based on decomposing the state space into two suitable subspaces and studying the projections of the initial system onto such subspaces. The obtained results are performed through various examples.

关键词： Linear systems Regional stabilization Riccati equation Decomposed method