Further generalizations of the Gale-Nikaido-Debreu theorem

A fixed point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subsets of a t.v.s. is applied to generalize Gwinner’s extensions of the Walras excess demand theorem and of the Gale-Nikaido-Debreu theorem.     

Generalized KKM theorems,minimax inequalities,and their applications

This paper extends the well-known KKM theorem and variational inequalities by relaxing the closedness of values of a correspondence and lower semicontinuity of a function. The approach adopted is based on Michael's continuous selection theorem. As applications, we provide theorems for the existence of maximum elements of a binary relation, a price equilibrium, and the complementarity problem. Thus our theorems, which do not require the openness of lower sections of the preference correspondences and the lower semicontinuity of the excess demand functions, generalize many of the existence theorems such as those in Sonnenschein (Ref. 1), Yannelis and Prabhakar (Ref. 2), and Border (Ref. 3).The author is grateful to Professor Franco Giannessi for helpful comments and suggestions.     

Expectations equilibria with dispersed forecasts

A dispersion condition for traders' forecasts in a general equilibrium model with uncertainty and asymmetric information yields improved results for some (microeconomic) situations in which rational expectations equilibria need not exist. The hypothesis of suitably dispersed forecasts implies that consumers' aggregate excess demand is a continuous function and therefore a fixed point theorem may be applied to obtain a price vector (for each state of the world) such that markets clear. Stronger assumptions give existence of approximately rational expectations equilibria and the convergence of forecast distributions to rational expectations.     

The Alchian-Allen theorem and the law of relative demand: The case of multiple quality-differentiable brands

The Alchian-Allen theorem of “shipping the good apples out” (the AA theorem) is based on a law of relative demand which states that as the price ratio of one good to another becomes larger, the demand for the former good becomes smaller relative to the demand for the latter good. However, both the AA theorem and the law of relative demand have only been discussed in the context where a commodity group has just two quality-differentiable versions. This paper defines relative demands and investigates their properties for the more general situation where a commodity group consists of more than two similar but quality-differentiable brands. The results obtained extend the AA theorem and the law of relative demand.     

An existence and uniqueness theorem for an optimal inventory problem with forecasting

An existence and uniqueness theorem is proved for an optimal inventory problem with forecasting. The model assumes costs are fixed and that unsatisfied demand is lost. At each stage a forecast is obtained on the basis of which the decisionmaker has a known conditional probability distribution of demand. The theorem is a generalization of a result stated but not proved by White.     

Algebraic characterizations of regularity properties in bipartite graphs

Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph Γ$\Gamma$ is distance-regular if and only if its spectral excess (a number that can be computed from the spectrum) equals the average excess (the mean of the numbers of vertices at extremal distance from every vertex). The aim of this paper is to derive new characterizations of regularity and distance-regularity for the more restricted family of bipartite graphs. In this case, some characterizations of (bi)regular bipartite graphs are given in terms of the mean degrees in every partite set and the Hoffman polynomial. Moreover, it is shown that the conditions for having distance-regularity in such graphs can be relaxed when compared with general graphs. Finally, a new version of the spectral excess theorem for bipartite graphs is presented.     

ERM learning algorithm for multi-class classification

The multi-class classification problem is considered by an empirical risk minimization (ERM) approach. The hypothesis space for the learning algorithm is taken to be a ball of a Banach space of continuous functions. When the regression function lies in some interpolation space, satisfactory learning rates for the excess misclassification error are provided in terms of covering numbers of the unit ball of the Banach space. A comparison theorem is proved and is used to bound the excess misclassification error by means of the excess generalization error.     

Excess Inventory with Stochastic Demand: Continuous Reporting Model

In this paper we consider the problem of finding the greatest level of excess inventory to be allowed and not scrapped. If excess items are not scrapped, then they are eliminated by natural attrition. The procedure used in finding the maximum excess inventory to be allowed is to maximize the function: net benefits = immediate scrap revenues - present value of attrition-period holding costs - present value of all other future costs. This procedure is only approximate. However, it will provide significant improvement on the previous treatment of this problem in that it will allow for backordering costs and for stochastic demand. In particular, deterministic demand and Poisson demand are examined.     

Optimal control policy for a standing order inventory system

In this paper, we consider a standing order inventory system in which an order of fixed size arrives in each period. Since demand is stochastic, such a system must allow for procurement of extra units in the case of an emergency and sell-offs of excess inventory. Assuming the average-cost criterion, Rosenshine and Obee (Operations Research 24 (1976) 1143–1155) first studied such a system and devised a 4-parameter inventory control policy that is not generally optimal. The current paper uses dynamic programming to determine the optimal control policy for a standing order system, which consists of only two operational parameters: the dispose-down-to level and order-up-to level. Either the average-cost or discounted-cost criterion can be assumed in the proposed model. Also, both the backlogged and lost-sales problems are investigated in this paper. By using a convergence theorem, we stop the dynamic programming computation and obtain the two optimal parameters.     

