Formulation of linear problems and solution by a universal machine

Using the predicate language for ordered fields a class of problems referred to aslinear problems is defined. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the testing of whether sets that are defined by linear inequalities are semilattices, all satisfiability problems in sentenial logic, the rank-computation of matrices, the computation of row-reduced echelon forms of matrices, and all quadratic programming problems with bounded variables. A single, one, algorithm, to which we refer as theUniversal Linear Machine, is described. It solves any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates alinear algorithm for the problem. Then, given an instance of the linear problem, in the second phase the linear algorithm solves the particular instance of the linear problem. The linear algorithm is finite, deterministic, loopless and executes only the five ordered field operations — additions, multiplications, subtractions, divisions and comparisons. Conversely, we show that for each linear algorithm there is a linear problem which the linear algorithm solves uniquely. Finally, it is shown that with a linear algorithm for a linear problem, one can solve certain parametric instances of the linear problem.Research was supported in part by the National Science Foundation Grant DMS 92-07409, by the Department of Energy Grant DE-FG03-87-ER-25028, by the United States—Israel Binational Science Foundation Grant 90-00434 and by ONR Grant N00014-92-J1142.Corresponding author.     

A double-stage piecewise recursive filter for real-time applications

This paper examines the basic problem of estimating the state of a system described by a set of dynamical equations. The state estimation is performed by means of optimal filtering techniques in which the state observation is given by a set of nonlinear equations.The basic issue encountered in most engineering problems is the availability of more observable information than the processor can effectively process in real-time, while performing full optimal filtering on all available observable data. To alleviate this deficiency, an algorithm is developed in which the rate of information processing is kept at a high value, while the system statistics are evaluated at a much slower rate.The method utilizes a combination of fast and slow filtering loops, in which the observable data are processed at a high rate during the fast loop, while the system error covariance, gain computations, and all other system statistics are processed at a lower rate in the slow loop. Methods are provided to resolve any incompatibility in the system statistics resulting from this fast-loop/slow-loop processing combination.Applications describing problems pertaining to aircraft navigation are presented. Specifically, applications to aircraft navigation through a satellite network are studied. Appropriate simulation results from the above studies are shown.This work was performed under contract with the Department of the Air Force, Space and Missile Organization (SAMSO), Los Angeles, California, Contract No. F04-701-75-C-0180.The authors are indebted to Dr. C. Johnson, GPS System Engineer, Mr. G. Consolver, GPS Software Manager, and Mr. W. Riley, Communications/Navigation Department, Texas Instruments for their continuous encouragement in the course of this work. Also, they are indebted to Major M. Birnbaum, SAMSO, for his constructive criticism on the conceptual design of this work, and to Mr. A. Bierman, Aerospace Corporation, for kindly providing simulation data of aircraft trajectories. Finally, the authors would like to express their gratitude to Dr. N. Carlson, Intermetrics, for valuable consultation during the progress of this work.Portions of this paper were presented by the senior author at the GSP Conference, Plan 76, IEEE Position, Location, and Navigation Symposium, San Diego, California, 1976.     

基于模糊FNN-ELECTRE法的国有商业银行竞争力评价

随着金融业全方位开放,国有商业银行已成为国家经济命脉的核心,其竞争力强弱关系着国家经济的繁荣与衰退。本文基于模糊FNN-ELECTRE方法建立国有商业银行竞争力评价模型,以因素神经网络理论(FNN)与ELECTRE融合方法为基础,以现有商业银行竞争力评价指标为着眼,把国有商业银行竞争力的评价体系从现实竞争力和潜在竞争力两个因素抽取为一级指标,以规模、质量、业务结构、效率、成长性五个因素设为二级指标。从实证的角度对银行A、银行B、银行C、银行D、银行E五大国有银行进行分析验证,对其属性值进行和谐性与非和谐性检验得出,银行B竞争能力最强,银行E竞争能力最弱,五大国有银行均有改进空间。     

Representation of the solution to a model problem in semiconductor physics

We study a mixed type problem for the Poisson equation arising in the modeling of charge transport in semiconductor devices [V. Romano, 2D simulation of a silicon MESFET with a non-parabolic hydrodynamical model based on the maximum entropy principle, J. Comput. Phys. 176 (2002) 70-92; A.M. Blokhin, R.S. Bushmanov, A.S. Rudometova, V. Romano, Linear asymptotic stability of the equilibrium state for the 2D MEP hydrodynamical model of charge transport in semiconductors, Nonlinear Anal. 65 (2006) 1018-1038]. Unlike well-studied elliptic boundary-value problems in domains with smooth boundaries (see, for example, [O.A. Ladyzhenskaya, N.N. Uralceva, Linear and Quasilinear Elliptic Equations, Nauka, Moscow, 1973; D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983]), our problem has two significant features: firstly, the boundary is not a smooth curve and, secondly, the type of boundary conditions is mixed (the Dirichlet condition is satisfied on the one part of the boundary whereas the Neumann condition on the other part). The well-posedness of the problem in Hölder and Sobolev spaces is proved. The representation of the solution to the problem is obtained in an explicit form.     

