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Algorithms for enumeration problem of linear congruence modulo m as sum of restricted partition numbers

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Frontiers of Mathematics in China 2015年第1期10卷 69-89页

作者： Tian-Xiao HE Peter J. -S. SHIUE Department of Mathematics Illinois Wesleyan University Bloomington IL 61702 USA Department of Mathematical Sciences University of Nevada Las Vegas Las Vegas NV 89154-4020 USA

We consider the congruence x1＋ x2 ＋… ＋ xr - c （mod m）, wherem and r are positive integers and c ∈Zm ：= {0, 1, ..., m- 1} （m ≥ 2）. Recently,W.-S. thou, T. X. He,and Peter J.-S. Shiue considered the enumerationproblems of this congruence, namely, the number of solutions with the restriction x1≤~ x2≤ ... ≤ xr, and got some properties and a neat formula ofthe solutions. Due to the lack of a simple computational method for calculating the number of the solution of the congruence, we provide an algebraic and a recursive algorithms for those numbers. The former one can also give a new and simple approach to derive some properties of solution numbers.

关键词： congruence multiset congruence solution restricted integerpartition

The K°-relation on the congruence Lattice of a Regular Semigroup with an Inverse Transversal

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Acta Mathematica Sinica,English Series 2012年第5期28卷 1061-1074页

作者： Ying Ying FENG Li Min WANG Department of Information Science and Mathematics Foshan University School of Mathematics South China Normal University

Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.

关键词： Regular semigroup inverse transversal congruence K°-relation

P-congruence-free Epigroups

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Communications in Mathematical Research 2017年第2期33卷 97-109页

作者： Liu Jing-guo Zhang Jin-ling School of Mathematics and Statistics Linyi UniversityLinyiShandong276005 Lanshan Education and Physical Education Bureau LinyiShandong276005

Let P denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any congruence either contains P or its join with P is the identity relation on epigroups. As a special subclass of epigroups, completely 0-simple semigroups having the same property are also described.

关键词： congruence epigroup completely 0-simple semigroup

Low degree cohomologies of congruence groups

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Science China Mathematics 2019年第11期62卷 2287-2308页

作者： Jian-Shu Li Binyong Sun Institute for Advanced Study in Mathematics Zhejiang UniversityHangzhou 310058 China Department of Mathematics Hong Kong University of Science and TechnologyHong KongChina Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.

关键词： cohomology congruence group automorphic form

Conditional congruence Closure over Uninterpreted and Interpreted Symbols

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Journal of Systems Science & Complexity 2019年第1期32卷 317-355页

作者： KAPUR Deepak Department of Computer Science University of New Mexico

A framework for generating congruence closure and conditional congruence closure of ground terms over uninterpreted as well as interpreted symbols satisfying various properties is proposed. It is based on some of the key concepts from Kapur's congruence closure algorithm(RTA97)for ground equations based on introducing new symbols for all nonconstant subterms appearing in the equation set and using ground completion on uninterpreted constants and puri?ed equalities over interpreted symbols belonging to different theories. In the original signature, the resulting rewrite systems may be nonterminating but they still generate canonical forms. A byproduct of this framework is a constant Horn completion algorithm using which ground canonical Horn rewrite systems can be generated for conditional ground theories.New effcient algorithms for generating congruence closure of conditional and unconditional equations on ground terms over uninterpreted symbols are presented. The complexity of the conditional congruence closure is shown to be O(n*log(n)), which is the same as for unconditional ground equations.The proposed algorithm is motivated by our attempts to generate effcient and succinct interpolants for the quanti?er-free theory of equality over uninterpreted function symbols which are often a conjunction of conditional equations and need additional simpli?cation. A completion algorithm to generate a canonical conditional rewrite system from ground conditional equations is also presented. The framework is general and ?exible and is used later to develop congruence closure algorithms for cases when function symbols satisfy simple properties such as commutativity, nilpotency, idempotency and identity as well as their combinations. Interesting outcomes include algorithms for canonical rewrite systems for ground equational and conditional theories on uninterpreted and interpreted symbols leading to generation of canonical forms for ground terms, constrained terms and Horn equations.