A note on continuously decomposed evolving exchange economies

It is routine to demonstrate in the exchange economy framework that small changes of individual preferences and endowments always result in small changes of the derived excess demand functions as one should expect. Though being as desirable for reasons of the consistency of the whole approach, however, a precise proof of the converse direction so far is still open to question. The present paper shows that it is actually true. We use a decomposition method for aggregate excess demand functions developed by Mas-Colell which is derived from the well-known decomposition method developed by Sonnenschein and perfected by Debreu and Mantel. Our result fills in a notorious gap in the line of economic justification usually given for this decomposition, or disaggregation, method in that comparative static analysis would be restricted if the decomposition of excess demand functions would not be continuous.     

超额市场需求函数

本文通过研究超额需求函数与多项式的关系得：（１）对于（ｎ—１）个关于ｐ１,ｐ２…,ｐｎ－１的多项式Ｅ。（ｐ１,ｐ２,…,ｐｎ－１）,ｓ＝１,２,…,ｎ—１,若满足条件：则Ｅｓ,ｓ＝１,２,…,ｎ—１均为一个经济的超额需求函数．（２）对无穷级数ｇ（ｐ）,也存在含有两个消费者与无穷种商品的经济,使得其超额需求函数恰好为ｇ（ｐ）．     

A Rigidity Phenomenon on Riemannian Manifolds with Reverse Excess Pinching

The authors introduce the Hausdorff convergence to discuss the differentiable sphere theorem with excess pinching. Finally, a type of rigidity phenomenon on Riemannian manifolds is derived.     

On sufficient optimality conditions : PMM vol. 42, no. 6, 1978, pp. 1131–1135

Sufficient conditions of optimality of the control in a nonlinear system are given. This involves a demand for existence of a function with specified properties. If this function is defined in a special manner, then the theorem derived in the paper yields the known theorem of Krotov [1]. A certain relaxation of the sufficient conditions given in [1] is obtained for the problems of the time optimal response in autonomous systems.     

An Inventory Model for Deteriorating Items and Stock-dependent Consumption Rate

An order-level inventory model is developed for deteriorating items with uniform rate of production and stock-dependent demand. Shortages are allowed, and excess demand is backlogged. Results are illustrated with numerical examples.

     

A mathematical model for asset pricing

Asset price dynamics is studied by using a system of ordinary differential equations which is derived by utilizing a new excess demand function introduced by Caginalp [4] for a market involving more information on demand and supply for a stock rather than their values at a particular price. Derivation is based on the finiteness of assets (rather than assuming unbounded arbitrage) in addition to investment strategies that are based on not only price momentum (trend) but also valuation considerations. For this new model and the older models which were extracted using the classical excess demand function by Caginalp and Balenovich [2] and [3], time evolutions of asset price are compared through numerical simulations.     

Optimal location-size of a facility on an plane with interaction effects of distance

A binomial model for the interaction effects of distance is used to obtain the probable demand for a facility located on a plane. Such demand expressed as a function of size, location, population profile and distribution on the plane, is shown (using arguments leading to the central limit theorem) to be normal. Optimization of expected cost criteria is then used to obtain optimal locations under uncertainty. Examples are resolved and the practical implications of the model suggested are drawn.     

向多个供应商采购的存贮模型研究

本文研究当需求量巨大、单一供应商无法满足供货要求情况下的多供应商采购-库存问题,建立了一个向多个有能力约束的供应商采购的库存模型;将模型简化以后用Kuhn-Tucker条件分析了其松弛问题的最优解的必要条件及其相应的搜索算法;随后给出了模型的整数近似解算法,最后给出本文结论以及未来的研究方向。     

A Divisibility Theorem for the Alexander Polynomial of a Plane Algebraic Curve

An upper estimate for the Alexander polynomial of an algebraic curve is obtained, which sharpens Libgober's estimate in terms of the local polynomials at the singular points of the curve: only those singular points may contribute to the Alexander polynomial of the curve that are in the excess of the hypothesis of Nori's vanishing theorem. Bibliography: 19 titles.     

Axiomatic characterizations of the CEA solution for rationing problems

Situations abound in the real world, where aggregate demand for a commodity exceeds aggregate supply. When such situations of excess demand occur, what is required is some kind of rationing. The literature on rationing problems has an interesting origin in the Babylonian Talmud. The purpose of this paper is to characterize axiomatically and analyze the constrained equal award solution for rationing problems.     

A simple proof of the spectral excess theorem for distance-regular graphs

The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained by using a local approach, so giving a characterization of the so-called pseudo-distance-regularity around a vertex. In this paper we present a new simple projection method based in a global point of view, and where the mean excess plays an essential role.