Conditions for finite moments of waiting times inG/G/1 queues

We find conditions for E(W ) to be finite whereW is the stationary waiting time random variable in a stableG/G/1 queue with dependent service and inter-arrival times.Supported in part by KBN under grant 640/2/9, and at the Center for Stochastic Processes, Department of Statistics at the University of North Carolina Chapel Hill by the Air Force Office of Scientific Research Grant No. 91-0030 and the Army Research Office Grant No. DAAL09-92-G-0008.     

On the volume of convex hulls of sets on spheres

We prove that for a measurable subset of S ^n–1 with fixed Haar measure, the volume of its convex hull is minimized for a cap (i.e. a ball with respect to the geodesic measure). We solve a similar problem for symmetric sets and n=2, 3. As a consequence, we deduce a result concerning Gaussian measures of dilatations of convex, symmetric sets in R ² and R ³.Partially supported by KBN (Poland), Grant No. 2 1094 91 01.     

A characterization of strong measure zero sets

We show that a setXυR has strong measure zero iff for every closed measure zero setFυR,F+X has measure zero. Supported by KBN grant PB 2 1017 91 01.     

Classification of lattice-regular lattice convex polytopes

We completely describe lattice convex polytopes in ℝ ⁿ (for any dimension n) that are regular with respect to the group of affine transformations preserving the lattice. Supported in part by the RFBR (Grant Nos. SS-1972.2003.1 and 05-01-01012a) and the NWO-RFBR (Grant No. 047.011.2004.026/RFBR No. 05-02-89000-NWO_a).     

Integral formulas for compact spaceliken-submanifolds in de Sitter spaces applications to the parallel mean curvature vector case

We introduce a new method to study compact spaceliken-submanifolds in de Sitter spacesS _q ^n+q by means of certain integral formulas which have a very clear geometric meaning. As a first application of them we obtain a Bernstein type result for complete maximal submanifolds inS _q ^n+q . As for surfaces, we also get a uniqueness result for compact spacelike surfaces inS _q ^2+q with parallel mean curvature vector field. Partially supported by a DGICYT Grant No. PB91-0705-C02-02 Partially supported by a DGICYT Grant No. PB91-0731     

A polynomial ring that is Jacobson radical and not nil

In [1] Amitsur conjectured that if a polynomial ring in one indeterminate is Jacobson radical then it is a nil ring. We shall construct an example disproving this conjecture. Supported by Foundation for Polish Science and KBN Grant 2 P03A 057 15. Supported by KBN Grant 2 P03A 039 14.     

An integral inequality for compact maximal surfaces inn-dimensional de Sitter space and its applications

In this paper we prove an integral inequality for the Gaussian curvature of compact maximal surfaces inn-dimensional de Sitter space. Some applications of that inequality are given in order to solve the associated Bernstein type problem as well as to characterize the totally geodesic immersion in terms of its area and the first nontrivial eigenvalue of its Laplacian.Partially supported by a DGICYT Grant No. PB91-0705-C02-02Partially supported by a DGICYT Grant No. PB91-0731     

Embedding of Hyperbolic Spaces in the Product of Trees

We show that for each n ≥ 2 there is a quasi-isometric embedding of the hyperbolic space Hⁿ in the product Tⁿ=T × ··· × T of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding for any metric tree T and any m ≥ 0.Mathematics Subject classification (2000). 54Exx.Supported by RFFI Grant 02-01-00090, CRDF Grant RMI-2381-ST-02 and SNF Grant 20-668 33.01. Supported by Swiss National Science Foundation.     

Upper bounds for configurations and polytopes inR d

We give a new upper bound onn ^d(d+1)n on the number of realizable order types of simple configurations ofn points inR ^d , and ofn2d ² n on the number of realizable combinatorial types of simple configurations. It follows as a corollary of the first result that there are no more thann ^d(d+1)n combinatorially distinct labeled simplicial polytopes inR ^d withn vertices, which improves the best previous upper bound ofn ^{cn d/2}.Supported in part by NSF Grant DMS-8501492 and PSC-CUNY Grant 665258.Supported in part by NSF Grant DMS-8501947.     

<Emphasis Type="Italic">W</Emphasis><Superscript>1,<Emphasis Type="Italic">p</Emphasis></Superscript>(R<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>)-boundedness for maximal functions

In this paper, we get W ^1,p (R ⁿ )-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and Tananka’s results. Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural Science Foundation of China.     

