Domains of attraction and regular variation in IRd

A general form for regular variation in IR² is introduced and applied to domains of attraction of stable distribution in IR² where the components have different indices. The situation in IR^d with d > 2 is more complicated but not essentially different. For simplicity this paper is limited to IR².     

Computing the number of ways of representing primes by a norm form

Formulae for the number of different integral solutions ofa ²+b²+c²+d²+ac+bd=p are given wherep is a prime and the solution satisfies certain natural congruence conditions. Similar formulae are given for the case of the quadratic forma ²+b²+2c²+2d²+ac+bd.     

On the prediction of vector-valued random fields and the spectral distribution of their evanescent component

Let (X_m,n)_(m,n)∈Z² be a C^p-valued wide sense stationary process. We study the prediction theory of such processes according to different total orders on Z². In the case of a “rational order”, we give the spectral distribution of the resulting evanescent component and prove that for two different rational orders, the resulting evanescent components are mutually orthogonal.     

Null Sequences in Coechelon Spaces

Rotundity of finite -dimensional Orlicz spaces l^?_n equipped with the Luxemburg norm is considered. It is proved that criteria for rotundity of l^?_nfor n ≥ 3 does not depend on n and are the same as the criteria for rotundity of the inhite-dimensional subspace h^? of an Orlicz sequence spacel^?. Criteria for rotundity of l^?₂ are different. Next, criteria for exposed points, (H)- points, strongly exposed points and LUR- points of the unit sphere of l^? and of its subspace h^? are given.     

Cauchy problems for linear thermoelastic systems of type III in one space variable

The goal of the paper is to analyse properties of solutions for linear thermoelastic systems of type III in one space variable. Our approach does not use energy methods, it bases on a special diagonalization procedure which is different in different parts of the phase space. This procedure allows to derive explicit representations of solutions. These representations help to prove results for well‐posedness of the Cauchy problem, L^P–L^q decay estimates on the conjugate line and results for propagation of singularities. Copyright © 2005 John Wiley & Sons, Ltd.     

Direct Evaluation of Nonlinear Gradient Elasticity in 2D with C1 Continuous Discretization Methods

In this contribution, we present a study on the performance of four different subparametric triangular finite element formulations for linear and nonlinear strain gradient elastic continua. Fully C¹ and nonconforming C^* finite elements are considered for a numerical analysis. The results are demonstrated by means of two computational examples together with the L², H¹ and H² error norms. An interesting aspect concerning the linear geometry approximation is revealed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On semilattice relevant logics

The semilattice relevant logics ^∪ R , ^∪ T , ^∪ RW , and ^∪ TW (slightly different from the orthodox relevant logics R , T , RW , and TW ) are defined by semilattice models in which conjunction and disjunction are interpreted in a natural way. For each of them, there is a cut‐free labelled sequent calculus with plural succedents (like LK ). We prove that these systems are equivalent, with respect to provable formulas, to the restricted systems with single succedents (like LJ ). Moreover, using this equivalence, we give a new Hilbert‐style axiomatizations for ^∪ R and ^∪ T and prove equivalence between two semantics (commutative monoid and distributive semilattice) for the contractionless logics ^∪ RW and ^∪ TW .     

Tight Multiwavelet Frames with Different Matrix Dilations and Matrix Translations

The characterization of tight multiwavelet frames with different matrix dilations and matrix translations for L ²(R ^d ) is established. The result contains and further extends the generalizations that have appeared in the literature. Two sufficient conditions for affine frames are also presented.     

The 2/3-Convergence Rate for the Poisson Bracket

In this paper we introduce a new method for approaching the C ⁰-rigidity results for the Poisson bracket. Using this method, we provide a different proof for the lower semi-continuity under C ⁰ perturbations, for the uniform norm of the Poisson bracket. We find the precise rate for the modulus of the semi-continuity. This extends the previous results of Cardin–Viterbo, Zapolsky, Entov and Polterovich. Using our method, we prove a C ⁰-rigidity result in the spirit of the work of Humilière. We also discuss a general question of the C ⁰-rigidity for multilinear differential operators.     

On the Asymptotic Behavior of Weighted U-Statistics

A sufficient condition for the convergence of degenerated weighted U-statistics of order k is proved. From this, the previous results by O'Neil and Redner⁽¹⁰⁾ for k = 2 and Major,⁽⁷⁾ which appeared to be very different, are related.     

