Local approximation of functions with several variables

This paper presents the problem of local approximation of scalar functions with several variables, including points of non-differentiability. The procedure considers that the mapping displays rates of change of power type with respect to linear changes in the coordinate domain, and the exponents are not necessarily integer. The approach provides a formula describing the local variability of scalar fields which contains and generalizes Taylor’s formula of first order. The functions giving the contact are Müntz polynomials. The knowledge of their coefficients and exponents enables the finding of local extremes including cases of non-smoothness. Sufficient conditions for the existence of global maxima and minima of concave-convex functions are obtained as well.     

以零向量问题为例浅谈发散性思维的培养

探讨零向量的性质，并利用这些性质得出了正多边形中1个有关零向量命题的6种证明方法。运用1题多解的方法，培养学生分析、解决问题和创新的能力。     

Summability of Fourier orthogonal series for Jacobi weight on a ball in

Fourier orthogonal series with respect to the weight function
on the unit ball in are studied. Compact formulae for the sum of the product of orthonormal polynomials in several variables and for the reproducing kernel are derived and used to study the summability of the Fourier orthogonal series. The main result states that the expansion of a continuous function in the Fourier orthogonal series with respect to is uniformly summable on the ball if and only if .

     

λ-Divergence of the Fourier Series of Continuous Functions of Several Variables

In this paper, we consider the behavior of rectangular partial sums of the Fourier series of continuous functions of several variables with respect to the trigonometric system. The Fourier series is called -convergent if the limit of rectangular partial sums over all indices for which for all j and k exists. In the space of arbitrary even dimension 2m we construct an example of a continuous function with an estimate of the modulus of continuity such that its Fourier series is -divergent everywhere for any .     

高阶导数的插值公式

本文我们得到一种插值公式,它通过一系列点,且满足该点列上的初始高阶导数值.最后还给出这种插值公式的误差估计.     

一类具有多时滞的差分系统的振动准则

研究了如下时滞差分系统Δxj(n)+∑li=1∑mr=1birj(n)xr(n-i)=0,j=1,2,…,m的振动性,给出了系统所有解振动的若干充分条件.     

Simultaneous measurements of thermal diffusivity, thermal conductivity and thermopower with application to copper and ceramic superconductors

A home made experimental set-up allows us to measure the thermal conductivity, the thermopower and the thermal diffusivity simultaneously in the temperature range (20-300 K). Therefore the specific heat can be deduced. The role of a radiation shield is shown to be relevant. Tests of the system are made on a 99.9% pure Cu sample and two polycrystalline cuprate ceramics for illustration. Without any complicated optimisation, the technique indicates much promise already due to its efficiency and rapidity. Received 9 November 1998 and Received in final form 12 July 1999     

Effects of Volume Changes on the Thermal Performance of PCM Layers Subjected to Oscillations of the Ambient Temperature: Transient and Steady Periodic Regimes

The Stefan problem regarding the formation of several liquid–solid interfaces produced by the oscillations of the ambient temperature around the melting point of a phase change material has been addressed by several authors. Numerical and semi-analytical methods have been used to find the thermal response of a phase change material under these type of boundary conditions. However, volume changes produced by the moving fronts and their effects on the thermal performance of phase change materials have not been addressed. In this work, volume changes are incorporated through an additional equation of motion for the thickness of the system. The thickness of the phase change material becomes a dynamic variable of motion by imposing total mass conservation. The modified equation of motion for each interface is obtained by coupling mass conservation with a local energy–mass balance at each front. The dynamics of liquid–solid interface configurations is analyzed in the transient and steady periodic regimes. Finite element and heat balance integral methods are used to verify the consistency of the solutions to the proposed model. The heat balance integral method is modified and adapted to find approximate solutions when two fronts collide, and the temperature profiles are not smooth. Volumetric corrections to the sensible and latent heat released (absorbed) are introduced during front formation, annihilation, and in the presence of two fronts. Finally, the thermal energy released by the interior surface is estimated through the proposed model and compared with the solutions obtained through models proposed by other authors.     

On Goppa Codes and Weierstrass Gaps at Several Points

We generalize results of Homma and Kim [J. Pure Appl. Algebra Vol. 162, (2001), pp. 273–290] concerning an improvement on the Goppa bound on the minimum distance of certain Goppa codes.This paper was written while the second author was visiting The University of Valladolid (Dpto. Algebra, Geometría y Topología; Fac. de Ciencias) supported by the Grant SB2000-0225 from the Secretaria de Estado de Educacíon y Universidades del Ministerio de Educacíon, Cultura y Deportes de España.