The Invariant and Quasi-invariant Transformations of the Stable Lévy Processes

Let ξ(t),t∈[0,1] be a strictly stable Lévy process with the index of stability α∈(0,2). By ℘ _ξ we denote the law of ξ in the Skorokhod space . For arbitrary ξ we construct ℘ _ξ -quasi-invariant semigroup of transformations of . Under some nondegeneracy condition on the spectral measure of the stable process we construct ℘ _ξ -quasi-invariant group of transformations of . In symmetric case this group is a group of the invariant transformations.      

Exponents for three-dimensional simultaneous Diophantine approximations

Let Θ = (θ ₁,θ ₂,θ ₃) ∈ ℝ³. Suppose that 1, θ ₁, θ ₂, θ ₃ are linearly independent over ℤ. For Diophantine exponents

Bass Numbers of Local Cohomology Modules with Respect to an Ideal

Let be a commutative Noetherian local ring and let be an ideal of R. We give some inequalities between the Bass numbers of an R–module and those of its local cohomology modules with respect to . As an application of these inequalities, we recover results of Delfino-Marley and Kawasaki by showing that for a minimax R-module M and for any non-negative integer i, the Bass numbers of the ith local cohomology module are finite if one of the following holds:

Compactness results for divergence type nonlinear elliptic equations

Let M be a compact manifold of dimension n ≥ 2 and 1 < p < n. For a family of functions F _α defined on TM, which are p-homogeneous, positive, and convex on each fiber, of Riemannian metrics g _α and of coefficients a _α on M, we discuss the compactness problem of minimal energy type solutions of the equation

Mean-value theorems and extensions of the Elliott-Daboussi theorem on additive arithmetic semigroups

We present more general forms of the mean-value theorems established before for multiplicative functions on additive arithmetic semigroups and prove, on the basis of these new theorems, extensions of the Elliott-Daboussi theorem. Let be an additive arithmetic semigroup with a generating set ℘ of primes p. Assume that the number G(m) of elements a in with “degree” ∂(a)=m satisfies

Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case

Given (M,g) a smooth compact Riemannian manifold of dimension n ≥ 5, we consider equations like

Composition operators on the Lipschitz space in polydiscs

Let Un be the unit polydisc of Cn and φ= (φ1,...,φn? a holomorphic self-map of Un. Let 0≤α< 1. This paper shows that the composition operator Cφ, is bounded on the Lipschitz space Lipa(Un) if and only if there exists M > 0 such thatfor z∈Un. Moreover Cφ is compact on Lipa(Un) if and only if Cφ is bounded on Lipa(Un) and for every ε > 0, there exists a δ > 0 such that whenever dist(φ(z),σUn) <δ     

Primitive Ideals and Automorphisms of Quantum Matrices

Let be a field and q be a nonzero element of that is not a root of unity. We give a criterion for 〈0〉 to be a primitive ideal of the algebra of quantum matrices. Next, we describe all height one primes of ; these two problems are actually interlinked since it turns out that 〈0〉 is a primitive ideal of whenever has only finitely many height one primes. Finally, we compute the automorphism group of in the case where m ≠ n. In order to do this, we first study the action of this group on the prime spectrum of . Then, by using the preferred basis of and PBW bases, we prove that the automorphism group of is isomorphic to the torus when m ≠ n and (m,n) ≠ (1, 3),(3, 1). This research was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme and by Leverhulme Research Interchange Grant F/00158/X.     

Freeknot splines approximation of Sobolev-type classes of <Emphasis Type="Italic">s</Emphasis>-monotone functions

Let I be a finite interval, s ∈ ℕ₀, and r,ν,n ∈ ℕ. Given a set M, of functions defined on I, denote by M the subset of all functions y ∈ M such that the s-difference is nonnegative on I, ∀τ > 0. Further, denote by the Sobolev class of functions x on I with the seminorm . Also denote by Σ _ν,n , the manifold of all piecewise polynomials of order ν and with n – 1 knots in I. If ν ≥ max {r,s}, 1 ≤ p,q ≤ ∞, and (r,p,q) ≠ (1,1,∞), then we give exact orders of the best unconstrained approximation and of the best s-monotonicity preserving approximation . Part of this work was done while the first author visited Tel Aviv University in May 2003 and in March 2004.     

Slices of Essentially Algebraic Categories

This paper is a contribution to the theory of functor slices of J. Sichler and V. Trnková. For every ordinal α we introduce a basket , prove that every essentially algebraic category of height α is a slice of , characterize small slices of and give a common generalization of known results about slices of the algebraic basket .      

