<Emphasis Type="Italic">f</Emphasis>-Vectors of barycentric subdivisions

For a simplicial complex or more generally Boolean cell complex Δ we study the behavior of the f- and h-vector under barycentric subdivision. We show that if Δ has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney–Davis conjecture for spheres that are the subdivision of a Boolean cell complex or the subdivision of the boundary complex of a simple polytope. For a general (d − 1)-dimensional simplicial complex Δ the h-polynomial of its n-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this h-polynomial there is one converging to infinity and the other d − 1 converge to a set of d − 1 real numbers which only depends on d. F. Brenti and V. Welker are partially supported by EU Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272 and the program on “Algebraic Combinatorics” at the Mittag-Leffler Institut in Spring 2005.     

Approximations for the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">N</Emphasis>+<Emphasis Type="Italic">GI</Emphasis> type call center

In this paper, we propose approximations to compute the steady-state performance measures of the M/GI/N+GI queue receiving Poisson arrivals with N identical servers, and general service and abandonment-time distributions. The approximations are based on scaling a single server M/GI/1+GI queue. For problems involving deterministic and exponential abandon times distributions, we suggest a practical way to compute the waiting time distributions and their moments using the Laplace transform of the workload density function. Our first contribution is numerically computing the workload density function in the M/GI/1+GI queue when the abandon times follow general distributions different from the deterministic and exponential distributions. Then we compute the waiting time distributions and their moments. Next, we scale-up the M/GI/1+GI queue giving rise to our approximations to capture the behavior of the multi-server system. We conduct extensive numerical experiments to test the speed and performance of the approximations, which prove the accuracy of their predictions.      

<Emphasis Type="Italic">k</Emphasis>-factors in regular graphs

Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.     

Consecutive customer losses in regular and oscillating <Emphasis Type="Italic">M</Emphasis><Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">G</Emphasis>/1/<Emphasis Type="Italic">n</Emphasis> systems

We derive fast recursions to compute the probability that k or more consecutive customer losses take place during a busy period of a queue, the so called k-CCL probability, for regular and oscillating M ^X /G/1/n systems.     

The flatness properties of <Emphasis Type="Italic">S</Emphasis>-poset <Emphasis Type="Italic">A</Emphasis>(<Emphasis Type="Italic">I</Emphasis>) and Rees factor <Emphasis Type="Italic">S</Emphasis>-posets

Let S be a pomonoid and I a proper right ideal of S. In a previous paper, using the amalgamated coproduct A(I) of two copies of _S S over I, we were able to solve one of the problems posed in S. Bulman-Fleming et al. (Commun. Algebra 34:1291–1317, 2006). In the present paper, we investigate further flatness properties of A(I). We also solve another problem stated in the paper cited above. Namely, we determine the condition under which Rees factor S-posets have property (P _w ). Research supported by nwnu-kjcxgc-03-18.     

<Emphasis Type="Italic">∂</Emphasis>-operations and <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">V</Emphasis></Subscript>-fields

The hyperoperations, called theta-operations （δ）, are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures.     

Localization of <Emphasis Type="Italic">LM</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-algebras

The aim of this paper is to define the localization LM _n -algebra of an LM _n —algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM _n -algebra of fractions (defined in [3]) and the LM _n -algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM _n -algebras of localization.     

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.     

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).     

<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-mixed intersection bodies

In this paper the author first introduce a new concept of L _p -dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L _p intersection body to L _p -mixed intersection body. Inequalities for L _p -dual mixed volumes of L _p -mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities. This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

Analysis of GI<Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">M</Emphasis>(<Emphasis Type="Italic">n</Emphasis>)//<Emphasis Type="Italic">N</Emphasis> systems with stochastic customer acceptance policy

We investigate GI ^X /M(n)//N systems with stochastic customer acceptance policy, function of the customer batch size and the number of customers in the system at its arrival. We address the time-dependent and long-run analysis of the number of customers in the system at prearrivals and postarrivals of batches and seen by customers at their arrival to the system, as well as customer blocking probabilities. These results are then used to derive the continuous-time long-run distribution of the number of customers in the system. Our analysis combines Markov chain embedding with uniformization and uses stochastic ordering as a way to bound the errors of the computed performance measures.      

