Approximation by Complex Baskakov-Sz ′asz-Durrmeyer Operators in Compact Disks

In this paper, we deal with the complex Baskakov-Sz ′asz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of ...     

Approximation by Complex Baskakov-Szsz-Durrmeyer Operators in Compact Disks

In this paper, we deal with the complex Baskakov-Szsz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR= {z ∈ C;|z| R}.Also, the exact order of approximation is found. The method used allows to construct complex Szsz-type and Baskakov-type approximation operators without involving the values on [0, ∞).     

Approximation by Complex q-Szász–Kantorovich Operators in Compact Disks, q>1

In this paper, the exact order $\frac{1}{q^{n}}, q>1$ , in approximation and Voronovskaja-type results for the complex $q$ -Szász–Kantorovich operators attached to analytic functions on compact disks are obtained.     

Voronovskaja’s Theorem and Iterations for Complex Bernstein Polynomials in Compact Disks

In this paper, firstly we prove the Voronovskaja’s convergence theorem for complex Bernstein polynomials in compact disks in , centered at origin, with quantitative estimates of this convergence. Secondly, we study the approximation properties of the iterates of complex Bernstein polynomials and we prove that they preserve in the unit disk (beginning with an index) the univalence, starlikeness, convexity and spirallikeness. Received: May 5, 2007 Revised: September 14, 2007 and November 11, 2007 Accepted: November 26, 2007     

The approximation by q-Bernstein polynomials in the case q ↓ 1

Let B_n (f, q; x), n=1, 2, ... , 0 < q < ∞, be the q-Bernstein polynomials of a function f, B_n (f, 1; x) being the classical Bernstein polynomials. It is proved that, in general, {B_n (f, q_n; x)} with q_n ↓ 1 is not an approximating sequence for f ∈C[0, 1], in contrast to the standard case q_n ↓ 1. At the same time, there exists a sequence 0 < δ_n ↓ 0 such that the condition implies the approximation of f by {B_n (f, q_n; x)} for all f ∈C[0, 1]. Received: 15 March 2005     

Differentiated Generalized Voronovskaja’s Theorem in Compact Disks

In this paper we obtain the differentiated generalized Voronovskaja’s theorem in complex setting with upper and exact quantitative estimates. The results extend that obtained in the real case on [0, 1] in Gonska and Ra?a (Mat Vesnik 61:53–60, 2009) and generalize those obtained in the complex case in Gal (Results Math 53:257–268, 2009).     

Some New Results Related to Compact Matrix Operators in the Class((l_p)T,l_∞)

The main goal of this paper is to establish necessary and sufficient conditions for a matrix A ∈((lp)T,l∞), where T is an arbitrary triangle, 1 ≤ p ≤∞, to be a compact operator. In the past,only sufficient conditions were established in almost all of those cases, by using the Hausdorff measure of noncompactness. We improve those results by applying another method for the characterizations of compact linear operators between BK spaces.     

Compact Ceshro Operators from Spaces H（p,q,u） to H（p, q, v）

Abstract Let μ and ν be normal functions and let T _g be the extended Cesàso operator in terms of the symbol g. In this paper, we will characterize those g so that T _g is bounded (or compact) from mixed norm spaces H(p, q, μ) to H(p, q, ν) in the unit ball of C ⁿ . Furthermore, as applications, some analogous results are also given on weighted Bergman spaces and Dirichlet type spaces. Supported by the National Natural Science Foundation of China (No.10571049, 10471039), the Natural Science Foundation of Zhejiang Province (No. M103085).     

On 1-Blocking Sets in PG(n,q), n ≥ 3

In this article we study minimal1-blocking sets in finite projective spaces _PG(n,q),n 3. We prove that in PG(n,q ²),q = p ^h , p prime, p > 3,h 1, the second smallest minimal 1-blockingsets are the second smallest minimal blocking sets, w.r.t.lines, in a plane of PG(n,q ²). We also study minimal1-blocking sets in PG(n,q ³), n 3, q = p ^h, p prime, p > 3,q 5, and prove that the minimal 1-blockingsets of cardinality at most q 3 + q ² + q + ¹ are eithera minimal blocking set in a plane or a subgeometry PG(3,q).     

