Linear Combinations of Gammaoperators in L p — Spaces

In 1951 P.L. Butzer defined in his thesis linear combinations of Bernstein polynomials. This type of combinations was extended to other operators by several authors. In this paper we define special linear combinations of Gammaoperators and we will prove a global direct result and an equivalence theorem. The proofs are based on a remarkable connection between the derivatives of the kernel of Gammaoperators and Laguerre polynomials and moreover between the moments of the Gammaoperators and Laguerre polynomials.     

Weighted Approximation by Left Quasi-interpolants of Derivatives of Gamma Operators

In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ （f,t）p. Cuo extended the MiiUer＇s results to wφ^24 （f, t）∞. In this paper we improve the previous results and give a weighted approximation equivalence theorem.     

Approximation of Parametric Derivatives by the Empirical Interpolation Method

We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory.     

金融衍生产品的力学方法分析（Ⅱ）—期权市场价格基本方程

类似固体力学建立基本方程方法，根据期权特点，采用一些假设，建立期权市场价格基本方程：hv0(t)=m1vo^-1(t)-n1vo(t) F,式中h,m1,n1,F为常数，主要假设有：期权市场价格vo(t)的升降由市场供求决定；影响v0(t)的因素如行使价，期限，波幅等用正或反比关系；买和卖用相反规律。文中给出不同情况下基本方程的解，并和期货市场价基本方程的解vf(t)相比较，以及用隐函数存在定理证明vf与v0(t)存在一一对应关系，为研究期货vf对期权价vo(t)的影响提供理论依据。     

金融衍生产品的力学方法分析（Ⅰ）——期指价格基本方程

类似连续介质力学方法,将期指价格变化看成是连续、有规律可寻的。根据期指特点,建立期指价格变化的基本方程。这是一个微分方程,其解显示时间与价格呈对数圆形关系。若将时间理解为相应价格的概率,则这一关系与基于统计理论分析的、著名的诺贝尔经济学奖（1997）获得者的期权定价Black-Scholes公式中主要假设-基础资产（在此为期指）价格呈对数正态分布-完全一致。表明了依据完全不同的两种分析方法,也会得到相同的结果。只是Black-Scholes是用假设给出,而作者则从微分方程的解推出。     

Bernstein-Durrmeyer算子的加权同时逼近等价定理

本文借助修正的Voronovskaja定理,用更一般的光滑模函数来刻划加权同时逼近阶,建立了加权同时逼近等价定理,统一了非最优逼近阶及饱和阶的特征刻划.     

Optimal Recovery in the Finite-Element Method, Part 1: Recovery from Weighted L2 Fits

Finite-element methods lead to approximations that are optimalor near-optimal in an associated energy norm. The consequentialproblem of recovering point values of the solution or its derivativesis addressed in this paper and its companion. A general frameworkis adopted, based on the seminal paper of Golomb & Weinberger(1959), which brings together several ideas such as superconvergence,local averaging and defect correction. Detailed results aregiven for piecewise constant and 2 linear approximations inone dimension: recovery from weighted L² fits is treated here,and from weighted H¹ fits in Part II     

Symmetry of Weighted L1-Algebras and the GRS-Condition

Let G be a compactly generated, locally compact group of polynomialgrowth. Removing a restrictive technical condition from a previouswork, we show that the weighted group algebra is a symmetric Banach *-algebra if and only if theweight function satisfies the GRS-condition. This conditionexpresses in a precise technical sense that grows subexponentially.2000 Mathematics Subject Classification 43A20, 22D15, 22D12.     

Weighted L p -algebras on groups

The space L _p (G), 1 > p < ∞, on a locally compact group G is known to be closed under convolution only if G is compact. However, the weighted spaces L _p (G, w) are Banach algebras with respect to convolution and natural norm under certain conditions on the weight. In the present paper, sufficient conditions for a weight defining a convolution algebra are stated in general form. These conditions are well known in some special cases. The spectrum (the maximal ideal space) of the algebra L _p (G,w) on an Abelian group G is described. It is shown that all algebras of this type are semisimple.     

关于加权差分方法的一点注记

在这篇短文中,对奇异摄动问题引进了新的差分逼近并证明了一致收敛的必要条件。选择适当的权因子可得到用Ilin方法所得的相同的差分格式。     

分区函数法在加权残数法中的应用

本文提出了一个分区函数法的概念.即根据边界形状或刚度、荷载的变化,将原受力体分成若干个分区.在每个分区中设定不同的试函数,并在各分区的交界上考虑了连续协调条件.这样共建立了内部平衡、外部边界和交线协调三种残数方程.文中给出了公式和例题.     

Weighted Interpolation: the L∞ Theory. I

In this paper we deal with weighted interpolation on the real line. We show that the Hermite-Fejér interpolation process is not optimal, but the Grünwald operator is the ideal case.     

Weighted median algorithms for L1 approximation

The weighted median problem arises as a subproblem in certain multivariate optimization problems, includingL ₁ approximation. Three algorithms for the weighted median problem are presented and the relationships between them are discussed. We report on computational experience with these algorithms and on their use in the context of multivariateL ₁ approximation.This work was supported in part by National Science Foundation Grant CCR-8713893 and in part by a grant from The City University of New York PSC-CUNY Research Award program.     

Propagation of the Invariance of Germs of Solutions of Quasilinear Differential Equations with Weighted Derivatives

The paper contains various theorems on the propagation of the invariance of germs of solutions for the class of quasilinear differential equations. This class contains model equations of nonlinear waves propagation: the nonlinear Schrödinger equation, the Korteweg--de Vries equation, and some others.     

On Weighted L~p-Approximation by Weighted Bernstein-Durrmeyer Operators

In the present paper,we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted L~p-norm with Jacobi weight w(x) = x~α(1-x)~β.All the results involved have no restriction α,β 1-1/p,which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.     

Weighted Composition Lambert-Type Operators on L p Spaces

In this paper boundedness of a weighted composition Lambert-type operator T = M _w EM _u C _φ acting between two different L ^p (Σ) spaces is characterized using some properties of conditional expectation operator. Moreover, we establish criteria for hyponormality for these types of operators on L ²(Σ).     

Direct and Converse Results on Weighted Simultaneous Approximation by the Method of Operators of Baskakov-Durrmeyer Type

We consider the n- th. operators of Baskakov-Durrmeyer type, which result from the classical Baskakov-type operators with weights p _nk, if the values f(k/n) are replaced by the integral terms \((n - c)\int_{I} p_{nk} (t) f(t) dt \) , where I denotes the corresponding interval which depends on the parameter c. For integrable functions the rate of weighted simultaneous approximation will be related to the Ditzian-Totik modulus of smoothness.     

加权季节性指数法及其应用

预测医院季度出院人数季度变动趋势;加权季节性指数法;用加权季节性指数法进行季度变动趋势的定量预测与分析,对历史数据样本数量要求不多,并且计算简便;计算结果更具客观性、真实性.