Ideals and atoms of <Emphasis Type="Italic">BZ</Emphasis>-algebras

Ideals and atoms are studied by various authors from different point of views. In different algebras there are studied different ideals, but obtained results are similar. Below we present a new method of study of ideals in BZ-algebras. Using this method we describe the connection between ideals of various types. Supported by Natural Science Foundation of China (Grant No. 60775038).     

Packing dimension estimation for exceptional parameters

We estimate by a combinatorial method the packing dimension of the set of parameters for which the limit set of an iterated function system has a drop of the Hausdorff dimension. Supported by Polish KBN Grant No 2 P03A 025 12 and Foundation for Polish Science.     

Index theory on locally homogeneous spaces

We describe how the equivariant K homology class of an invariant elliptic operator on a homogeneous space of a linear semisimple Lie group determines the L ²-index of the associated operator on a finite volume locally homogeneous space. The machinery of equivariant K homology and of KK theory can be used to prove theorems about L ²-indices. We give an application motivated by the problem of calculating multiplicities of subrepresentations of quasi-regular representations.Supported by the National Science Foundation under Grant No. DMS-8903472.Supported by the National Science Foundation under Grant No. DMS-8901436.     

Complex algebras of subalgebras

Let V be a variety of algebras. We specify a condition (the so-called generalized entropic property), which is equivalent to the fact that for every algebra A ∈ V, the set of all subalgebras of A is a subuniverse of the complex algebra of the subalgebras of A. The relationship between the generalized entropic property and the entropic law is investigated. Also, for varieties with the generalized entropic property, we consider identities that are satisfied by complex algebras of subalgebras. Dedicated to George Gr?tzer on the occasion of his 70th birthday Supported by INTAS grant No. 03-51-4110. Supported by MŠMTČR (project MSM 0021620839) and by the Grant Agency of the Czech Republic (grant No. 201/05/0002). Translated from Algebra i Logika, Vol. 47, No. 6, pp. 655–686, November–December, 2008.     

Cyclic homology of Dedekind domains

We compute the cyclic homology of the algebraR[t]/(P(t)) relative to an arbitrary integral domainR. As an application, we compute the cyclic homology of number rings.Supported by N.S.F. Grant No. DMS-8807203.     

Graded subalgebras of affine Kac-Moody algebras

We determine the maximal graded subalgebras of affine Kac-Moody algebras. We also show that the maximal graded subalgebras of loop algebras are essentially loop algebras. Supported by the Binational Science Foundation United States — Israel, Grant No. 92-00034.     

Artin algebras with only preprojective or preinjective modules are of finite type

This work was done while the second author visited Toru. This research was partially supported by the Polish Scientific Grant KBN No. 1222/2/91     

Quasiequational Theories of Flat Algebras

We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition are finitely q-based (possess a finite basis for their quasiequations). We also exhibit an example of a twelve-element compatible flat algebra that is not finitely q-based. The first author was partially supported by the grant # 201/02/0594 of the Grant Agency of the Czech Republic, and by the Institutional grant MSM0021620839; the second author was partially supported by the grant No. Tn37877 of the Hungarian National Foundation for Scientific Research (OTHA); the third author was supported by the NSF grant # DMS-9971352.     

Harmonic measure,L 2-estimates and the Schwarzian derivative

We consider several results, each of which uses some type of “L ²” estimate to provide information about harmonic measure on planar domains. The first gives an a.e. characterization of tangent points of a curve in terms of a certain geometric square function. Our next result is anL ^p estimate relating the derivative of a conformal mapping to its Schwarzian derivative. One consequence of this is an estimate on harmonic measure generalizing Lavrentiev’s estimate for rectifiable domains. Finally, we considerL ² estimates for Schwarzian derivatives and the question of when a Riemann mapping ϕ has log ϕ′ in BMO. Supported in part by NSF Grant DMS-91-00671. Supported in part by NSF Grant DMS-86-025000.     

Bounded Algebraic Geometry over a Free Lie Algebra

Bounded algebraic sets over a free Lie algebra F over a field k are classified in three equivalent languages: (1) in terms of algebraic sets; (2) in terms of radicals of algebraic sets; (3) in terms of coordinate algebras of algebraic sets.Supported by RFBR grant No. 02-01-00192a.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 269–304, May–June, 2005.