Uniformly summing sets of operators on spaces of vector–valued continuous functions

Let X, Y be Banach spaces. We say that a set is uniformly p–summing if the series is uniformly convergent for whenever (x_n) belongs to . We consider uniformly summing sets of operators defined on a -space and prove, in case X does not contain a copy of c₀, that is uniformly summing iff is, where T (φ x) = (T^#φ) x for all and x∈X. We also characterize the sets with the property that is uniformly summing viewed in . Received: 1 July 2005     

On Cesàro summability of vector valued multiplier spaces and operator valued series

In this paper, we introduce and study vector valued multiplier spaces with the help of the sequence of continuous linear operators between normed spaces and Cesàro convergence. Also, we obtain a new version of the Orlicz–Pettis Theorem by means of Cesàro summability.     

Construction of beam elements considering von Kármán nonlinear strains using B-spline wavelet on the interval

The current paper proposes the formulation of beam elements using B-spline wavelet on the interval based wavelet finite element method by incorporating von Kármán nonlinear strains. Formulation is proposed for both Euler–Bernoulli beam theory and Timoshenko beam theory. A background cell based Gauss quadrature is proposed for numerical integration. Numerical examples are solved for transverse deflections and stresses in axial direction, and are compared with the existing converged results from finite element method. The issues of membrane and shear locking for the proposed elements are examined and solution techniques are suggested to overcome the issues.     

Best Φ- and N Φ-approximants in Orlicz spaces of vector valued functions

Summary Let (, A, P) be a probability space and E be a Banach space. We study the approximation of an E-valued random variable X, which is an element of the Orlicz space L(, A, P; E), by a function YL, which is measurable with respect to a sub--field of A and takes values in a closed convex subset of E. Two types of approximation are considered: (X – Y) dP=inf, and N(X–Y)=inf with the Orlicz space norm N. We give conditions for the existence of best approximants. If E is reflexive, we obtain martingale type convergence theorems for best approximants and discuss the continuity of the operator X best approximant of X.This paper is a part of the authors doctoral thesis, written under the guidance of D. Landers     

A Construction of Multiresolution Analysis on Interval

We present a concrete method of constructing multiresolution analysis on interval. The method generalizes the corresponding results of Cohen, Daubechies and Vial [Appl. Comput. Harmonic Anal., 1（1993）, 54-81]. By the use of the subdivision operator, the expressions of the constructed functions are more compact. Furthermore, the method reveals more clearly some properties of multiresolution analysis with certain approximation order.     

Construction of a class of multivariate compactly supported wavelet bases for L 2(? d )

In this paper, for a given d×d expansive matrix M with |detM| = 2, we investigate the compactly supported M-wavelets for L ²(ℝ ^d ). Starting with a pair of compactly supported refinable functions ϕ and [(j)\tilde]\tilde \varphi satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet ψ such that {2 ^j/2 ψ(M ^j · −k): j ∈ ℤ, k ∈ ℤd} forms a Riesz basis for L ²(ℝ ^d ). The (anti-)symmetry of such ψ is studied, and some examples are also provided.     

Construction of nonseparable orthonormal compactly supported wavelet bases for L2（Rd）

Suppose M and N are two r × r and s × s dilation matrices,respectively.Let ΓM and ΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-TZr/Zr and N-TZs/Zs,respe...     

Cesaro Summability of Two-dimensional Walsh-Fourier Series on the Ring of Integers in a p-series Field

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Mean size formula of wavelet subdivision tree on Heisenberg group

The purpose of this paper is to investigate the mean size formula of wavelet packets （wavelet subdivision tree） on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree.     

A note on nonstable monomorphisms¶of vector bundles

In this paper we consider the question of the existence of a nonstable vector bundle monomorphism u:α→β over a closed, connected and smooth manifold M, when dimension of α= 3, dimension of β= dimension of M=n≡ 0(4). The singularity method provides the full obstruction to this problem and under some homological hypothesis we can compute it in terms of well known invariants. Received: 31 May 1999     

On Poincaré bundles of vector bundles on curves

An arbitrary cubic function field can have 0, 1, or 2 for its unit rank. This paper presents the complete classification of unit rank of an arbitrary cubic function field by its discriminant and the polynomial discriminant of its generating polynomial. The notions of Kummer Theory and Cardanos formula are used.Mathematics Subject Classification (2000): 11R27, 11R16Acknowledgement The author expresses her gratitude to the referee for very helpful comments.     

Birkhoff interpolation on unity and on Möbius transform of the roots of unity

In this paper the regularity of two interpolation problems is proved. One uses (0,1,..., r-2,r) interpolation with as nodes Möbius transforms of nth roots of unity with the point z=1 added and the other is concerned with Pál-type interpolation on the pair of polynomials (z+α)ⁿ+(1+α z)ⁿ and (z+α)ⁿ-(1+α z)ⁿ, where 0 < α < 1.     

Smooth classification of 1-resonant vector fields on ℝ3

In this paper we study on ⁿ a class of smoothly (C ) finitely determined vector fields which admit infinite many resonant relations. We give a complete classification of all such vector fields with arbitrarily degenerated nonlinear parts.     

L 1-spaces of vector measures defined on δ-rings

Given a vector measure v defined on a -ring with values in a Banach space, we study the relation between the analytic properties of the measure v and the lattice properties of the space L¹(v) of real functions which are integrable with respect to v.Received: 22 April 2004; revised: 5 October 2004     

Estimation of the pointwise Hölder exponent of hidden multifractional Brownian motion using wavelet coefficients

We propose a wavelet-based approach to construct consistent estimators of the pointwise Hölder exponent of a multifractional Brownian motion, in the case where this underlying process is not directly observed. The relative merits of our estimator are discussed, and we introduce an application to the problem of estimating the functional parameter of a nonlinear model.     

Time-dependent Schrödinger equation: Statistics of the distribution of Gaussian packets on a metric graph

We consider a time-dependent Schrödinger equation in which the spatial variable runs over a metric graph. The boundary conditions at the vertices of the graph imply the continuity of the function and the zero sum of the one-sided derivatives taken with some weights. In the semiclassical approximation, we describe a propagation of Gaussian packets on the graph that are localized at a point at the initial instant of time. The main focus is placed on the statistics of the behavior of asymptotic solutions as time increases. We show that the calculation of the number of quantum packets on a graph is related to the well-known number-theoretic problem of finding the number of integer points in an expanding simplex. We prove that the number of Gaussian packets on a finite compact graph grows polynomially. Several examples are considered. In a particular case, Gaussian packets are shown to be distributed on a graph uniformly with respect to the edge travel times.     

Remarks on Thurston’s Construction of Pseudo-Anosov Maps of Riemann Surfaces

It is well known that certain isotopy classes of oseudo-Anosov maos on a Riemann surface S of non-excluded type can be defined through Dehn twists tα and tβ along simple closed geodesics α and β on S,respectively. Let G be the corresponding Fuchsian group acting on the hyperbolic plane H so that H/G≌S.For any point α∈S,define S = S／{α}.In this article, the author gives explicit parabolic elements of G from which he constructs pseudo-Anosov classes on S that can be projected to a given pseudo-Anosov class on S obtained from Thurston＇s construction.     

A Construction of the Rational Function Sheaves on Elliptic Curves

Abstract The authors introduce an effective method to construct the rational function sheaf κ on an elliptic curve E, and further study the relationship between κ and any coherent sheaf on E. Finally, it is shown that the category of all coherent sheaves of finite length on E is completely characterized by κ.     

Bergman kernel function on Hua Construction of the second type

In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…,1/(pr-1) are positive integers and 1/pr is an arbitrary positive real number.