On the Distribution of the Number of Calls in the Queuing System Dη|Dξkappa|1

For the queuing system D |D ^kappa|1, we determine the distribution of the number of calls in transient and stationary modes.     

Main Probability Characteristics of the Queuing System Gκ|G|1

For the queuing system G |G|1 with batch arrivals of calls, we present the distributions of the following characteristics: the length of a busy period, queue length in transient and stationary modes of the queuing system, total idle time of the queuing system, virtual waiting time to the beginning of the service, input stream of calls, output stream of served calls, etc.     

On the neutrix composition of the distributions x −s ln m |x| and x r

Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F _n (f)}, where F _n (x) = F(x) * δ _n (x) and {δ _n (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). The composition of the distributions x ^?s ln ^m |x| and x ^r is proved to exist and be equal to r ^m x ^?rs ln ^m |x| for r, s, m = 2, 3….     

About the Cohomology of the Lie Superalgebra of Vector Fields on ℝ n|n

In this article, we compute the first space of cohomology of Vect (? ^n|n ), the Lie superalgebra of vector fields on the supermanifold ? ^n|n with coefficients in 𝒻 (? ^n|n ), the space of smooth functions on ? ^n|n . We give a super analog of the cohomologies of vector fields that where studied for instance by Fuchs [2 Fuchs , D. B. ( 1986 ). Cohomology of Infinite Dimensional Lie Algebras . New York : Consultants Bureau . [Google Scholar]]. This work allows us to classify the deformations of the action of Vect(? ^n|n ) on 𝒻 (? ^n|n ).     

Cohomology of osp(2|2) acting on spaces of linear differential operators on the superspace ℝ1|2

We compute the first differential cohomology of the orthosymplectic Lie superalgebra osp(2|2) with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the (1, 2)-dimensional real superspace. We also compute the same, but osp(1|2)-relative, cohomology. We explicitly give 1-cocycles spanning these cohomologies. This work is the simplest generalization of a result from [1].     

ON LAGRANGE INTERPOLATION FOR |X|~α (0 < α < 1)

We study the optimal order of approximation for |x|α (0 < α < 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson order of approximation is attained.     

关于问题Pm|intree;pj=1;rj|Cmax的分支定界算法

本文针对一个尚未解决的问题Pm|intree;pj=1;rj|Cmax进行了研究,借助于决策论中的递阶层次结构的概念提出一个全新的分支定界算法,并用这一算法得到了问题Pm|intree;pj=1;rj|Cmax的最优排序．     

A theorem of the alternatives for the equation |<Emphasis Type="Italic">Ax</Emphasis>| − |<Emphasis Type="Italic">B</Emphasis>||<Emphasis Type="Italic">x</Emphasis>| = <Emphasis Type="Italic">b</Emphasis>

A theorem of the alternatives for the equation \({|Ax|-|B||x|=b\ (A,B\in{\mathbb{R}}^{n\times n},\, b\in{\mathbb{R}}^n)}\) is proved and several consequences are drawn. In particular, a class of matrices A, B is identified for which the equation has exactly 2 ⁿ solutions for each positive right-hand side b.     

The hypertree poset and the ℓ<Superscript>2</Superscript>-Betti numbers of the motion group of the trivial link

We give explicit formulae for the Euler characteristic and ²-cohomology of the group of motions of the trivial link, or isomorphically the group of free group automorphisms that send each standard generator to a conjugate of itself. The method is primarily combinatorial and ultimately relies on a computation of the Möbius function for the poset of labelled hypertrees.Partially supported by NSF grant no. DMS-0101506Partially supported by an AMS Centennial Research Fellowship     

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Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions<Superscript>∗</Superscript>

We improve bounds of accuracy of the normal approximation to the distribution of a sum of independent random variables under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second. We extend these results to Poisson binomial, binomial, and Poisson random sums. Under the same conditions, we obtain bounds for the accuracy of approximation of the distributions of mixed Poisson random sums by the corresponding limit law. In particular, we construct these bounds for the accuracy of approximation of the distributions of geometric, negative binomial, and Poisson-inverse gamma (Sichel) random sums by the Laplace, variance gamma, and Student distributions, respectively.     

Accuracy of approximation in the Poisson theorem in terms of the χ<Superscript>2</Superscript>-distance

We study the limit behavior of the χ²-distance between the distributions of the nth partial sum of independent not necessarily identically distributed Bernoulli random variables and the accompanying Poisson law. As a consequence in the i.i.d. case we make the multiplicative constant preciser in the available upper bound for the rate of convergence in the Poisson limit theorem.     

On the Structure of Quantum Toroidal Superalgebra εm|n

Recently the quantum toroidal superalgebra ε_m|n associated with gl_m|n was introduced by L. Bezerra and E. Mukhin, which is not a quantum Kac-Moody algebra. The quantum toroidal superalgebra ε_m|n exploits infinite sequences of generators and relations of the form, which are called Drinfeld realization. In this paper, we use only finite set of generators and relations to define an associative algebra ε’_m|n and show that there exists an epimorphism from ε...     

On Hypercentral Groups G With |G:G n |<∞

In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G ^p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G ^p |<∞ (of course, it contains G = G ^p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞.     

Convergence of the variants of the Chebyshev–Halley iteration family under the Hölder condition of the first derivative

The present paper is concerned with the convergence problem of the variants of the Chebyshev–Halley iteration family with parameters for solving nonlinear operator equations in Banach spaces. Under the assumption that the first derivative of the operator satisfies the Hölder condition of order p$p$, a convergence criterion of order 1+p$1+p$ for the iteration family is established. An application to a nonlinear Hammerstein integral equation of the second kind is provided.     

System G|Gκ|1 with Batch Service of Calls

For the queuing system G|G |1 with batch service of calls, we determine the distributions of the following characteristics: the length of a busy period, the queue length in transient and stationary modes of the queuing system, the total idle time of the queuing system, the output stream of served calls, etc.     

Elementary transformations and the rationality of the Moduli Spaces of Vector Bundles on ℙ<Superscript>2</Superscript>

In this work, using elementary transformations and prioritary sheaves, we establish birational maps between certain moduli spaces of stable vector bundles over ² with the same rank and different Chern classes. As an application we give a simple proof of the rationality of the moduli spaces M(r; c ₁, c ₂) of rank r stable vector bundles over ² with given Chern classes for a huge families of the triples (r; c ₁, c ₂).Partially supported by BFM2001-3584 Mathematics Subject Classification (2000):Primary 14D20, 14D05; Secondary 14F05     

On the <Emphasis Type="Italic">ω</Emphasis><Subscript>1</Subscript> limits of subsets of the real line

We point out that it is consistent with ZFC that 2 ^ω > ℵ₁ and every subset of ℝ is the ω ₁ limit of a sequence of G _δ sets in ℝ. We prove also that assuming cov ( ) > ℵ₁, not every set in ℝ is the ω ₁ limit of a sequence of measurable sets. This solves two problems of T. Natkaniec and J. Wesołowska.      

The non-abelian simple groups g, |g| < 106— character tables

Character tables are presented for all the 56 non-abelian simple groups of order up to 10⁶, including three tables for the family PSL(2,q) and twenty tables for individual groups (with some overlap). Information presented includes the power maps, the orders of the centralizers of elements, and tables of structure constants for each class of involutions.