Metric Distance Function and Profit: Some Duality Results

In this paper, we intend to establish relations between the way efficiency is measured in the literature on efficiency analysis and the notion of distance in topology. To this effect, we are interested particularly in the Hölder norm concept, providing a duality result based upon the profit function. Along this line, we prove that the Luenberger shortage function and the directional distance function of Chambers, Chung, and Färe appear as special cases of some l_p distance (also called Hölder distance), under the assumption that the production set is convex. Under a weaker assumption (convexity of the input correspondence), we derive a duality result based on the cost function, providing several examples in which the functional form of the production set is specified.     

Profit,Directional Distance Functions,and Nerlovian Efficiency

The directional technology distance function is introduced, given an interpretation as a min-max, and compared with other functional representations of the technology including the Shephard input and output distance functions and the McFadden gauge function. A dual correspondence is developed between the directional technology distance function and the profit function, and it is shown that all previous dual correspondences are special cases of this correspondence. We then show how Nerlovian (profit-based) efficiency measures can be computed using the directional technology distance function.     

On Sequential Separability

A new criterion for the sequential separability of the space C(X) of continuous real-valued functions on X in the topology of simple convergence is obtained.     

偏好的对子态可分性

本文提出了消费者偏好的对子态可分性概念，并用来揭示一般选择集合上偏好的效用函数表示的特征，证明了偏好关系可用效用函数表示的充分必要条件是该偏好具有对子态可分性和可数满足性，还证明了偏好关系具有长直线ｗ１—表示的充分必要条件是该偏好具有对子态可分性．这两个结果，使得对子态可分性成为用直线上的序来表示消费偏好序之本质所在．     

On Subgroup Separability in Hyperbolic Coxeter Groups

We prove that certain hyperbolic Coxeter groups are separable on their geometrically finite subgroups.     

基于定向技术距离函数的投入产出型Malmquist指数

本在分析了基于产出距离函数的Malmquist指数的局限性后，定义了在t时期上的定向技术距离函数，提出了修正的Malmquist指数(简称ARD，AGL)，并用线性规划给出了求解方法。同时运用修正后的Malmquist指数对技术进步、技术效率变化和规模效率三方面进行了分解，并辅以经济解释。     

定向技术距离函数的探讨

将定向技术距离函数推广,还可定义在现有集合外的点上,给出了函数值存在的充分条件,其值为非负的充要条件,其值为零的充要条件,讨论了投影点的弱DEA有效性及另一个求函数值的方法.     

On a Profit Maximizing Location Model

In this paper we discuss a locational model with a profit-maximizing objective. The model can be illustrated by the following situation. There is a set of potential customers in a given region. A firm enters the market and wants to sell a certain product to this set of customers. The location and demand of each potential customer are assumed to be known. In order to maximize its total profit, the firm has to decide: (1) where to locate its distribution warehouse to serve the customers; (2) the price for its product. Due to existence of competition, each customer holds a reservation price for the product. This reservation price is a decreasing function in the distance to the warehouse. If the actual price is higher than the reservation price, then the customer will turn to some other supplier and hence is lost from the firm's market. The problem of the firm is to find the best location for its warehouse and the best price for its product at the same time in order to maximize the total profit. We show that under certain assumptions on the complexity counts, a special case of this problem can be solved in polynomial time.     

Impact of Partial Separability on Large-Scale Optimization

ELSO is an environment for the solution oflarge-scale optimization problems. With ELSO the user is required to provide only code for the evaluation of a partially separable function. ELSO exploits the partialseparability structure of the function to computethe gradient efficiently using automatic differentiation.We demonstrate ELSO's efficiency by comparing thevarious options available in ELSO.Our conclusion is that the hybrid option in ELSOprovides performance comparable to the hand-coded option, while having the significantadvantage of not requiring a hand-coded gradient orthe sparsity pattern of the partially separable function.In our test problems, which have carefully coded gradients,the computing time for the hybrid AD option is within a factor of two of thehand-coded option.     

