Infinitely divisible probabilities on discrete linear groups

We investigate the structure of infinitely divisible probability measures on a discrete linear group. It is shown that for any such measure there is an infinitely divisible elementz in the centralizer of the support of the measure, such that the translate of the measure byz is embeddable over the subgroup generated by the support of the measure. Examples are given to show that this reult is best possible.     

Recursive fault-tolerance of Fibonacci cube in hypercubes

Fibonacci cube is a subgraph of hypercube induced on vertices without two consecutive 1's. If we remove from Fibonacci cube the vertices with 1 both in the first and the last position, we obtain Lucas cube. We consider the problem of determining the minimum number of vertices in n-dimensional hypercube whose removal leaves no subgraph isomorphic to m-dimensional Fibonacci cube. The exact values for small m are given and several recursive bounds are established using the symmetry property of Lucas cubes and the technique of labeling. The relation to the problem of subcube fault-tolerance in hypercube is also shown.     

Further explorations into ternary complementary pairs

In [R. Craigen, C. Koukouvinos, A theory of ternary complementary pairs, J. Combin. Theory Ser. A 96 (2001) 358-375], we proposed a systematic approach to the theory of ternary complementary pairs (TCPs) and showed how all pairs known then could be constructed using a single elementary product, the natural equivalence relations, and a handful of pairs which we called primitive. We also introduced more new primitive pairs than could be inferred previously, concluding with some conjectures reflecting the patterns that were beginning to arise in light of the new approach.In this paper we take what appears to be the natural next step, by investigating these patterns among those lengths and weights that are within easy computational distance from the last length considered therein, length 14. We give complete results up to length 21, and partial results up to length 28. (Ironically, although we proceed analytically by weight first then length, for computational reasons we are bound, in this empirical investigation, to proceed according to length first.)Thus we provide support for the previous conjectures, and shed enough new light to speculate further as to the likely ultimate shape of the theory. Since short term work on TCPs will require massive acquisition of data about small pairs, we also discuss affixes—a computational strategy that arose out of the investigations culminating in this article.     

Consecutive-(r,f,k) out-of-n:F和Consecutive-(f,g)-out-of-(r,n):F线性系统的可靠性

Consecutive-(r,f,k)-out-of-n:F系统由n个单元顺序连结而成,仅当在连续的r个单元中,至少有f个失效或者至少连续k个失效,整个系统才失效;而Consecutive-(f,g)-out-of-(r,n):F系统由n个单元顺序连结而成,仅当在整个系统中至少有f个失效或者在连续的r个单元中,至少有g个失效,整个系统才失效。本文运用马氏链嵌入方法,在单元之间相互独立以及单元之间马氏相关这两种情况下,给出线性系统的可靠性。     

Representing homology classes by locally flat 2-spheres

We prove an existence result for topologically locally flat embeddings of 2-spheres in simply connected 4-manifolds. This topological result is deduced from a splitting theorem for pointed Hermitian modules over a cyclic group ring. A stability result for such modules is also proved. This applies to the isotopy classification of locally flat embeddings.Partially supported by the NSF.     

On the embedding of variational inequalities

This work is devoted to the approximation of variational inequalities with pseudo-monotone operators. A variational inequality, considered in an arbitrary real Banach space, is first embedded into a reflexive Banach space by means of linear continuous mappings. Then a strongly convergent approximation procedure is designed by regularizing the embedded variational inequality. Some special cases have also been discussed.

     

Nearly light cycles in embedded graphs and crossing‐critical graphs

We find a lower bound for the proportion of face boundaries of an embedded graph that are nearly light (that is, they have bounded length and at most one vertex of large degree). As an application, we show that every sufficiently large k‐crossing‐critical graph has crossing number at most 2k + 23. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 151–156, 2006     

A Domain Embedding Method Using the Optimal Distributed Control and a Fast Algorithm

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. The method is based on formulating the problem as an optimal distributed control problem inside a disc in which the arbitrary domain is embedded. The optimal distributed control problem inside the disc is solved rapidly using a fast algorithm developed by Daripa et al. [3,7,10–12]. The arbitrary domains can be simply or multiply connected and the proposed method can be applied, in principle, to a large number of elliptic problems. Numerical results obtained for Dirichlet problems associated with the Poisson equation in simply and multiply connected domains are presented. The computed solutions are found to be in good agreement with the exact solutions with moderate number of grid points in the domain.     

Lattice embeddings and array noncomputable degrees

We focus on a particular class of computably enumerable (c. e.) degrees, the array noncomputable degrees defined by Downey, Jockusch, and Stob, to answer questions related to lattice embeddings and definability in the partial ordering (??, ≤) of c. e. degrees under Turing reducibility. We demonstrate that the latticeM₅ cannot be embedded into the c. e. degrees below every array noncomputable degree, or even below every nonlow array noncomputable degree. As Downey and Shore have proved that M₅ can be embedded below every nonlow₂ degree, our result is the best possible in terms of array noncomputable degrees and jump classes. Further, this result shows that the array noncomputable degrees are definably different from the nonlow₂ degrees. We note also that there are embeddings of M₅ in which all five degrees are array noncomputable, and in which the bottom degree is the computable degree 0 but the other four are array noncomputable. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

CMDC:an iterative algorithm for complementary multi-view document clustering

In response to the problems traditional multi-view document clustering methods separate the multi-view document representation from the clustering process and ignore the complementary characteristics of multi-view document clustering,an iterative algorithm for complementary multi-view document clustering——CMDC was proposed,in which the multi-view document clustering process and the multi-view feature adjustment were conducted in a mutually unified manner.In CMDC algorithm,complementary text documents were selected from the clustering results to aid adjusting the contribution of view features via learning a local measurement metric of each document view.The complementary text document of the results among the dimensionality clusters was selected by CMDC,and used to promote the feature tuning of the clusters.The partition consistency of the multi-dimensional document clustering was solved by the measure consistency of the dimensions.Experimental results show that CMDC effectively improves multi-dimensional clustering performance.