On one extremal problem for numerical series

Let Γ be the set of all permutations of the natural series and let α = {α _j} _j∈ℕ, ν = {ν_j} _j∈ℕ, and η = {η_j} _j∈ℕ be nonnegative number sequences for which

Analytic and Asymptotic Properties of Multivariate Generalized Linnik’s Probability Densities

This paper studies the properties of the probability density function p _α,ν,n (x) of the n-variate generalized Linnik distribution whose characteristic function φ _α,ν,n (t) is given by

Crystal Graphs of Higher Level <Emphasis Type="Italic">q</Emphasis>-deformed Fock Spaces,Lusztig <Emphasis Type="Italic">a</Emphasis>-values and Ariki–Koike Algebras

We show that the different labelings of the crystal graph for irreducible highest weight -modules lead to different labelings of the simple modules for non semisimple Ariki–Koike algebras by using Lusztig a-values. Presented by Peter Littelman.     

Representations of Some Hopf Algebras Associated to the Symmetric Group S n

We prove that all irreducible representations of the bismash product have Frobenius–Schur indicator +1, where k is an algebraically closed field of characteristic 0. If n = p, a prime, we find all indicators for . We also study more general bismash products. Both authors were supported by NSF grants DMS-07-01291 and DMS-04-01399.     

Regolarità hölderiana delle derivate dei minimi di funzionali con parte principale quadratica

Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali dei funzionali sotto opportune ipotesi suA _ij ^αβ e sug.

---

Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA _ij ^αβ andg.

     

Two Inequalities for Convex Functions

Let a ₀ < a ₁ < ··· < a _n be positive integers with sums $ {\sum\nolimits_{i = 0}^n {\varepsilon _{i} a_{i} {\left( {\varepsilon _{i} = 0,1} \right)}} } Let a ₀ < a ₁ < ··· < a _n be positive integers with sums distinct. P. Erd?s conjectured that The best known result along this line is that of Chen: Let f be any given convex decreasing function on [A, B] with α ₀, α ₁, ... , α _n , β ₀, β ₁, ... , β _n being real numbers in [A, B] with α ₀ ≤ α ₁ ≤ ··· ≤ α _n , Then In this paper, we obtain two generalizations of the above result; each is of special interest in itself. We prove: Theorem 1 Let f and g be two given non-negative convex decreasing functions on [A, B], and α ₀, α ₁, ... , α _n , β ₀, β ₁, ... , β _n , α' ₀, α' ₁, ... , α' _n , β' ₀ , β' ₁ , ... , β' _n be real numbers in [A, B] with α ₀ ≤ α ₁ ≤ ··· ≤ α _n , α' ₀ ≤ α' ₁ ≤ ··· ≤ α' _n , Then Theorem 2 Let f be any given convex decreasing function on [A, B] with k ₀, k ₁, ... , k _n being nonnegative real numbers and α ₀, α ₁, ... , α _n , β ₀, β ₁, ... , β _n being real numbers in [A, B] with α ₀ ≤ α ₁ ≤ ··· ≤ α _n , Then      

Homogenization of two-phase metrics and applications

We consider two-phase metrics of the form ϕ(x, ξ) ≔ , where α,β are fixed positive constants and B _α, B _β are disjoint Borel sets whose union is ℝ^N, and prove that they are dense in the class of symmetric Finsler metrics ϕ satisfying

One-Parameter Families of Modules for Tame Algebras and Bocses

Let Λ be a finite-dimensional algebra over an algebraically closed field k. We denote by mod Λ the category of finitely generated left Λ-modules. Consider the family ℱ(u) of the indecomposables M∈mod Λ such that , where is the subspace of morphisms which factorize through semisimple modules. If P,Q are projectives in mod Λ, ℱ(u)(P,Q) is the family of those modules M∈ℱ(u) such that a minimal projective presentation is of the formf_M: P→Q. We prove that if Λ is of tame representation type then each ℱ(P,Q) has only a finite number of isomorphism classes or is parametrized by μ(u,P,Q) one-parameter families. We give an upper bound for this number in terms of u,P and Q. Then we give some sufficient conditions for tame of polynomial growth type. For the proof we consider similar results for bocses. Presented by Y. Drozd Mathematics Subject Classifications (2000) 16G60, 16G70, 16G20.