This paper discusses the total irredundance relations between the graph G and its clone-contraction graph H, that is, let H be the clone-contraction graph of G and v1,v2,...,vk be all contraction vertices ofH. IfS is ...This paper discusses the total irredundance relations between the graph G and its clone-contraction graph H, that is, let H be the clone-contraction graph of G and v1,v2,...,vk be all contraction vertices ofH. IfS is a maximal total irredundant set of H such that A = S ∩ {V1,V2,…,Vk} contains as few vertices as possible, then S＇= S-A is the maximal total irredundant set of G. Furthermore, we obtain the bound of the total irredundance A（G） number： irt ≤△（G）/2△（G）＋1 n, which n is the order of graph G, and △（G） is maximum degree in G.展开更多
This investigation deals with the intelligent system for parallel fault-tolerant diagnostic tests construction. A modified parallel algorithm for fault-tolerant diagnostic tests construction is proposed. The algorithm...This investigation deals with the intelligent system for parallel fault-tolerant diagnostic tests construction. A modified parallel algorithm for fault-tolerant diagnostic tests construction is proposed. The algorithm is allowed to optimize processing time on tests construction. A matrix model of data and knowledge representation, as well as various kinds of regularities in data and knowledge are presented. Applied intelligent system for diagnostic of mental health of population which is developed with the use of intelligent system for parallel fault-tolerant DTs construction is suggested.展开更多
The purpose of this paper is to establish two algorithms for decomposing the radical of a polynomial ideal into an irredundant intersection of prime ideals,which are created by rational univariate representations.In t...The purpose of this paper is to establish two algorithms for decomposing the radical of a polynomial ideal into an irredundant intersection of prime ideals,which are created by rational univariate representations.In the case of zero-dimensional polynomial sets,the calculation of Gr¨obner bases is not involved.In the case of arbitrary polynomial sets,the times of calculating Gr¨obner bases is less than r if a given set of polynomials is decomposed into r triangular chains.展开更多
In this paper,we introduce a concept of principal divisor lattice and describe the structure of its elements.We first give a necessary and sufficient condition for the existence of irredundant join irreducible decompo...In this paper,we introduce a concept of principal divisor lattice and describe the structure of its elements.We first give a necessary and sufficient condition for the existence of irredundant join irreducible decompositions in complete principal divisor distributive lattices,and prove that the complete lower continuous,principal divisor lattices have irredundant join irreducible decompositions.In the end,we show the descriptions of lattices that have unique(resp.replaceable)irredundant join irreducible decompositions in complete lower continuous principal divisor lattices.展开更多
基金Supported by the National Natural Science Foundation of China (10571071,10371048)
文摘This paper discusses the total irredundance relations between the graph G and its clone-contraction graph H, that is, let H be the clone-contraction graph of G and v1,v2,...,vk be all contraction vertices ofH. IfS is a maximal total irredundant set of H such that A = S ∩ {V1,V2,…,Vk} contains as few vertices as possible, then S＇= S-A is the maximal total irredundant set of G. Furthermore, we obtain the bound of the total irredundance A（G） number： irt ≤△（G）/2△（G）＋1 n, which n is the order of graph G, and △（G） is maximum degree in G.
文摘This investigation deals with the intelligent system for parallel fault-tolerant diagnostic tests construction. A modified parallel algorithm for fault-tolerant diagnostic tests construction is proposed. The algorithm is allowed to optimize processing time on tests construction. A matrix model of data and knowledge representation, as well as various kinds of regularities in data and knowledge are presented. Applied intelligent system for diagnostic of mental health of population which is developed with the use of intelligent system for parallel fault-tolerant DTs construction is suggested.
基金supported by the National Natural Science Foundation of China under Grant No.12161057。
文摘The purpose of this paper is to establish two algorithms for decomposing the radical of a polynomial ideal into an irredundant intersection of prime ideals,which are created by rational univariate representations.In the case of zero-dimensional polynomial sets,the calculation of Gr¨obner bases is not involved.In the case of arbitrary polynomial sets,the times of calculating Gr¨obner bases is less than r if a given set of polynomials is decomposed into r triangular chains.
基金supported by National Natural Science Foundation of China(Grant No.10671138)
文摘In this paper,we introduce a concept of principal divisor lattice and describe the structure of its elements.We first give a necessary and sufficient condition for the existence of irredundant join irreducible decompositions in complete principal divisor distributive lattices,and prove that the complete lower continuous,principal divisor lattices have irredundant join irreducible decompositions.In the end,we show the descriptions of lattices that have unique(resp.replaceable)irredundant join irreducible decompositions in complete lower continuous principal divisor lattices.
