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Correction of CT Burst Array Errors in the Generalized-Lee-RT Spaces

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Acta Mathematica Sinica,English Series 2010年第8期26卷 1475-1484页

作者： Sapna JAIN k.p.shum Department of Mathematics University of Delhi Department of Mathematics The University of Hong Kong

In [Jain, S.： Array codes in the generalized-Lee-RT-pseudo-metric （the GLRTp-metric）, to appear in Algebra Colloq.], Jain introduced a new pseudo-metric on the space Matm×s（Zq）, the module space of all m × s matrices with entries from the finite ring Zq, generalized the classical Lee metric [Lee, C. Y.： Some properties of non-binary error correcting codes. IEEE Trans. Inform. Theory, IT-4, 77- 82 （1958）] and array RT-metric [Rosenbloom, M. Y., Tsfasman, M. A.： Codes for m-metric. prob. Inf. Transm., 33, 45-52 （1997）] and named this pseudo-metric as the Generalized-Lee-RT-pseudo-Metric （or the GLRTp-Metric）. In this paper, we obtain some lower bounds for two-dimensional array codes correcting CT burst array errors [Jain, S.： CT bursts from classical to array coding. Discrete Math., 308-309, 1489-1499 （2008）] with weight constraints under the GLRTp-metric.

关键词： Linear array codes Lee metric RT metric CT burst array errors

On p-nilpotency and minimal subgroups of finite groups

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Science China Mathematics 2003年第2期46卷 176-186页

作者：郭秀云 k.p.shum Department of Mathematics Shanxi University Department of Mathematics The Chinese University of Hong Kong

We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup k ofG such that G = Hk and H ∩k ≤ core(H). In this paper it is proved that a finite group G is p-nilpotentif G is S4-free and every minimal subgroup of p ∩ GN is c-supplemented in NG(p), and when p = 2 p isquaternion-free, where p is the smallest prime number dividing the order of G, p a Sylow p-subgroup of *** some applications of this result, some known results are generalized.

关键词： p-nilpotent groups, minimal subgroups, formation.

On Almost Armendariz Ring

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Algebra Colloquium 2020年第2期27卷 199-212页

作者： Om prakash Sushma Singh k.p.shum Department of Mathematics Indian Institute of Technology Patna PatnaBihar 801106India Department of Mathematics John Fulton Center The Chinese University of Hong KongShatinN.T.Hong KongChina

In this paper,we introduce the notion of an almost Armendariz ring,which is a generalization of an Armendariz ring,and discuss some of its *** has been found that every almost Armendariz ring is weak Armendariz but the converse is not *** prove that a ring R is almost Armendariz if and only if R[x]is almost *** is also shown th at if R/I is an almost Armendariz ring and I is a semicommutative ideal,then H is an almost Armendariz ***,the class of minimal non-commutative almost Armendariz rings is completely determined,up to isomorphism(minimal means having smallest cardinality).

关键词： Armendariz ring almost Armendariz ring weak Armendariz ring lower nil radical reduced ring semicommutative ring

On f-Disjunctive Languages, f-Disjunctive Domains and Solid Codes(Dedicated to the late professor Xu Yonghua (1932-2019))

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Algebra Colloquium 2020年第2期27卷 331-342页

作者： Jing Leng Yuqi Guo k.p.shum School of Mathematics and Statistics Lanzhou University Lanzhou 730000China Institute of Mathematics Yunnan University Kunming 650091China

Every language is either the disjoint union or the intersection of two disjunctive *** family of f-disjunctive languages is a natural generalization of the family of disjunctive *** domains(f-disjunctive domains)are defined as the languages which can be checked whether a given language is disjunctive(f-disjunctive)or *** f-disjunctive domains were first studied by Guo et *** *** continue their study on f-disjunctive *** new results for f-disjunctive domains,containing a relation between disjunctive domains and f-disjunctive domains,are *** this respect,we also make an appropriate opening for the completely dense languages and solid codes.

关键词： f-disjunctive languages f-disjunctive domains completely dense languages solid codes

Novel applications of bipolar single-valued neutrosophic competition graphs

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Applied Mathematics(A Journal of Chinese Universities) 2018年第4期33卷 436-467页

作者： Muhammad Akram Maryam Nasir k.p.shum Department of Mathematics University of the PunjabNew Campus Institute of Mathematics Yunnan University

Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We first introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propositions related to bipolar single-valued neutrosophic competition graphs. We define bipolar single-valued neutrosophic economic competition graphs and m-step bipolar single-valued neutrosophic economic competition graphs. Further, we describe applications of bipolar single-valued neutrosophic competition graphs in organizational designations and brands competition. Finally, we present our improved methods by algorithms.

关键词： bipolar single-valued neutrosophic digraphs m-step bipolar single-valued neutrosophic economic competition graphs algorithm

Bipolar Neutrosophic planar Graphs

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Journal of Mathematical Research with Applications 2017年第6期37卷 631-648页

作者： Muhammad AkRAM k.p.shum Department of Mathematics University of the PunjabNew Campus Institute of Mathematics Yunnan University

Fuzzy graph theory is used for solving real-world problems in different fields,including theoretical computer science,engineering,physics,combinatorics and medical *** this paper,we present conepts of bipolar neutrosophic multigraphs,bipolar neutrosophic planar graphs,bipolar neutrosophic dual graphs,and study some of their related *** also describe applications of bipolar neutrosophic graphs in road network and electrical connections.

关键词： Bipolar neutrosophic planar graphs bipolar neutrosophic dual graphs

Sturdy Frame of Type (2,2) Algebras With Application to Semigroup Structure of Semirings

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数学进展 2002年第3期31卷 290-292页

作者：赵宪钟郭聿琦 k.p.shum Dept.ofMath. Northwestuniv.xianShanxi710069PR.China

W irst Introduce the concept *** We call txne(2,2)alsebr洲;+;·)a w。e If B Is elldowed with an upp。rsc。lllattlce order‘”<”“satlsfyingthe Nil。

关键词：半群结构半环 (2,2)型代数

Generalized Fuzzy Lie Ideals of Lie Algebras

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模糊系统与数学 2010年第4期24卷 48-55页

作者： M.Akram B.Davvaz k.p.shum punjab University College of Information Technology University of the PunjabOld Campus Department of Mathematics Yazd University Department of Mathematics The University of Hong Kong

In this paper we introduce new generalized fuzzy Lie ideals of Lie algebras and study some of their important *** characterize these generalized Lie ideals of Lie algebras by their level *** characterization of the ge... 详细信息

关键词： Lie Algebras (∈,∈∨q)-fuzzy Lie Ideals Lie Ideals with Thresholds

Implicative Ideals and Fuzzy Implicative Ideals of a Distributive Implication Groupoid

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Journal of Mathematical Research with Applications 2014年第6期34卷 631-639页

作者： Ravi kumar BANDARU k.p.shum Department of Engineering Mathematics GITAM University Hyderabad Campus Institute of Mathematics Yunnan University

We introduce the notions of implicative ideals and fuzzy implicative ideals of a distributive implication groupoid. Some properties of these ideals will be investigated. In particular, the necessary and sufficient conditions for an ideal(fuzzy ideal) to be an implicative ideal(fuzzy implicative ideal) is given. By using the concept of level sets, we will characterize the fuzzy implicative ideals of a distributive implication groupoid. Finally, an extension property for fuzzy implicative ideals is given.

关键词： implication groupoids distributive implication groupoids fuzzy ideals implicative ideals fuzzy implicative ideals