Small Compact Perturbation of Operators in B∞（Ω）

Abstract： We consider an approximation problem related to strongly irreducible operators, that is, does the direct sum of a strongly irreducible operator in B∞（Ω） and certain operator have a small compact perturbation which is a strongly irreducible operator in B∞（Ω）？ In this paper, we prove that the direct sum of any strongly irreducible operator in B∞（Ω） and certain biquasitriangular operator have small compact perturbations which are strongly irreducible operators in B∞（Ω）.     

Cuttings for Disks and Axis-Aligned Rectangles in Three-Space

We present new asymptotically tight bounds on cuttings, a fundamental data structure in computational geometry. For n objects in space and a parameter r∈?, a $\frac{1}{r}We present new asymptotically tight bounds on cuttings, a fundamental data structure in computational geometry. For n objects in space and a parameter r∈ℕ, a \frac1r\frac{1}{r} -cutting is a covering of the space with simplices such that the interior of each simplex intersects at most n/r objects. For n pairwise disjoint disks in ℝ³ and a parameter r∈ℕ, we construct a \frac1r\frac{1}{r} -cutting of size O(r ²). For n axis-aligned rectangles in ℝ³, we construct a \frac1r\frac{1}{r} -cutting of size O(r ^3/2). As an application related to multi-point location in three-space, we present tight bounds on the cost of spanning trees across barriers. Given n points and a finite set of disjoint disk barriers in ℝ³, the points can be connected with a straight line spanning tree such that every disk is stabbed by at most O(?n)O(\sqrt{n}) edges of the tree. If the barriers are axis-aligned rectangles, then there is a straight line spanning tree such that every rectangle is stabbed by O(n ^1/3) edges. Both bounds are best possible.     

Some Results for Decomposition Numbers for the Hecke Algebra of Type A with q = −1

Let ? = ?_{?, ?1}(𝔖 _n ) be the Hecke algebra of the symmetric group 𝔖 _n . For partitions λ and ν with ν 2 ? regular, define the Specht module S(λ) and the irreducible module D(ν). Define d _λν = [S(λ): D(ν)] to be the composition multiplicity of D(ν) in S(λ). In this paper we compute the decomposition numbers d _λν for all partitions of the form λ = (a, c, 1 ^b ) and ν 2 ? regular.     

On Huppert’s conjecture for G2(q), q≥7

Let $G$ be a finite group and let $\mathrm{cd}\left(G\right)$ be the set of all complex irreducible character degrees of $G$. Bertram Huppert conjectured that if $H$ is a finite nonAbelian simple group such that $\mathrm{cd}\left(G\right)=\mathrm{cd}\left(H\right)$, then $G?H\times A$, where $A$ is an Abelian group. In this paper, we verify the conjecture for the family of simple exceptional groups of Lie type $G_2\left(q\right)$ for $q\ge 7$.     

Inverse Uniqueness Results for Schrödinger Operators Using de Branges Theory

We utilize the theory of de Branges spaces to show when certain Schrödinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness theorem for perturbed spherical Schrödinger operators.     

On Huppert’s Conjecture for 3 D 4(q), q ≥ 3

Let G be a finite group and cd(G) be the set of all complex irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G???H × A, where A is an abelian group. In this paper, we verify the conjecture for the family of simple exceptional groups of Lie type ³ D ₄(q), when q?≥?3.     

Existence Results for Nonlinear Elliptic Equations with Leray–Lions Operators in Sobolev Spaces with Variable Exponents

Mathematical Notes - This paper deals with the existence of a solution of a problem involving Leray–Lions type operators in Sobolev spaces with variable exponent. The proofs of our main...     

A Jackson Type Estimate for Shepard Operators in L p Spaces for p≧ 1

This paper considers the approximation of the Kantorovich–Shepard operators in spaces for . For the Kantorovich–Shepard operators are defined by (1.1). Then

On the Size of a Cap in PG(n,q) with q Even and n ≥ 3

Let m2(n,q), m2(n,q) be, respectively, the maximum value, the second largest value of k for which there exists a complete k-cap in PG(n,q). In this paper, the known upper bound on m2(3,q), q even, q 8, is improved. This new upper bound on m2(3,q) is then used to improve the upper bounds on m2(n,q), q even, q 8 and n 4.