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43 results on '"Shum, K. P."'

2. Concurrent Regenerating Codes and Scalable Application in Network Storage

Author

Zhang, Huayu, Li, Hui, Hou, Hanxu, Shum, K. W., and Li, ShuoYen Robert

Subjects
Computer Science - Information Theory
Abstract

To recover simultaneous multiple failures in erasure coded storage systems, Patrick Lee et al introduce concurrent repair based minimal storage regenerating codes to reduce repair traffic. The architecture of this approach is simpler and more practical than that of the cooperative mechanism in non-fully distributed environment, hence this paper unifies such class of regenerating codes as concurrent regenerating codes and further studies its characteristics by analyzing cut-based information flow graph in the multiple-node recovery model. We present a general storage-bandwidth tradeoff and give closed-form expressions for the points on the curve, including concurrent repair mechanism based on minimal bandwidth regenerating codes. We show that the general concurrent regenerating codes can be constructed by reforming the existing single-node regenerating codes or multiplenode cooperative regenerating codes. Moreover, a connection to strong-MDS is also analyzed. On the other respect, the application of RGC is hardly limited to "repairing". It is of great significance for "scaling", a scenario where we need to increase(decrease) nodes to upgrade(degrade) redundancy and reliability. Thus, by clarifying the similarities and differences, we integrate them into a unified model to adjust to the dynamic storage network., Comment: 12 pages, 7 figures

Published
2016

3. Some new results on Gr\'obner-Shirshov bases

Author

Bokut, L. A., Chen, Yuqun, and Shum, K. P.

Subjects
Mathematics - Rings and Algebras, 16S15, 13P10, 13N10, 16-xx, 17-xx, 17B01, 17B66, 18Axx, 20F36, 20M18, 17B37, 18D50
Abstract

In this survey article, we report some new results of Gr\"obner-Shirshov bases, including new Composition-Diamond lemmas and some applications of some known Composition-Diamond lemmas., Comment: 50 pages

Published
2011

4. Cubic Intuitionistic Structures Applied to Ideals of BCI-Algebras

Author

Senapati Tapan, Jun Young Bae, Muhiuddin G., and Shum K. P.

Subjects
cubic intuitionistic subalgebra, closed cubic intuitionistic ideal, cubic intuitionistic p-ideal, cubic intuitionistic a-ideal, cubic intuitionistic q-ideal, 06f35, 03g25, 94d05, Mathematics, QA1-939
Abstract

In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals in BCI-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic q-ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic p-ideal are provided. Characterizations of a cubic intuitionistic a-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic a-ideal is established.

Published
2019
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5. Markov and Artin normal form theorem for braid groups

Author

Bokut, L. A., Chaynikov, V. V., and Shum, K. P.

Subjects
Mathematics - Group Theory, Mathematics - Combinatorics
Abstract

In this paper we will present the results of Artin--Markov on braid groups by using the Groebner--Shirshov basis. As a consequence we can reobtain the normal form of Artin--Markov--Ivanovsky as an easy corollary.

Published
2008

6. Rosso-Yamane Theorem on PBW basis of $U_q(A_N)$

Author

Chen, Yuqun, Shao, Hongshan, and Shum, K. P.

Subjects
Mathematics - Rings and Algebras, Mathematics - Quantum Algebra, 20G42, 16S15, 13P10
Abstract

Let $U_q(A_N)$ be the Drinfeld-Jimbo quantum group of type $A_N$. In this paper, by using Groebner-Shirshov bases, we give a simple (but not short) proof of the Rosso-Yamane Theorem on PBW basis of $U_q(A_N)$.

Published
2008

7. Construction of composition (m, n, k)-hyperrings

Author

Davvaz B., Rakhsh-Khorshid N., and Shum K. P.

Subjects
hyperring, composition (m, k)-hyperring, strong homomorphism, primary 16y99, secondary 20n20, Mathematics, QA1-939
Abstract

In this paper, our aim is to introduce the notion of a composition (m, n, k)-hyperring and to analyze its properties. We also consider the algebraic structure of (m, n, k) hyperrings which is a generalization of composition rings and composition hyperrings. Also, the isomorphism theorems of ring theory are derived in the context of composition (m, n, k)-hyperrings.

