一类函数增量的局部渐近性质

文章研究了一类函数增量的局部渐近性质,发现这类函数增量的局部渐近性对于一元实函数,二元及多元实函数,向量值函数和复函数在一定条件下都会保持不变,进而提出了两个相关的猜想:此类函数增量的渐近性是关于函数变换的拓扑不变量。     

On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions

This paper aims to present non-linear CES (Constant Elasticity of Substitution)–CET (Constant Elasticity of Transformation) Directional Distance Functions. These measures inherit the structure of the standard Directional Distance Functions and that of the CES–CET technology. These functions allow non-parametric estimation of efficiency scores through linear programming method. Besides, the CES –CET technology gives the opportunity to explore α-returns to scale assumption for the new distance functions. The duality theory is investigated through pseudo profit, cost and revenue functions. The dual standpoint provides non-linear adjusted prices that can occur into non-linear pricing practices. An application is proposed to give an illustrative example of the primal CES–CET Directional Distance Functions.     

On a Function Related to Multinomial Coefficients (I)

Let F _p,t (n) denote the number of the coefficients of (x ₁+1x ₂+...+x _t ) ^j , 0 ≤j≤n− 1, which are not divisible by the prime p. Define G _p,t (n) = F _p,t /n ^θ and β(p,t) = lim infF _p,t )(n)/n ^θ, where θ = (log)/(log p). In this paper, we mainly prove that G _p,t can be extended to a continuous function on ℝ⁺, and the function G _p,t is nowhere monotonic. Both the set of differential points of the function G _p,t and the set of non-differential points of the function G _p,t are dense in ℝ⁺. Received February 18, 2000, Accepted December 7, 2000     

Inverse estimation of temperature dependent emissivity of solid metals

An algorithm in the form of inverse problem to estimate the surface emissivity versus temperature of solids of variable thermal properties separated by a non-participating medium is proposed. The estimations are reproduced by the connection of variable slope stretches (piece-wise function) with no information of the temperature dependence of the emissivity. The input data (measurements) come from the solution of the direct problem by adding a random error to the temperature field. Both the direct and inverse problem are numerically solved by means of the network simulation method. The influence of different parameters in the estimation is studied and the resulting estimations are compared with exact solutions in order to verify the effectiveness of the proposed method.     

一类六参数非协调任意凸四边形单元

本文构造了一类六参数非协调四边形单元,证明由此产生的有限元对任意四边形网格通过Irons分片检查,其收敛效果同Wilson元相当且形状函数的选择不依赖于单元本身。类Wilson元及改进的Wilson任意四边形单元是其中的特例。     

论一类整函数的牛顿级数展式

本文给出级小于1的整函数的牛顿级数展式的充要条件．     

命题逻辑系统L*的有效集

针对命题逻辑系统L*,以及增加一元联结词△后的系统L*△,研究了该逻辑系统有效集的特征,进而以有效集为工具得到公式集F(S)的一类分划,即可将L*与L*△中的公式集F(S)分别分为16和20个等价类;最后给出了L*中对M P规则封闭的有效集的特征。     

D.C.隶属函数模糊集及其应用(II)——D.C.隶属函数模糊集的万能逼近性

本文是D.C.隶属函数模糊集及其应用系列研究的第二部分。指出在实际问题中普遍选用的三角形、半三角形、梯形、半梯形、高斯型、柯西型、S形、Z形、π形隶属函数模糊集等均为D.C.隶属函数模糊集,建立了D.C.隶属函数模糊集对模糊集的万有逼近性。探讨了D.C.隶属函数模糊集与模糊数之间的关系,给出了用D.C.隶属函数模糊集逼近模糊数的-εC e llina逼近形式,得到模糊数与D.C.函数之间的一个对应算子,指出了用模糊数表示D.C.函数的问题。     

Weighted Commutator and Weighted BMO Martingales

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