Convergence Rates in the Law of Large Numbers under Sublinear Expectations

In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong L^p-convergence version and a strongly quasi sure convergence version of the law of large numbers.     

Fast algorithms for determining the linear complexities of sequences over GF(pm) with the period 3n

In this paper, for the the primes p such that 3 is a divisor of p − 1, we prove a result which reduces the computation of the linear complexity of a sequence over GF(p ^m) (any positive integer m) with the period 3n (n and p ^m − 1 are coprime) to the computation of the linear complexities of three sequences with the period n. Combined with some known algorithms such as generalized Games-Chan algorithm, Berlekamp-Massey algorithm and Xiao-Wei-Lam-Imamura algorithm, we can determine the linear complexity of any sequence over GF(p ^m) with the period 3n (n and p ^m − 1 are coprime) more efficiently.     

Upper Bounds to the Number of Vertices in a k-Critically n-Connected Graph

 Let k≤n be positive integers. A finite, simple, undirected graph is called k-critically n-connected, or, briefly, an (n,k)-graph, if it is noncomplete and n-connected and the removal of any set X of at most k vertices results in a graph which is not (n−|X|+1)-connected. We present some new results on the number of vertices of an (n,k)-graph, depending on new estimations of the transversal number of a uniform hypergraph with a large independent edge set. Received: April 14, 2000 Final version received: May 8, 2001     

RICE CONDITION NUMBERS OF CERTAIN CHARACTERISTIC SUBSPACES

This paper proposes the Rice condition numbers for invariant subspace, singular sub-spaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.     

Sizes of Critical Graphs with Small Maximum Degrees

In this paper, we give new lower bounds for the size of Δ-critical graphs with Δ=8,9 which improve the partial results of Luo [6] and Y. Zhao [12].     

一些特殊图类乘积的离散度

连通图的离散度是用s(G)来表示的,s(G)=max{ω(G-S)-|S|:ω(G-S)>1,SV(G)}.给出了两个完全图乘积的和一个完全图与路的乘积的离散度.还给出了两个完全图乘积的坚韧度.     

Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

A note on the computational complexity of graph vertex partition

A stable set of a graph is a vertex set in which any two vertices are not adjacent. It was proven in [A. Brandstädt, V.B. Le, T. Szymczak, The complexity of some problems related to graph 3-colorability, Discrete Appl. Math. 89 (1998) 59-73] that the following problem is NP-complete: Given a bipartite graph G, check whether G has a stable set S such thatG-Sis a tree. In this paper we prove the following problem is polynomially solvable: Given a graph G with maximum degree 3 and containing no vertices of degree 2, check whether G has a stable set S such thatG-Sis a tree. Thus we partly answer a question posed by the authors in the above paper. Moreover, we give some structural characterizations for a graph G with maximum degree 3 that has a stable set S such that G-S is a tree.     

A graphical approach to computing Selmer groups of congruent number curves

Let E _n:y ²=x ³−n ² x denote the family of congruent number elliptic curves. Feng and Xiong (2004) equate the nontriviality of the Selmer groups associated with E _n to the presence of certain types of partitions of graphs associated with the prime factorization of n. In this paper, we extend the ideas of Feng and Xiong in order to compute the Selmer groups of E _n. 2000 Mathematics Subject Classification Primary—11G05; Secondary—14H52, 14H25, 05C90     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy