The equivalence of Side-Angle-Side and Side-Angle-Angle in the absolute plane

Following the approach of G.D. Birkhoff, we develop a new axiom system for a continuous absolute plane. In this new axiom system we remove Side-Angle-Side as an axiom and replace it with Side-Angle-Angle as a new axiom. We prove that the new axiom system is also a continuous absolute plane, and in particular, that Side-Angle-Side holds in the new axiom system. In addition, we give new proofs of well known results. These new proofs do not depend on Side-Angle-Side, but instead use Side-Angle-Angle.     

Heuristics with guaranteed performance bounds for a manufacturing system with product recovery

We consider a manufacturing system with product recovery. The system manufactures a new product as well as remanufactures the product from old, returned items. The items remanufactured with the returned products are as good as new and satisfy the same demand as the new item. The demand rate for the new item and the return rate for the old item are deterministic and constant. The relevant costs are the holding costs for the new item and the returned item, and the fixed setup costs for both manufacturing and remanufacturing. The objective is to determine the lot sizes and production schedule for manufacturing and remanufacturing so as to minimize the long-run average cost per unit time. We first develop a lower bound among all classes of policies for the problem. We then show that the optimal integer ratio policy for the problem obtains a solution whose cost is at most 1.5% more than the lower bound.     

关于Michael选择问题

本文得到一个新的逼近选择定理及一个新的连续选择定理.作为这个新的连续选择定理的应用,我们给出一个新的不动点定理和一个新的重合定理(见文[1-27]).     

Regularization Tools version 4.0 for Matlab 7.3

This communication describes version 4.0 of Regularization Tools, a Matlab package for analysis and solution of discrete ill-posed problems. The new version allows for under-determined problems, and it is expanded with several new iterative methods, as well as new test problems and new parameter-choice methods.      

EM 2000 Mathématiques, quel avenir?

Delivered as the closing session, this talk was supposed to be an opening towards the future, both of children and humankind. There will be problems and challenges. How is math involved? Math has permanent values, recognized by other scientists, and also stable notions, some of them going back to the ancient Greeks. However math is in a perpetual motion. Old notions get a new look, new notions appear, as well as new relations with other sciences, international relations, including developing countries, new trends and a new conception of mathematical sciences. Math teaching should express both permanence and mobility of the subject, utility and beauty. Informatics, probability and statistics, geometry and all kinds of computing are subjects of reports under preparation, for a long term view of math education.     

The equivalence of Side-Angle-Side with Side-Side-Side and the general triangle inequality in the absolute plane

We show that if we start with an absolute plane, remove Side-Angle-Side as an axiom, and replace it with Side-Side-Side together with a weakened version of the triangle inequality as new axioms, then the new resulting axiom system is also an absolute plane. In particular, we show that Side-Angle-Side still holds in the new axiom system. In addition, we give a new proof of the two-circle theorem which does not depend on Side-Angle-Side, but instead uses Side-Side-Side and the weakened version of the triangle inequality.     

Extrapolation for Higher Orders of Convergence

A new extrapolation procedure which encompasses Aitken's 2 processand extends to higher orders of convergence is presented. Thenew extrapolation yields information as to whether an algorithmis converging or diverging as well as a new approximation tothe solution point. The new extrapolation technique is comparedwith existing higher order extrapolation techniques. The valueof the new extrapolation is demonstrated analytically and empirically.     

An extension of the associated rational functions on the unit circle

A special class of orthogonal rational functions (ORFs) is presented in this paper. Starting with a sequence of ORFs and the corresponding rational functions of the second kind, we define a new sequence as a linear combination of the previous ones, the coefficients of this linear combination being self-reciprocal rational functions. We show that, under very general conditions on the self-reciprocal coefficients, this new sequence satisfies orthogonality conditions as well as a recurrence relation. Further, we identify the Carathéodory function of the corresponding orthogonality measure in terms of such self-reciprocal coefficients.The new class under study includes the associated rational functions as a particular case. As a consequence of the previous general analysis, we obtain explicit representations for the associated rational functions of arbitrary order, as well as for the related Carathéodory function. Such representations are used to find new properties of the associated rational functions.     

GMW序列的迹表示

研究了长度为2n-1的二元GMW序列的迹表示,用从F2n到F2的迹函数的和式给出了GMW序列的一种简洁的迹表示,并且通过这种迹表示得到了一种新的快速生成GMW序列的方法和一种求GMW序列的极小多项式的方法.最后,还证明了两个GMW序列具有相同极小多项式的一个充要条件.     

Wolfe线搜索下一类混合共轭梯度法的全局收敛性

本文给出了一个新的共轭梯度公式,新公式在精确线搜索下与DY公式等价,并给出了新公式的相关性质.结合新公式和DY公式提出了一个新的混合共轭梯度法,新算法在Wolfe线搜索下产生一个下降方向,并证明了算法的全局收敛性,并给出了数值例子.     

A CLASS OF DECOMPOSITION METHODS FOR LARGE-SCALE SYSTEMS OF NONLINEAR EQUATIONS

This paper presents a new decomposition method for solving large-scale systems of nonlinear equations. The new method is of superlinear convergence speed and has rather less computa tional complexity than the Newton-type decomposition method as well as other known numerical methods, Primal numerical experiments show the superiority of the new method to the others.     

Optimal product rollover strategies

As product life cycles shortened, many firms introduce new products and phase out old products frequently. To plan for a successful product rollover; i.e., introduce a new product and eliminate an old product successfully, a firm needs to determine the prices of both products as well as the time to launch the new product and the time to phase out the old product. In this paper, we develop an analytical model to analyze the profits associated with two product rollover strategies: single-product rollover and dual-product rollover. The single-product rollover strategy calls for simultaneous introduction of the new product and elimination of the old product. For the dual-product rollover, we introduce the new product first and then phase out the old product eventually. We determine the optimal prices of both products as well as the optimal time to execute these product rollover strategies. Moreover, we determine the conditions under which the dual-product rollover strategy is optimal.     

Local balance in queueing networks with positive and negative customers

This paper investigates to what extent a recently developed new product form result for queueing networks with positive and negative customers fits into the class of product form queueing networks that satisfy a notion of partial or local balance. As such, this paper investigates whether this new product form is still a consequence of an appropriate notion of local balance. To this end, a new and non-standard type of local balance is introduced as an extension of standard local balance. This new type of local balance appears more restrictive and is no longer directly sufficient for global balance. Nevertheless, based on this new type of local balance, some extensions such as blocking phenomena for queueing networks with positive and negative customers can be concluded.     

关于《中国城镇新增用地供给量的预测及其修正方法》的新模型建立及其比较

本文对文献［１］中的数据重新以时间序列为变量建立回归模型,通过比较新老模型的检验效果,显示新模型的优良性．又结合新模型重新给出了更为合理的新增用地控制方法     

Optimal timing decisions for the introduction of new technologies

High technology industries, such as the communications industry, are characterized by frequent development of new technologies. These new technologies are often available before the capacities of existing facilities that use an old technology are exhausted. Whenever a new technology facility is introduced, a fixed set-up cost is generally incurred; however, the annual operating costs are often reduced. The optimal timing of the introduction of new facilities is therefore of interest.In this paper, we examine such timing decisions. The study was motivated by an application involving electronic plug-in units that enhance the operation of communication facilities. First, we develop optimal timing decisions for linearly growing demand. The analysis is then extended to nonlinear demand. For linear demand, one of two decisions is optimal: Either introduce the new technology immediately, or as late as possible. However, for nonlinear demand, these decisions may be nonoptimal.     

Cognitive modeling of socially transmitted affordances: a computational model of behavioral adoption tested against archival data from the Stanford Prison Experiment

Social learning and adoption of new affordances govern the rise of new a variety of behaviors, from actions as mundane as dance steps to those as dangerous as new ways to make improvised explosive device (IED) detonators. Traditional diffusion models and social network structures fail to adequately explain who would be likely to imitate new behavior and why some agents adopt the behavior while others do not. To address this gap, a cognitive model was designed that represents well-known socio-cognitive factors of attention, social influence, and motivation that influence learning and adoption of new behavior. This model was implemented in the Performance Moderator Function Server (PMFServ) agent-based cognitive architecture, enabling the creation of simulations where affordances spread memetically through cognitive mechanisms. This approach models facets of behavioral adoption that have not been explored by existing architectures: unintentional learning, multi-layered social and environmental attention cues, and contextual adoption. To examine the effectiveness of this model, its performance was tested against data from the Stanford Prison Experiment collected from the Archives of the History of American Psychology.     

General WP-Bailey chains

Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree), including chains found by Andrews, Warnaar and Liu and Ma, arise as special cases of these general WP-Bailey chains. We exhibit three new branches of the WP-Bailey tree, branches which also follow as special cases of these general WP-Bailey chains. Finally, we describe a number of new transformation formulae for basic hypergeometric series which arise as consequences of these new WP-Bailey chains.     

Two-particle wave function as an integral operator and the random field approach to quantum correlations

We propose a new interpretation of the wave function Ψ (x, y) of a two-particle quantum system, interpreting it not as an element of the functional space L ₂ of square-integrable functions, i.e., as a vector, but as the kernel of an integral (Hilbert-Schmidt) operator. The first part of the paper is devoted to expressing quantum averages including the correlations in two-particle systems using the wave-function operator. This is a new mathematical representation in the framework of conventional quantum mechanics. But the new interpretation of the wave function not only generates a new mathematical formalism for quantum mechanics but also allows going beyond quantum mechanics, i.e., representing quantum correlations (including those in entangled systems) as correlations of (Gaussian) random fields.     

A new asymmetric pyramidally solvable class of the traveling salesman problem

We present a new method of identifying a class of asymmetric matrices for which an optimal traveling salesman tour exists that is pyramidal. The new class generalizes two previously known classes of matrices and includes some new matrices as well.     

一种新的梯形模糊数间距离及在投资组合模型选择中的应用

给出一种新的模糊数间的距离公式.用新定义的距离公式来度量给定优先资产的条件下投资组合的分散度.用可能性均值度量投资组合的收益,可能性半方差度量投资组合的风险,在收益和风险满足一定的条件下构造分散度模型.通过实例分析,给出的方法不仅分散度更好,而且资产分配多元化程度更高,计算也更简单.