关键词： Completion congruence closure conditional congruence closure intepreted symbols rewrit-ing uninterpreted symbols

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congruence浅议

外国语 2001年第6期24卷 43-48页

作者：刘宇红复旦大学外文系上海200433

本文在对congruence的涵义和理论发展脉络进行归纳和清理的基础上,从认知语言学的视角提出了三条判别一致式与非一致式的标准,即主语典型性标准,是否隐涵根隐喻的标准和是否体现人体活动的标准。在总结名词化的范围时,作者发现,名词化... 详细信息

本文在对congruence的涵义和理论发展脉络进行归纳和清理的基础上,从认知语言学的视角提出了三条判别一致式与非一致式的标准,即主语典型性标准,是否隐涵根隐喻的标准和是否体现人体活动的标准。在总结名词化的范围时,作者发现,名词化可以存在于六种不同的及物性过程中,而且不同的及物性过程均可通过名词化而以语法隐喻的形式实现对语义的编码,这样一来,不同过程间的相互隐喻和名词化隐喻间的非对称性被消解。

关键词：认知语言学语法隐喻理论语义 congruence 主语典型性标准

From moral leadership to positive work behaviors: the mediating roles of value congruence and leader-member exchange

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Frontiers of Business Research in China 2019年第1期13卷 1-18页

作者： Yuanjie Bao Chaoping Li School of Public Administration and Policy Renmin University of China Room 422b Qiushi Building No. 59 Zhongguancun avenue Haidian district Beijing 100872 China

Limited empirical investigation has been devoted to understanding the multipleeffect mechanisms of moral leadership, especially the relationship between mediators. Drawing from both social learning and social exchange theories, this study examines whether value congruenee and leader-member exchange (LMX) mediate the effect of moral leadership on followers' positive work behaviors. Using two-wave survey data from 395 Chinese employees, the results indicate that both value congruence and LMX act as mediators in the relationship between moral leadership and positive work behaviors. Furthermore, a sequential mediation link from moral leadership to value congruenee, then to LMX, and finally to positive work behaviors was established. Theoretical and practical implications are further discussed.

关键词： Moral leadership Value congruence Leader-member exchange (LMX) Positive work behaviors Social learning Social exchange

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父母参与的一致性与儿童主观幸福感的关系

心理学

A fully abstract semantics for value-passing CCS for trees

心理学 2024年第5期

作者：鞠佳雯周欣然梁丽婵边玉芳

本研究通过问卷法对1145个双职工家庭中的四年级学生进行了连续两年的追踪测查，探讨父母参与一致性与儿童主观幸福感的关系以及儿童性别在其中的作用。结果表明：(1)父母参与是否一致对儿童的主观幸福感影响不显著；(2)父母参与一致时... 详细信息

本研究通过问卷法对1145个双职工家庭中的四年级学生进行了连续两年的追踪测查，探讨父母参与一致性与儿童主观幸福感的关系以及儿童性别在其中的作用。结果表明：(1)父母参与是否一致对儿童的主观幸福感影响不显著；(2)父母参与一致时，父母参与都高要比都低的情况下，儿童主观幸福感更高；(3)父母参与不一致时，在父亲参与高于母亲参与的情况下，男生当年和第二年的主观幸福感都较高，而在女生群体无此结果。

关键词：主观幸福感父母参与一致性响应面分析性别差异 subjective well-being parental involvement congruence response surface analysis gender difference

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Frontiers of Computer Science 2019年第4期13卷 828-849页

作者： Ying JIANG Shichao LIU Thomas EHRHARD State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of Sciences Beijing 100049 China CNRS IRIF UMR 8243 Univ Paris Diderot Sorbonne Paris Cite F-75205 Paris France

We propose a fully abstract semantics for valuepassing CCS for trees (VCCTS) with the feature that processes are located at the vertices of a graph whose edges describe possible interaction capabilities. The operational semantics is given both in terms of a reduction semantics and in terms of a labelled transition semantics. We develop a theory of behavioral equivalences by introducing both weak barbed congruence and weak bisimilarity. In particular, we show that, on image-finite processes, weak barbed congruence coincides with weak bisimilarity. To illustrate potential applications and the powerful expressiveness of VCCTS, we formally compare VCCTS with some well-known models, e.g., dynamic pushdown networks, top-down tree automata and value-passing CCS.

关键词： process calculus non-interleaving semantics barbed congruence bisimulation