A new Leray formula for smooth functions on bounded domains in C n

By means of a new technique of integral representations in C ⁿ given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in C ⁿ , which is different from the well-known Leray formula. This new formula eliminates the term that contains the parameter A from the classical Leray formula, and especially on some domains the uniform estimates for the $\bar \partial - equation$ are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in C ⁿ , which are different from the classical ones, when we properly select the vector function W.     

Nonnegative (s, t)-potent matrices

This paper contains a study of matrices satisfying A^s = A^t for different positive integers s and t. Representations, similar to Flor's well-known characterization of a nonnegative idempotent matrix, are obtained for nonnegative matrices of this type.     

Zero-sets of complex homogeneous polynomials

In this paper we study the zero-sets of continuous n-homogeneous polynomials on complex nonseparable Banach spaces. We prove that the zero-set of any complex n-homogeneous polynomial P is a subspace if, and only if, there is a functional ? such that P(x)=? (x)ⁿ for every x. We give sufficient conditions on the Banach space to ensure that every continuous 2-homogeneous polynomial is identically zero on a nonseparable subspace. Also, we prove that, in the 2-homogeneous case, one of the following three properties holds: P ^?1(0) is a subspace; P ^?1(0) is the union of two different subspaces; and P ^?1(0) is the union of infinitely many different subspaces.     

Self-Intersection Local Time for Some S′(ℝd)-Ornstein-Uhlenbeck Processes Related to Inhomogeneous Fields

We study existence and path continuity of the self-intersection local time (SILT) for some S′(ℝ^d)-valued Ornstein-Uhlenbeck processes. Examples of such processes arise in particular as fluctuation limits ofparticle systems. We analyze the effect that different types ofmeasures involved in the covariances of the processes have on existence and continuity of SILT. These measures do not necessarily have the regularity and homogeneity properties of those that have been considered before; this precludes some key ingredients of the previous techniques. We develop new technical tools and prove sufficient conditions and some necessary conditions for existence of SILT, and sufficient conditions for path continuity of SILT. The questions of existence and continuity involve problems of existence of integrals and singular integrals. We give examples which illustrate how different types of measures e.g., atomic or with L²-density) may produce different critical dimensions for existence of SILT. One of our motivations is the desire for a better understanding ofwhat SILT represents for S′(ℝ^d)-valued processes.     

The Recursive Solution for Geom/G/1（E,SV） queue with Feedback and Single Server Vacation

Using recursive method,this paper studies the queue size properties at any epoch n + in Geom/G/1(E,SV) queueing model with feedback under LASDA (late arrival system with delayed access) setup.Some new results about the recursive expressions of queue size distribution at different epoch (n+,n,n-) are obtained.Furthermore the important relations between stationary queue size distribution at different epochs are discovered.The results are different from the relations given in M/G/1 queueing system.The model discussed in this paper can be widely applied in many kinds of communications and computer network.     

A new proof of the odd primary homotopy exponent of spheres

We give a different proof of Cohen, Moore and Neisendorfer’s theorem stating that for odd primes p the homotopy exponent of S ²ⁿ⁺¹ is p ⁿ . This is done using methods recently introduced by Gray and the author to give a new construction of Anick’s fibration.     

Zero sets and multiplier theorems for star-invariant sub spaces

Given an inner function θ, let {Kskθ/p}:= H^p ∩θ {Hsk0/p} be the corresponding star-invariant subspace of the Hardy spaceH ^p. We show that, unless θ is a finite Blaschke product, the zero sets for K _θ ^p -spaces are different for different p’s. We also investigate the (non)stability of zero sets when passing from {Kskθ/p} to {Ksku/q}, whereq > p and u is an inner function divisible by θ. This problem is motivated by the Beurling-Malliavin multiplier theorem for entire functions, and we solve it (at least in a natural special case) by proving an appropriate multiplier theorem for K _θ ^p .     

Improving an inequality for sums of elements of matrix powers

The inequality 3su A³ ⩾ su A su A², which is known to hold for any symmetric nonnegative 3 X 3 matrix A, is sharpened in three different ways. Here su denotes the sum of elements.     

Group Rings Whose Symmetric Units Generate an n-Engel Group

Let F be an infinite field of characteristic different from 2 and G a torsion group. Write 𝒰⁺(FG) for the set of units in the group ring FG that are symmetric with respect to the classical involution induced from the map g ? g ^?1, for all g ∈ G. We classify the groups such that ?𝒰⁺(FG)? is n-Engel.