On locally <Emphasis Type="Italic">A</Emphasis>-convex <Emphasis Type="Italic">H</Emphasis>*-algebras

We endow any proper A-convex H*-algebra (E, τ) with a locally pre-C*-topology. The latter is equivalent to that introduced by the pre C*-norm given by Ptàk function when (E, τ) is a Q-algebra. We also prove that the algebra of complex numbers is the unique proper locally A-convex H*-algebra which is barrelled and Q-algebra.      

<Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-nearest neighbor estimators of entropy

For estimating the entropy of an absolutely continuous multivariate distribution, we propose nonparametric estimators based on the Euclidean distances between the n sample points and their k _n -nearest neighbors, where {k _n : n = 1, 2, …} is a sequence of positive integers varying with n. The proposed estimators are shown to be asymptotically unbiased and consistent.      

On the prime graph of <Emphasis Type="Italic">PSL</Emphasis>(2, <Emphasis Type="Italic">p</Emphasis>) where <Emphasis Type="Italic">p</Emphasis> > 3 is a prime number

Let G be a finite group. We define the prime graph Γ(G) as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge if there is an element in G of order pq. Recently M. Hagie [5] determined finite groups G satisfying Γ(G) = Γ(S), where S is a sporadic simple group. Let p > 3 be a prime number. In this paper we determine finite groups G such that Γ(G) = Γ(PSL(2, p)). As a consequence of our results we prove that if p > 11 is a prime number and p ≢ 1 (mod 12), then PSL(2, p) is uniquely determined by its prime graph and so these groups are characterizable by their prime graph. The third author was supported in part by a grant from IPM (No. 84200024).     

An <Emphasis Type="Italic">ω</Emphasis>-category with all Duals is an <Emphasis Type="Italic">ω</Emphasis>-groupoid

We make a definition of ω-precategory which should underlie any definition of weak ω-category. We make a precise definition of pseudo-invertible cells in this setting. We show that in an ω-precategory with all weak duals, every cell is pseudo-invertible. We deduce that in any “sensible” theory of ω-categories, an ω-category with all weak duals is an ω-groupoid. We discuss various examples and open questions involving higher-dimensional tangles and cobordisms.      

<Emphasis Type="Italic">p</Emphasis>-Ideals in <Emphasis Type="Italic">p</Emphasis>-Regular Semirings

In this paper, we introduce p-ideals in semirings. A new form of regularity, which is compatible with p-ideals, is defined. Our aim is to explore the possibilities of establishing an ideal theory in semirings, going alongside the existing literature of semiring theory.AMS Subject Classification (2000): Primary 16Y60     

<Emphasis Type="Italic">m</Emphasis> Components-admissible solutions of systems of higher-order partial differential equations on <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions.Some related results will also be obtained.     

Multiple <Emphasis Type="Italic">q</Emphasis>-zeta functions and multiple <Emphasis Type="Italic">q</Emphasis>-polylogarithms

For every positive integer d we define the q-analog of multiple zeta function of depth d and study its properties, generalizing the work of Kaneko et al. who dealt with the case d=1. We first analytically continue it to a meromorphic function on ℂ ^d with explicit poles. In our Main Theorem we show that its limit when q ↑1 is the ordinary multiple zeta function. Then we consider some special values of these functions when d=2. At the end of the paper we also propose the q-analogs of multiple polylogarithms by using Jackson’s q-iterated integrals and then study some of their properties. Our definition is motivated by those of Koornwinder and Schlesinger although theirs are slightly different from ours. Partially supported by NSF grant DMS0139813 and DMS0348258.     

On potentially <Emphasis Type="Italic">H</Emphasis>-graphic sequences

For given a graph H, a graphic sequence π = (d ₁, d ₂,..., d _n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K ₅ − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to be potentially K ₅-graphic, where K _r is a complete graph on r vertices and K _r-e is a graph obtained from K _r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence π to be potentially K ₆-graphic. Project supported by National Natural Science Foundation of China (No. 10401010).     

Busy period analysis for <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">PH</Emphasis>/1 queues with workload dependent balking

We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order linear differential equations for the mean and LST (Laplace-Stieltjes Transform) of the busy period in this model and solve them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with workload-dependent balking as a special limiting case of this fluid model. We illustrate the results with numerical examples.