The minimum degree of recursively representable choice functions

We show that the minimum degree of Turing complexity of a recursively representable choice function is Õ″, the degree of a complete ∑₂ set in the Kleene-Mostowski hierarchy. A consequence of this result is that the complexity of such choice functions in this sense is bounded strictly above the degrees of R.E. subsets on $\text{N}$.     

From social welfare ordering to acyclic aggregation of preferences

One way to overcome Arrow's impossibility theorem is to drop the requirement that the collective preference be transitive. If it is quasi-transitive (strict preferences are transitive) an oligarchy emerges. If it is only acyclic, many non-oligarchic aggregation rules are available, yet the resulting decision rules are poorly decisive: Nakamura's theorem characterizes acyclic and neutral Arrowian aggregators. We propose a parallel characterization of acyclic and anonymous aggregation methods.     

Yield design of thin periodic plates by a homogenization technique and an application to masonry wallsCalcul à la rupture des plaques minces périodiques par une technique d'homogénéisation et une application aux murs en maçonnerie

A homogenization method for determining overall yield strength properties of thin periodic plates from their local strength properties is proposed within the framework of the yield design theory. The proposed method is applied to the determination of the in-plane and out of plane strength criterion for masonry described as a regular assemblage of infinitely resistant bricks separated by Coulomb interfaces. To cite this article: K. Sab, C. R. Mecanique 331 (2003).     

On efficient stopping times

This paper is devoted to efficient sequential estimation in stochastic processes whose corresponding sufficient statistics are processes with stationary independent increments. It is proved that a stopping time is efficient if and only if it represents a time of the first attaining of a hyperplane., which cannot ‘be passed’, in the sense which is made precise below. The problem of determining the explicit form of the hyperplanes which cannot ‘be passed’ is also discussed.     

Estimation of Transit Origin–Destination Matrices from Passenger Counts Using a Frequency-Based Approach

This paper investigates the transit passenger origin–destination (O–D) estimation problem in congested transit networks where updated passenger counts and outdated O–D matrices are available. The bi-level programming approach is used for the transit passenger O–D estimation problem. The upper level minimizes the sum of error measurements in passenger counts and O–D matrices, and the lower level is a new frequency-based stochastic user equilibrium (SUE) assignment model that can determine simultaneously the passenger overload delays and passenger route choices in congested transit network together with the resultant transit line frequencies. The lower-level problem can be formulated as either a logit-type or probit-type SUE transit assignment problem. A heuristic solution algorithm is developed for solving the proposed bi-level programming model which is applicable to congested transit networks. Finally, a case study on a simplified transit network connecting Kowloon urban area and the Hong Kong International Airport is provided to illustrate the applications of the proposed bi-level programming model and solution algorithm. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sum List Coloring Graphs

Let G=(V,E) be a graph with n vertices and e edges. The sum choice number of G is the smallest integer p such that there exist list sizes (f(v):v ∈ V) whose sum is p for which G has a proper coloring no matter which color lists of size f(v) are assigned to the vertices v. The sum choice number is bounded above by n+e. If the sum choice number of G equals n+e, then G is sum choice greedy. Complete graphs K_n are sum choice greedy as are trees. Based on a simple, but powerful, lemma we show that a graph each of whose blocks is sum choice greedy is also sum choice greedy. We also determine the sum choice number of K_2,n, and we show that every tree on n vertices can be obtained from K_n by consecutively deleting single edges where all intermediate graphs are sc-greedy.     

多产品销售薪酬机制的最优提成率研究

多产品销售的提成率由于其直接影响销售人员的精力投入和分配，一直是销售人员薪酬合同设计的焦点。以往最优提成率研究没有区分环境因素和销售努力对销售量的影响。本文运用代理理论设计了一种基于销售人员对产品销售的贡献的多产品销售合同模型，论证了该合同具有激励销售人员努力销售和使其如实上报定额的特性，并对多产品销售相对独立的情况下销售提成率设置进行了分析，推出了各产品提成率与销售反应参数之间的关系特点，提出了一些指导性结论。     

Global convergence without the assumption of linear independence for a trust-region algorithm for constrained optimization

A trust-region algorithm for solving the equality constrained optimization problem is presented. This algorithm uses the Byrd and Omojokun way of computing the trial steps, but it differs from the Byrd and Omojokun algorithm in the way steps are evaluated. A global convergence theory for this new algorithm is presented. The main feature of this theory is that the linear independence assumption on the gradients of the constraints is not assumed.This research was supported in part by the Center for Research on Parallel Computation, by Grant NSF-CCR-91-20008, and by the REDI Foundation.     

Domain Closedness Conditions and Rational Choice

The rationalizability of a choice function on an arbitrary domain under various coherence properties has received a considerable amount of attention both in the long-established and in the recent literature. Because domain closedness conditions play an important role in much of rational choice theory, we examine the consequences of these requirements on the logical relationships among different versions of rationalizability. It turns out that closedness under intersection does not lead to any results differing from those obtained on arbitrary domains. In contrast, closedness under union allows us to prove an additional implication.