Quasi Lp-Intersection Bodies

The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established.     

Intrinsic normalizations of a nonholonomic hypersurface with <Emphasis Type="Italic">m</Emphasis>-dimensional generators in affine space <Emphasis Type="Italic">A</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

We consider some intrinsic normalizations of a nonholonomic hypersurface with m-dimensional generators in the n-dimensional affine spaced. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 532–562, October–December, 2007.     

The Petty Projection Inequality for Lp-Mixed Projection Bodies

Recently, Lutwak, Yang and Zhang posed the notion of Lp-projection body and established the Lp-analog of the Petty projection inequality. In this paper, the notion of Lp-mixed projection body is introduced--the Lp-projection body being a special case. The Petty projection inequality, as well as Lutwak＇s quermassintegrals （Lp-mixed quermassintegrals） extension of the Petty projection inequality, is established for Lp-mixed projection body.     

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).     

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.      

On <Emphasis Type="Italic">l</Emphasis><Subscript>2,<Emphasis Type="Italic">p</Emphasis></Subscript>-circle numbers

Circle numbers are defined to reflect the Euclidean area-content and, for p ≠ 2, suitably defined non-Euclidean circumference properties of the l _2,p -circles, p ∈ [1, ∞]. The resulting function is continuous, increasing, and takes all values from [2, 4]. The actually chosen dual l _2,p -geometry for measuring the arc-length is closely connected with a generalization of the method of indivisibles of Cavalieri and Torricelli in the sense that integrating such arc-lengths means measuring area content. Moreover, this approach enables one to look in a new way into the co-area formula of measure theory which says that integrating Euclidean arc-lengths does not yield area content except for p = 2. The new circle numbers play a natural role, e.g., as norming constants in geometric measure representation formulae for p-generalized uniform probability distributions on l _2,p -circles.     

Finite presentability of <Emphasis Type="Italic">SL</Emphasis><Subscript>1</Subscript>(<Emphasis Type="Italic">D</Emphasis>)

Let D be a finite dimensional division algebra over a local field of characteristic p and let SL ₁(D) denote the group of elements of reduced norm 1 in D. In this paper we prove that SL ₁(D) is finitely presented as a profinite group. This work is part of the author’s Ph.D. Thesis at Yale University.     

On the existence of <Emphasis Type="Italic">F</Emphasis>-crystals

Let (N,F) be an F-isocrystal, with associated Newton vector ν in . To any lattice M in N (an F-crystal) is associated its Hodge vector in . By Mazur's inequality we have . We show that, conversely, for any with , there exists a lattice M in N such that . We also give variants of this existence theorem for symplectic F-isocrystals, and for periodic lattice chains. Received: March 1, 2002     

A note on <Emphasis Type="Italic">f</Emphasis><Subscript><Emphasis Type="Italic">I</Emphasis></Subscript>-sets and <Emphasis Type="Italic">f</Emphasis><Subscript><Emphasis Type="Italic">I</Emphasis></Subscript> -continuous functions

Summary In [6] we introduced and investigated the notions of f_I -sets and f_I -continuous functions in ideal topological spaces. In this paper, we investigate their further important properties.     

<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.     

Lacunary Strong (<Emphasis Type="Italic">A</Emphasis><Subscript><Emphasis Type="Italic">σ</Emphasis></Subscript><Emphasis Type="Italic">, p</Emphasis>)-Convergence

The definition of lacunary strongly convergence is extended to the definition of lacunary strong (A _σ , p)-convergence with respect to invariant mean when A is an infinite matrix and p = (p _i ) is a strictly positive sequence. We study some properties and inclusion relations.     

<Emphasis Type="Italic">Q</Emphasis>-measures on <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">κ</Emphasis></Subscript>λ

 We give a characterization of strongly compact cardinals in terms of Q _κ λ. We also prove that weakly normal Q-measures on Q _κ λ are ⊂κ-normal. Received: 29 September 2000 / Revised version: March 2002 Published online: 5 November 2002 This project is supported by the New Zealand Marsden Fund. The author wishes to thank the referee for numerous comments and suggestions which have been incorporated into this version of the paper.     

Cc （X） Spaces with X Locally Compact

In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc （X） has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc （X） contains a dense （LM） subspace and if and only if X is a-compact.     

Local Convergence Behavior of Some Projection-Type Methods for Affine Variational Inequalities

In this paper, we study the local convergence behavior of four projection-type methods for the solution of the affine variational inequality (AVI) problem. It is shown that, if the sequence generated by one of the methods converges to a nondegenerate KKT point of the AVI problem, then after a finite number of iterations, some index sets in the dual variables at each iterative point coincide with the index set of the active constraints in the primal variables at the KKT point. As a consequence, we find that, after finitely many iterations, the four methods need not compute projections and their iterative equations are of reduced dimension.     

<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis>,<Emphasis Type="Italic">q</Emphasis></Subscript>-Cohomology and Normal Solvability

We consider some problems concerning the L _p,q -cohomology of Riemannian manifolds. In the first part, we study the question of the normal solvability of the operator of exterior derivation on a surface of revolution M considered as an unbounded linear operator acting from L_p^k (M) into L^k+1_q (M). In the second part, we prove that the first L _p,q-cohomology of the general Heisenberg group is nontrivial, provided that p < q. Received: 17 January 2006 Supported by INTAS (Grant 03–51–3251) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grants NSh 311.2003.1, NSh 8526.2006.1).     

Polyhedral <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">2</Emphasis></Subscript>

 Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional case provides interesting classes of groups. Received: 13 December 2001 / Revised version: 24 June 2002 The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107 Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20     

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.     

<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)