金融风险在股票市场的传染效应及联动行为分析

近年来金融危机频发并表现出了易传染性,引起了众多学者的高度关注。以动态条件相关模型研究美欧股市与中、日、韩股市间的时变相关性,并结合内生多重结构突变模型划分危机传染阶段,选用溢出指数模型分析股市间的风险溢出特性;随后,定义股市间相互影响的联动模式并构建不同传染阶段的加权有向网络图分析股市间的联动行为。研究表明:美欧股市对中日韩股市有明显的传染效应,被传染的速度和持续时间均不相同;金融传染和风险溢出展现出一定的不一致性,危机期间日股的风险溢出效应强于美股;传染效应在联动网络中表现为联动模式的高聚类性和高联动性,相比欧债危机,次贷危机时期股市间展现出更强的联动行为;日股与美欧股市在两次危机中均表现出最强的联动性,其所受影响也最大。     

Wave parameter identification problem for ocean test structure data,part 2, discrete formulation

This paper deals with the solution of the wave parameter identification problem for ocean test structure data. A discrete formulation is assumed. An ocean test structure is considered, and wave elevation and velocities are assumed to be measured with a number of sensors. Within the frame of linear wave theory, a Fourier series model is chosen for the wave elevation and velocities. Then, the following problem is posed: Find the amplitudes of the various wave components of specified frequency and direction, so that the assumed model of wave elevation and velocities provides the best fit to the measured data. Here, the term best fit is employed in the least-square sense over a given time interval.At each time instant, the wave representation involves four indexes (frequency, direction, instrument, time); hence, four-dimensional arrays are required. This formal difficulty can be avoided by switching to an alternative representation involving only two indexes (frequency-direction, instrument-time); hence, standard vector-matrix notation can be used. Within this frame, optimality conditions are derived for the amplitudes of the assumed wave model.A characteristic of the wave parameter identification problem is that the condition number of the system matrix can be large. Therefore, the numerical solution is not an easy task and special procedures must be employed. Specifically, Gaussian elimination is avoided and advantageous use is made of the Householder transformation, in the light of the least-square nature of the problem and the discretized approach to the problem.Numerical results are presented. The effect of various system parameters (number of frequencies, number of directions, sampling time, number of sensors, and location of sensors) is investigated in connection with global or strong accuracy, local or weak accuracy, integral accuracy, and condition number of the system matrix.From the numerical experiments, it appears that the wave parameter identification problem has a unique solution if the number of directions is smaller than or equal to the number of sensors; it has an infinite number of solutions otherwise. In the case where a unique solution exists, the condition number of the system matrix increases as the size of the system increases, and this has a detrimental effect on the accuracy. However, the accuracy can be improved by proper selection of the sampling time and by proper choice of the number and location of the sensors.Generally speaking, the computations done for the discrete case exhibit better accuracy than the computations done for the continuous case (Ref. 5). This improved accuracy is a direct consequence of having used advantageously the Householder transformation and is obtained at the expense of increased memory requirements and increased CPU time.This work was supported by Exxon Production Research Company, Houston, Texas. This paper is based partly on Refs. 1–4.     

On the mechanical and thermomechanical properties of low-density polyethylene/ethylene-α-octene copolymer blends

Blends of low-density polyethylene (LDPE) and ethylene-octene copolymer (EOC) were obtained. The effect of EOC content and absorbed radiation dose on the mechanical and thermomechanical properties of LDPE/EOC blends are investigated. Particular attention is given to a tensile stress-strain analysis and the “form-memory” effect of the blends. With growing LDPE content, the elastic modulus, the yield stress, and the thermorelaxation and residual stresses of the blends increase, but the ultimate elongation at break decreases, which is caused by the higher crystallinity of polyethylene. As a result of radiation-induced cross-linking, the elastic modulus, the yield stress (at a 1% strain), the ultimate yield strength, and the thermorelaxation and residual stresses increase, while the ultimate elongation at break and the melt flow-behavior index decrease, which is confirmed by the growing gel fraction in the blend. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 279–286, March–April, 2008.     

考虑成本、等待时间和安全水平的分类安检模式研究

近年来,随着民航机场旅客吞吐量快速增加,机场安检部门的工作压力正不断加大,旅客等待时间也正在逐渐增加。针对该问题,引入了分类安检模式。然而,分类安检模式通常需要额外的投资成本,可能会产生较大的财务负担。因此,以成本为目标,综合考虑旅客等待时间和安全水平的要求,研究了分类安检模式和传统安检模式的比较以及最优决策性质等相关问题。首先,考虑安全水平和旅客等待时间的约束,分别为传统安检模式和分类安检模式建立了模型,并分析了其最优运营决策性质。其次,从成本的角度,对两种安检模式做了比较研究。研究结果表明,当旅客数量多、安检犯错容忍度较高或旅客等待敏感时,分类安检模式比传统安检模式表现更优;反之,传统安检模式更优。此外,在分类安检模式中,分配到高风险安检通道的旅客比例存在一个最优值,并且其通常在20%到30%之间取到。最后,通过数值分析验证了分类安检模式的最优服务配置。     

绿色产品定价与市场入侵研究:基于市场权力结构的视角

为研究绿色产品定价与市场入侵问题,针对由两个制造商和一个零售商组成的系统,构建了制造商主导、零售商主导以及供需双方均势等三种权力结构模型,分析了权力结构、消费者绿色偏好等因素对绿色产品定价和市场入侵的影响。研究发现:绿色产品入侵市场存在可行条件,并且绿色产品市场入侵会导致普通产品制造商的利润损失;市场入侵对零售商有利,说明零售商会有动机引入绿色产品;绿色产品入侵市场和市场权力结构均会影响各个企业最优定价策略,其中拥有主导权的企业会选择高价策略;权力结构会影响供需双方的利润分配,以及导致系统利润的损失。     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

基于多技能多渠道变成本的物流联络中心排班

物流联络中心的人力成本随着坐席拥有的技能、服务渠道的多少以及服务时段的不同而不同,对人员进行合理班次设计以节省人力成本尤为必要。考虑现实联络中心工作时间的连续与中断、技能组和渠道组的匹配等,提出采用分阶段法优化班次。首先给出不考虑时间中断的坐席的排班模型A,求得排班方案;接下来,在此基础上将中断时间约束加入,建立模型B,求得班次覆盖矩阵;最后加入排班调整约束,建立模型C,对多技能组中各渠道组进行调整,给出最符合实际情况的最优排班调整方案。数值实验结合物流企业实例和各方案的比较,验证了模型的有效性。该方法为联络中心排班提供了新思路,对其它服务行业的排班也具有一定的参考价值。     

非对称的Lax-Milgram引理对非关联塑性的一个应用

在塑性势和屈服面的广泛假设下,研究了非关联塑性的某些性质.对强化材料,通过使用非对称的Lax-Milgram引理,证明了当强化参数A>‖?F/?σ‖?Q/?σ‖-时,应力位移增量分布的存在唯一性.     

A theoretical study of the effect of intraventricular pulsations on the pathogenesis of hydrocephalus

Hydrocephalus, a condition which affects thousands of people annually in the US alone, arises as a result of a build-up of cerebrospinal fluid (CSF) in the brain’s ventricular cavity due to an imbalance between the rates of CSF production and absorption. Although the earliest known instances of hydrocephalus date back to the time of Hippocrates, the pathophysiology of hydrocephalus is still poorly understood, and is the subject of active debate in the literature. Recently, the pulsations of the cerebrospinal fluid have been suggested as a possible mechanism for ventricular expansion. In this paper, we attempt to determine the significance of these pulsations in the development of hydrocephalus by simulating their mechanical effects on the brain. The brain parenchyma is modelled as a fractional Zener viscoelastic solid, which extends the work previously presented in Sivaloganathan et al. [S. Sivaloganathan, M. Stastna, G. Tenti, J. Drake, A viscoelastic model of the brain parenchyma with pulsatile ventricular pressure, Appl. Math. Comput. 165 (2005) 687-698]. Explicit solutions for the displacement and stresses are obtained by solving the boundary value problems corresponding to the cases of infant and adult hydrocephalus. As expected, when the cranial vault is a rigid container, as in adult hydrocephalus, very small displacements are predicted.     

社会互动,投资者情绪传染与资产泡沫——基于股票论坛发帖的实证研究

在资本市场中,投资者并不是相互独立的个体,而是相互学习、相互交流的。随着互联网的迅猛发展,这种社会互动变得更为频繁和普遍,因此社会互动对资产价格的影响也不容小觑。本文先通过理论建模提出理论假设:社会互动存在条件下,投资者互动会加剧市场情绪的传染,进而增加资产泡沫;当投资者情绪高涨时,投资者互动强度显著正向影响泡沫;当投资者情绪低落时,投资者互动强度显著负向影响泡沫;受社会互动影响,投资者活跃的交易会加剧市场情绪的传染,进而增加资产泡沫。之后本文基于股票论坛发帖构建社会互动、投资者情绪指标,验证了中国股票市场中本文理论假设的正确性。     

Personae at play. ‘Men of Mathematics’ in commentary

Mathematical writers, above all, Euclid, tend to present their theorems as decontextualized, abstract propositions, which has become the standard modus of textual presentation in theoretical mathematics. Mathematical commentators, however, provide their readers with personal names and historical facts in order to elucidate problems, provide contexts of discovery, or construct doxographies, among other things. Modern readers have used such information for the construction of histories of science. When we look at these passages, however, we see that personal names and information about mathematicians of the past can serve quite a range of different objectives, such as the strategic self-positioning of the commentator vis-à-vis the past or present of mathematics, the education of the reader, mathematical or moral, the construction of the history of the field, etc. Not only does the commentator present a persona of himself to the reader, he can also turn colleagues and predecessors into personae. This paper attempts to elucidate the practice, by offering four examples of such plays of and with personae, in Pappus, Eutocius, al-Nayrīzī, and Proclus.     

On maximum bifurcation delay in real planar singularly perturbed vector fields

In singularly perturbed vector fields, where the unperturbed vector field has a curve of singularities (a “critical curve”), orbits tend to be attracted towards or repelled away from this curve, depending on the sign of the divergence of the vector field at the curve. When at some point, this sign bifurcates from negative to positive, orbits will typically be repelled away immediately after passing the bifurcation point (“turning point”). Atypical behaviour is nevertheless observed as well, when orbits follow the critical curve for some distance after the turning point, before they repel away from it: a delay in the bifurcation is present. Interesting are systems that have a maximum bifurcation delay, i.e. there is a point on the critical curve beyond which orbits cannot stay close to the critical curve. This behaviour is known to appear in some systems in dimension 3 (see [E. Benoît (Ed.), Dynamic Bifurcations, in: Lecture Notes in Mathematics, vol. 1493, Springer-Verlag, Berlin, 1991]), and it is commonly believed that it is not an issue in (real) planar systems. Beside making the observation that it does appear in non-analytic planar systems, it is shown that whenever bifurcation delay appears, it has no non-trivial maximum for analytic planar vector fields. The proof is based on the notion of family blow-up at the turning point, on formal power series in terms of blow-up variables, the study of their Gevrey properties and analytic continuation of their Borel transform. These results complement existing results concerning the equivalence of local and global canard solutions in [A. Fruchard, R. Schäfke, Overstability and resonance, Ann. Inst. Fourier (Grenoble) 53 (1) (2003) 227–264].     

极限概念教学难点分析及其突破策略

多年来,我国不少学者就极限概念教学难的问题做了大量研究,但该问题并未得到根本解决。通过对极限概念教学进行全面系统的研究,将会发现,在我国的教材体系下,极限概念教学的最大特点是难点多而密集。具体表现在极限的精确定义被高度形式化,且逻辑结构复杂、极限精确定义种类繁多、用精确定义验证极限的证明形式独特、证明技巧性强等方面。因此,为使极限概念教学难的问题得到根本解决,需采取充分铺垫、分散难点、淡化形式、借助直观、梯式演练和因材施教等策略。     

基于EGB2分布族的GAS-EGARCH模型与VaR预测

GARCH族模型是刻画资产收益率的常用工具,在风险度量领域具有广泛应用。为了更有效地描述收益率的偏斜厚尾等特征,越来越多学者对GARCH族模型的条件分布形式进行了研究。但是仅对GARCH模型条件分布进行修正是不够的,还需要对模型本身的函数形式进行修正。基于得分函数的时变参数建模思想近年来受到广泛关注,本文借助这一思想对EGARCH模型中对数标准差进行时变波动建模,并利用EGB2分布族作为模型的条件分布,进而建立GAS-EGARCH-EGB2模型。以我国10只中证行业指数为研究对象考察GAS-EGARCH-EGB2模型的风险预测效果,GAS-EGARCH-EGB2模型样本外VaR预测表现普遍优于ACM-EGARCH-EGB2模型。     

Moment information for probability distributions,without solving the moment problem,II: Main-mass,tails and shape approximation

How much information does a small number of moments carry about the unknown distribution function? Is it possible to explicitly obtain from these moments some useful information, e.g., about the support, the modality, the general shape, or the tails of a distribution, without going into a detailed numerical solution of the moment problem? In this, previous and subsequent papers, clear and easy to implement answers will be given to some questions of this type. First, the question of how to distinguish between the main-mass interval and the tail regions, in the case we know only a number of moments of the target distribution function, will be addressed. The answer to this question is based on a version of the Chebyshev–Stieltjes–Markov inequality, which provides us with upper and lower, moment-based, bounds for the target distribution. Then, exploiting existing asymptotic results in the main-mass region, an explicit, moment-based approximation of the target probability density function is provided. Although the latter cannot be considered, in general, as a satisfactory solution, it can always serve as an initial approximation in any iterative scheme for the numerical solution of the moment problem. Numerical results illustrating all the theoretical statements are also presented.