On Resolvable Multipartite <Emphasis Type="Italic">G</Emphasis>-Designs

A necessary and sufficient condition for the existence of a _km–factorization of the complete symmetric k–partite multi-digraph K*(n₁,n₂,...,n_k) is obtained for odd k. As a consequence, a resolvable (k,n,km,) multipartite _km–design exists for odd k if and only if m|n. This deduces a result of Ushio when m=1 and k=3. Further, a necessary and sufficient condition for the existence of a _km–factorization of is established for even k, where denotes the wreath product of graphs. Finally, a simple and short proof for the non-existence of a _k–factorization of is obtained for odd k.Acknowledgments.The author thanks Dr. P. Paulraja for his useful ideas in writing this paper and the Department of Science and Technology, New Delhi, for its support (Project Grant No. DST/MS/103/99).Final version received: November 17, 2003     

On <Emphasis Type="Italic">G</Emphasis>-invex multiobjective programming. Part II. Duality

This paper represents the second part of a study concerning the so-called G-multiobjective programming. A new approach to duality in differentiable vector optimization problems is presented. The techniques used are based on the results established in the paper: On G-invex multiobjective programming. Part I. Optimality by T.Antczak. In this work, we use a generalization of convexity, namely G-invexity, to prove new duality results for nonlinear differentiable multiobjective programming problems. For such vector optimization problems, a number of new vector duality problems is introduced. The so-called G-Mond–Weir, G-Wolfe and G-mixed dual vector problems to the primal one are defined. Furthermore, various so-called G-duality theorems are proved between the considered differentiable multiobjective programming problem and its nonconvex vector G-dual problems. Some previous duality results for differentiable multiobjective programming problems turn out to be special cases of the results described in the paper.     

On the asymptotic number of non-equivalent q-ary linear codes

Let be the group of monomial matrices, i.e., the group generated by all permutation matrices and diagonal matrices in . The group acts on the set of all subspaces of . The number of orbits of this action, denoted by N_n,q, is the number of non-equivalent linear codes in . It was conjectured by Lax that as n→∞. We confirm this conjecture in this paper.     

On <Emphasis Type="Italic">k</Emphasis>-pairable graphs from trees

The concept of the k-pairable graphs was introduced by Zhibo Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter p(G), called the pair length of a graph G, as the maximum k such that G is k-pairable and p(G) = 0 if G is not k-pairable for any positive integer k. In this paper, we answer the two open questions raised by Chen in the case that the graphs involved are restricted to be trees. That is, we characterize the trees G with p(G) = 1 and prove that p(G □ H) = p(G) + p(H) when both G and H are trees.     

Applications of k-covers

We investigate a role of k-covers in selection principles theory. Some results about relationships between Ramsey theory and game theory and selection principles that involve k-covers are also given.     

On the multi-phase M/G/1 queueing system with random feedback

In this paper we consider an M/G/1 queue with k phases of heterogeneous services and random feedback, where the arrival is Poisson and service times has general distribution. After the completion of the i-th phase, with probability θ _i the (i + 1)-th phase starts, with probability p _i the customer feedback to the tail of the queue and with probability 1 − θ _i − p _i  = q _i departs the system if service be successful, for i = 1, 2 , . . . , k. Finally in kth phase with probability p _k feedback to the tail of the queue and with probability 1 − p _k departs the system. We derive the steady-state equations, and PGF’s of the system is obtained. By using them the mean queue size at departure epoch is obtained.     

Amply regular graphs and block designs

We study the amply regular diameter d graphs Γ such that for some vertex a the set of vertices at distance d from a is the set of points of a 2-design whose set of blocks consists of the intersections of the neighborhoods of points with the set of vertices at distance d-1 from a. We prove that the subgraph induced by the set of points is a clique, a coclique, or a strongly regular diameter 2 graph. For diameter 3 graphs we establish that this construction is a 2-design for each vertex a if and only if the graph is distance-regular and for each vertex a the subgraph Γ₃(a) is a clique, a coclique, or a strongly regular graph. We obtain the list of admissible parameters for designs and diameter 3 graphs under the assumption that the subgraph induced by the set of points is a Seidel graph. We show that some of the parameters found cannot correspond to distance-regular graphs.     

On the complete monotonicity of the waiting time density in some GI/G/k systems

In this note the complete monotonicity of the waiting time density in GI/G/k queues is proved under the assumption that the service time density is completely monotone. This is an extension of Keilson's [3] result for M/G/1 queues. We also provide another proof of the result that complete monotonicity is preserved by geometric compounding.     