Published
2016
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8. Neutrosophic implicative UP-filters, neutrosophic comparative UP-filters, and neutrosophic shift UP-filters of UP-algebras

Author

Songsaeng, M., Shum, K. P., Ronnason Chinram, and Iampan, A.

Subjects
Mathematics::Algebraic Geometry, Mathematics::General Mathematics, UP-algebra, neutrosophic implicative UP-filter, neutrosophic comparative UP-filter, neutrosophic shift UP-filter
Abstract

The notions of neutrosophic UP-subalgebras, neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, and neutrosophic strong UP-ideals were introduced by Songsaeng and Iampan [M. Songsaeng, A. Iampan, Neutrosophic set theory applied to UP-algebras, Eur. J. Pure Appl. Math., 12 (2019), 1382-1409]. In this paper, we introduce the notions of neutrosophic implicative UP-filters, neutrosophic comparative UP-filters, and neutrosophic shift UP-filters of UP-algebras by applying the notions of implicative UP-filters, comparative UP-filters, and shift UP-filters of UP-algebras to neutrosophic set, and investigate some of their important properties. Relations between neutrosophic implicative UP-filters (resp., neutrosophic comparative UP-filters, neutrosophic shift UP-filters) and their level subsets are considered.

Published
2021
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23. Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT

Author

LİU, Xianping, XİANG, Dajing, SHUM, K. P., and ZHAN, Jianming

Subjects
Astrophysics::High Energy Astrophysical Phenomena, Soft rings,Idealistic soft rings,Bi-idealistic soft rings,Quasi-idealistic softrings,(∈,∈ ∨q)-fuzzy subrings,(∈,∈ ∨ q)-fuzzy subrings,regular rings,soft regularrings
Abstract

We deal with soft rings based on some fuzzy sets, in particular, byusing the so called ∈ −soft sets and q-soft sets. Some characterizationtheorems of soft rings defined on soft sets are given and soft regularrings are hence characterized by special soft sets.

Published
2014

34. Naturally Ordered Abundant Semigroups for which each Idempotent has a Greatest Inverse.

Author

Xiaojiang Guo and Shum, K. P.

Subjects
*MATHEMATICS, *IDEMPOTENTS, *INVERSE semigroups, *LINEAR algebra, *MATHEMATICAL analysis, *ORDERED groups
Abstract

G-regular and reflexive naturally ordered abundant semigroups each of whose idempotents has a greatest inverse are studied. In this paper, we give a construction theorem for such ordered semigroups. Our theorem extends a previous structure theorem on naturally ordered abundant semigroups of X.J. Guo and X.Y. Xie [13]. Some other results related to naturally ordered regular semigroups are amplified and strengthened. [ABSTRACT FROM AUTHOR]

Published
2011

35. On Epiorthodox Semigroups.

Author

Shouxu Du, Xinzhai Xu, and Shum, K. P.

Subjects
SEMIGROUPS (Algebra), IDEMPOTENTS, HOMOMORPHISMS, LATTICE theory, GROUP theory, MATHEMATICS
Abstract

It has been well known that the band of idempotents of a naturally ordered orthodox semigroup satisfying the "strong Dubreil-Jacotin condition" forms a normal band. In the literature, the naturally ordered orthodox semigroups satisfying the strong Dubreil-Jacotin condition were first considered by Blyth and Almeida Santos in 1992. Based on the name "epigroup" in the paper of Blyth and Almeida Santos and also the name "epigroups" proposed by Shevrin in 1955; we now call the naturally ordered orthodox semigroups satisfying the Dubreil-Jacotin condition the epiorthodox semigroups. Because the structure of this kind of orthodox semigroups has not yet been described, we therefore give a structure theorem for the epi-orthodox semigroups. [ABSTRACT FROM AUTHOR]

Published
2011
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38. Finite p?nilpotent groups with some subgroups c?supplemented

Author

Guo, Xiuyun and Shum, K. P.

Abstract

AbstractA subgroup Hof a finite group Gis said to be c?supplemented in Gif there exists a subgroup Kof Gsuch that G= HKand HKis contained in coreG(H). In this paper some results for finite p?nilpotent groups are given based on some subgroups of Pc?supplemented in G, where pis a prime factor of the order of Gand Pis a Sylow p?subgroup of G. We also give some applications of these results.

Published
2005
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