On Lower Bounds for Lp Norms in the Central Limit Theorem for Independent and m-Dependent Random Variables

We derive lower bounds for L_p norms , in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments.     

Operator ideal norms on

Let be a real number such that and its conjugate exponent . We prove that for an operator defined on with values in a Banach space, the image of the unit ball determines whether belongs to any operator ideal and its operator ideal norm. We also show that this result fails to be true in the remaining cases of . Finally we prove that when the result holds in finite dimension, the map which associates to the image of the unit ball the operator ideal norm is continuous with respect to the Hausdorff metric.

     

An algorithm for fitting circular arcs to data using the <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">1</Emphasis></Subscript> norm

There are many applications of fitting circular arcs to data. We have for example, system control, using a computer controlled cutting machine, approximating hulls of boats, drawing and image techniques. Out of these applications comes the least squares norm to be the most commonly used criterion. This paper examines how the l ₁ norm is used which seems to be more appropriate than the use of least squares in the context of wild points in the data. An algorithm and different methods to determine the starting points are developed. However, numerical examples are given to help illustrate these methods.      

Inequalities for formal power series and entire functions

We present several integral and exponential inequalities for formal power series and for both arbitrary entire functions of exponential type and generalized Borel transforms. They are obtained through certain limit procedures which involve the multiparameter binomial inequalities, integral inequalities for continuous functions, and weighted norm inequalities for analytic functions. Some applications to the confluent hypergeometric functions, Bessel functions, Laguerre polynomials, and trigonometric functions are discussed. Also some generalizations are given.     

A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces

In this paper, we study the existence of solutions and approximation of the solutions by using a Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. The results presented in this paper generalize the corresponding results of J. Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115-126].     

On the generation of updates for quasi-Newton methods

We present a unified technique for updating approximations to Jacobian or Hessian matrices when any linear structure can be imposed. The updates are derived by variational means, where an operator-weighted Frobenius norm is used, and are finally expressed as solutions of linear equations and/or unconstrained extrema. A certain behavior of the solutions is discussed for certain perturbations of the operator and the constraints. Multiple secant relations are then considered. For the nonsparse case, an explicit family of updates is obtained including Broyden, DFP, and BFGS. For the case where some of the matrix elements are prescribed, explicit solutions are obtained if certain conditions are satisfied. When symmetry is assumed, we show, in addition, the connection with the DFP and BFGS updates.This work was partially supported by a grant from Control Data     

Inversion of the Bessel potential operator in weighted variable Lebesgue spaces

We study the inversion problem of the Bessel potential operator within the frameworks of the weighted Lebesgue spaces with variable exponent. The inverse operator is constructed by using approximative inverse operators. This generalizes some classical results to the variable exponent setting.     

Banach空间中的拟范均值

在算术平均值和几何平均值的基础上,给出了一种新的平均值—拟算数平均值以及拟几何平均值,并将它们引入到Banach空间进行了讨论.给出了一些定义并在其基础上得到了这几类平均值在Banach空间中的几个有用的性质.     

Bessel functions of third order and the distribution of cyclic planar motions with three directions

The exact distribution of a cyclic planar motion with three directions is explicitly derived in terms of Bessel functions of order three (suitably combined). The absolutely continuous part of the distribution is proved to satisfy suitable boundary conditions and some of its properties are analyzed. The transformations converting the governing equations of order three is presented and its solutions (used here) derived by applying the Frobenius method.     

Quadratic nonlinear torsional hyperelastic waves in isotropic cylinders: Primary analysis of evolution

Nonlinear torsional waves propagating along an infinite isotropic cylinder are considered. The hyperelasticity of the cylinder is described by the Murnaghan potential. An approximate analytical solution of the problem is obtained. The evolution of the initial waveprofile in cylinders made of composite materials reinforced with microscale particles is simulated numerically. It is shown that the approximation used to describe the variation in the amplitude inward the cylinder is quite accurate. Three-dimensional plots of evolution are presented __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 75–85, March 2008.