On extremal k-outconnected graphs

Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n?3k-2 then m?k(n-k), and for n?3k-1 an equality is possible if, and only if, G is the complete bipartite graph K_k,n-k. Cai proved that if n?3k-2 then m?⌊(n+k)²/8⌋, and listed the cases when this bound is tight.In this paper we prove a more general theorem, which implies similar results for minimally k-outconnected graphs; a graph is called k-outconnected from r if it contains k internally disjoint paths from r to every other node.     

β级星像函数类和凸像函数类的扩展问题

本文利用文[2,3]的引理和算子L(a,c)f(z)的一些性质.结合Hadamard乘积,研究了算子L(a,c)f(z),获得了L(a,c)f(z)∈S*(β)和L(a,c)f(z)∈K(β)的充分条件,推广了文[2,3]的相关结论.     

具有对称自同态与对称导子的环

本文研究具有对称自同态和对称导子的环. 利用性质nil(R[x]) =nil(R)[x], 我们证明了: 如果R是弱2-primal 环, 则R 是弱对称(σ, δ)-环当且仅当R[x] 是弱对称(σ,δ) -环. 本文结论拓展了关于对称环和弱对称环的研究.     

On multiparameter distributions of order k

A multiparameter negative binomial distribution of order k is obtained by compounding the extended (or multiparameter) Poisson distribution of order k by the gamma distribution. A multiparameter logarithmic series distribution of order k is derived next, as the zero truncated limit of the first distribution. Finally a few genesis schemes and interrelationships are established for these three multiparameter distributions of order k. The present work extends several properties of distributions of order k.     

On a conjecture concerningk-Hamilton-nice sequences

In this paper, we prove that a non-negative rational number sequence (a ₁,a ₂, ...,a _k+1) isk-Hamilton-nice, if (1)a _k+12, and (2) _j ^=1/h (i _j –1)k–1 implies for arbitraryi ₁,i ₂,...i _h {1,2,... ,k}. This result was conjectured by Guantao Chen and R.H. Schelp, and it generalizes several well-known sufficient conditions for graphs to be Hamiltonian.This project is supported by the National Natural Science Foundation of China.     

Notes on symmetric g-functions

A number of generalized metric spaces have been defined or characterized in terms of g-functions. Symmetric g-functions are discussed by C. Good, D. Jennings and A. M. Mohamad. In this paper, some questions about symmetric g-functions are answered, particularly it is shown that every sym-wg-space is expandable. The project is supported by the NNSF (10571151) and NSF (2006J0397) of Fujian Province of China.     

On Quasi-invariance of Infinite Product Measures

Quasi-invariance of infinite product measures is studied when a locally compact second countable group acts on a standard Borel space. A characterization of l ²-quasi-invariant infinite product measures is given. The group that leaves the measure class invariant is also studied. In the case where the group acts on itself by translations, our result extends previous ones obtained by Shepp (Ann. Math. Stat. 36:1107–1112, 1965) and by Hora (Math. Z. 206:169–192, 1991; J. Theor. Probab. 5:71–100, 1992) to all connected Lie groups.      

On <Emphasis Type="Italic">k</Emphasis>-Spaces and <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">R</Emphasis></Subscript>-Spaces

In this note we study the relation between k _R -spaces and k-spaces and prove that a k _R -space with a σ-hereditarily closure-preserving k-network consisting of compact subsets is a k-space, and that a k _R -space with a point-countable k-network consisting of compact subsets need not be a k-space. This work was supported by the NSF of China (10271056).     

On weak neighborhood systems and spaces

We introduce and study the concepts of weak neighborhood systems, weak neighborhood spaces, ω(ψ, ψ′)-continuity, ω-continuity and ω*-continuity on WNS’s. This work was supported by a grant from Research Institute for Basic Science at Kangwon National University.     

On the Pancyclicity of Lexicographic Products

We prove that if G and H are graphs containing at least one edge each, then their lexicographic product G[H] is weakly pancyclic, i. e., it contains a cycle of every length between the length of a shortest cycle and that of a longest one. This supports some conjectures on locally connected graphs and on product graphs. We obtain an analogous result on even cycles in products G[H] that are bipartite. We also investigate toughness conditions on G implying that G[H] is hamiltonian (and hence pancyclic). Supported by the project LN00A056 of the Czech Ministry of Education     

Transient and Stationary Distributions for the GI/G/k Queue with Lebesgue-Dominated Inter-Arrival Time Distribution

In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator–geometric stationary distribution. Thus it is shown that matrix–analytical methods can be extended to provide a modeling tool even for the general multi-server queue.     

On τ-centralizers of semiprime rings

Let R be a semiprime 2-torsion free ring, and let τ be an endomorphism of R. Under some conditions we prove that a left Jordan τ-centralizer of R is a left τ-centralizer of R. Under the same conditions we also prove that a Jordan τ-centralizer of R is a τ-centralizer of R. We thus generalize Zalar’s results to the case of τ-centralizers of R.