On Bounds for the Concentration Function II

We derive an upper bound for the concentration of the sum of i.i.d. random variables with values in by appealing to functions of positive type and the structure theory of set addition.     

Separability of normalizable superintuitionistic propositional logics

The problem of separability of superintuitionistic propositional logics that are extensions of the intuitionistic propositional logic is studied. A criterion of separability of normal superintuitionistic propositional logics, as well as results concerning the completeness of their subcalculi is obtained. This criterion makes it possible to determine whether a normalizable superintuitionistic propositional logic is separable. By means of these results, the mistakes discovered by the author in the proofs of certain statements by McKay and Hosoi are corrected.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 606–615, October, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 94-01-00944.     

Profinite群的共轭分离性和全形

本文讨论了profinite群的共轭分离性和全形，把关于无限群的结果推广到了profinite群。     

某可微函数类在Orlicz空间内的宽度估计

本文首先研究了Υ阶广义样条类在Orlicz空间内的极值问题,由此进一步考虑了光滑函数类Ω_∞~Υ[0,1]在Orlicz空间内的n宽度的精确估计问题.最后还讨论了相应的对偶情形.     

Profit optimization for cattle growing in a randomly fluctuating environment

A class of stochastic differential equation models was applied to describe the evolution of the weight of Mertolengo cattle. We have determined the optimal mean profit obtained by selling an animal at the cattle market, using two approaches. One consists in determining the optimal selling age (independently of the weight) and the other consists in selling the animal when a fixed optimal weight is achieved for the first time (independently of the age). The profit probability distribution can be computed for such optimal age/weight. For typical market values, we observed that the second approach achieves a higher optimal mean profit compared with the first one, and, in most cases, even provides a lower standard deviation.     

On the structure of convex piecewise quadratic functions

Convex piecewise quadratic functions (CPQF) play an important role in mathematical programming, and yet their structure has not been fully studied. In this paper, these functions are categorized into difference-definite and difference-indefinite types. We show that, for either type, the expressions of a CPQF on neighboring polyhedra in its domain can differ only by a quadratic function related to the common boundary of the polyhedra. Specifically, we prove that the monitoring function in extended linear-quadratic programming is difference-definite. We then study the case where the domain of the difference-definite CPQF is a union of boxes, which arises in many applications. We prove that any such function must be a sum of a convex quadratic function and a separable CPQF. Hence, their minimization problems can be reformulated as monotropic piecewise quadratic programs.This research was supported by Grant DDM-87-21709 of the National Science Foundation.     

On the duality between the profit and the indirect distance functions in production theory

Färe and Primont [3] stated, without proofs, duality results between the profit and the indirect distance functions in production theory. The aim of this note is to state these duality results in precise terms and to prove them.     

On an Arithmetical Function

In this paper we introduce an arithmetical function (n), the difference between the number of divisors of n congruent to 1 mod 3 and those congruent to –1 mod 3. This function then is related to the classical function (n) which is the sum of the divisors of n. In particular we prove the identity

On Duality for a Class of Quasiconcave Multiplicative Programs

Multiplicative programs are a difficult class of nonconvex programs that have received increasing attention because of their many applications. However, given their nonconvex nature, few theoretical results are available. In this paper, we study a particular case of these programs which involves the maximization of a quasiconcave function over a linear constraint set. Using results from conjugate function theory and generalized geometric programming, we derive a complete duality theory. The results are further specialized to linear multiplicative programming.     

基于广义平均的方向距离函数效率测量方法

在DEA数据标准化、基于弱有效和算术平均的方向距离函数模型效率测量方法的基础上,定义了一组基于强有效和广义平均的具备单位不变性的方向距函数效率测量方法,并进一步定义了基于强有效和广义平均的效率测量方法,克服了效率测量投入指标和产出指标作用不平衡的问题.     

关于Finsler流形中的距离函数与测地球

利用 Finsler流形中的切曲率和旗曲率 ,研究了距离函数与测地球的凸性 ;指出了在单连通完备 Minkowski空间中测地球正好是平面的一部分