A Modified Rank One Update Which Converges Q-Superlinearly

Quasi-Newton methods are generally held to be the most efficient minimization methods for small to medium sized problems. From these the symmetric rank one update of Broyden (Math. Comp., vol. 21, pp. 368–381, 1967) has been disregarded for a long time because of its potential failure. The work of Conn, Gould and Toint (Math. Prog., vol. 50, pp. 177–195, 1991), Kelley and Sachs (COAP, vol. 9, pp. 43–64, 1998) and Khalfan, Byrd and Schnabel (SIOPT, vol. 3, pp. 1–24, 1993; SIOPT, vol. 6, pp. 1025–1039, 1996) has renewed the interest in this method. However the question of boundedness of the generated matrix sequence has not been resolved by this work. In the present paper it is shown that a slightly modified version of this update generates bounded updates and converges superlinearly for uniformly convex functions. Numerical results support these theoretical considerations.     

A Possibility for Studying Gravitational Properties of the Neutrino

We consider the effect that the gravitational field of a neutrino pulse radiated in the collapse of presupernova nuclei has on the observable optical radiation spectra of atoms at the supernova surface. We show that at the modern level of development of experimental methods, neutrino monitoring supplemented by optical monitoring of supernova candidates provides a unique possibility to check whether the Einstein equivalence principle is satisfied for neutrinos of each of the three types (electron, muon, and tau-lepton) and their antiparticles, to estimate the change of the gravitational potential at the surface of the star at the instant of the neutrino radiation pulse, and to obtain upper limits on the mass values of these neutrinos in a new way.     

2500年研究探寻相亲数

设σ(n)为n的所有正因子(包括1和n本身在内)之和.正整数对(m,n)被称之为相亲数(或双亲数,因为这种数总是成双成对出现的)如果他们满足 σ(m)=σ(n) = m + n.如果n=n, σ(m)=2m,则m被称之为完全数(或单亲数,因为这种数总是单独出现的).更一般的,如果κ个(κ＞2)正整数(m1,m2,…mmk)满足下列条件σ(m1)=m1+m2,σ(m2)=m2+m3,σ(mk)=mκ+m1.则这κ个正整数被称之为多亲数.第一对相亲数(220,284)是在2500年前的古希腊数学家毕达哥拉斯发现的.不过迄今为止,人们对相亲数的情况、尤其对相亲数的分布情况仍然知之甚少.与相亲数有关的难题、尤其是悬而未决千百年的难题还很多就是在今夭,我们仍然不知道是不是有无穷多对相亲数,我们甚至连一个生成相亲数的充分必要条件(定义除外)都没有.在这篇文章中,我们试图给出人类在2500年的漫长历史长河中研究、探寻相亲数的大致情况与重要结果,并着重介绍从古至今生成相亲数的各种数值方法与代数方法.完全数的研究探寻史几乎与相亲数的研究探寻史是一样长的.比如2350年前的古希腊数学家欧几理德就在其数学名著<几何原本>中列出了前四个完全数,不过迄今为止,人们总共也只找到39个完全数,并且这些完全数还都是偶完全数.至于有没有奇完全数的存在,则是一个悬而未决两千多年的著名数学难题.最早的两串多亲数(一串为5个.另一串为28个),则是由法国数学家Poulet于1918年发现的.多亲数的研究探寻史虽然比相亲数的研究探寻史要短得多,但目前人们对它们的注意力与日俱增.由于相亲数与完全数及多亲数密切相关、紧密相连(我们可以将其统一称之为亲和数,因为它们都与相关数的因子和有关),因此在本文中,我们除了要讨论介绍相亲数外,也将顺便介绍完全数与多亲数的研究与探寻简史、以及人们在研究探寻这些数时所获得的一些重要结果.附注截止2004年3月25日作者校勘清样时,人们已经发现了共40个完全数和6262871对相亲数.     

POLITICS,ENVIRONMENT, AND FISHERIES: EMPIRICAL EVIDENCE FROM PACIFIC SALMON FISHERIES

Pacific salmon have always been a lucrative commodity in Alaska history. The primary contribution of this paper is to assess the effects of statewide policy changes such as the 1959 Alaska Statehood and the 1974 Limited Entry Act on the harvest of Pacific salmon in Alaska, controlling for changes in oceanic environmental conditions such as the Pacific Decadal Oscillation. An autoregressive distributed lag approach is employed to annual time‐series data for 1899–1996. We find that, while the 1974 Limited Entry Act has a significant effect on Alaska salmon harvests, the 1959 Alaska Statehood had little impact. In addition, the oceanic environment has an important determinant of long‐run Alaska salmon harvests.     

The vibrations of a rotating thin piezoceramic cylindrical shell

G. H. Bryan [8] discovered and studied the dynamic phenomena that arise during the vibrations of thinwalled shells in natural modes while rotating uniformly about an axis of symmetry. In the present article a more detailed mathematical analysis has been conducted for the solution of the problem of the vibrations of a ring rotating with constant angular velocity under feasible conditions of perturbation of the vibrations and realistic mechanical properties of ceramic materials. It is established that two slowly precessing waves arise during the vibration of the ring, one of which (the one discovered by Bryan) is an inverse precession wave having an angular velocity of precession less than the angular velocity of rotation of the ring, while the second is a direct precession wave having angular velocity larger than the angular velocity of rotation of the ring. Under the actual working conditions for piezoceramic resonators the amplitudes of the direct and inverse wave become comparable. Consequently the vibrations present as a modulated standing wave, that is, the phenomenon of beats in the mode of steady-state normal vibration occurs. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 7–18.     

Regional Bell Operating Company entry into long‐distance and non‐price discrimination against rival interexchange carriers: empirical evidence from panel data

The incentive of the Regional Bell Operating Companies (RBOCs) to degrade the quality of interstate access services, an essential input provided to rival long‐distance carriers, once they begin offering long‐distance services has been a controversial issue in the academic literature. Using a panel of state‐level data over the years 1996–2001, this paper investigates whether the RBOCs engage in such ‘non‐price discrimination’ upon entering the long‐distance market. The results suggest the RBOCs improve the quality of some of their interstate access service offerings before entering the interexchange market, but begin degrading the quality of these services immediately afterward. Copyright © 2003 John Wiley & Sons, Ltd.     

A new distribution-free adaptive sample size control chart for a finite production horizon and its application in monitoring fill volume of soft drink beverage bottles

Nonparametric control charts have received increasing attention in process monitoring. In this article, a new nonparametric sign (SN) control chart with variable sample size (VSS) for a finite horizon process is developed. The novelty of this research lies in the incorporation of the VSS technique into the nonparametric SN chart for a finite horizon process, hence, resulting in the development of a more sensitive nonparametric short run chart. The statistical performance of the new nonparametric VSS SN control chart is evaluated and compared with the existing fixed sample size (FSS) SN chart for a finite horizon process. The charts' performances are compared using the truncated average run length (TARL) and truncated standard deviation of the run length (TSDRL) criteria. The results obtained show that the nonparametric VSS SN short run chart is always quicker than the FSS SN short run chart in detecting process shifts for various underlying process distributions, hence, reducing scrap and rework cost. Finally, an application of the proposed control charting scheme is shown through a real-life example on the fill volume of soft drink beverage bottles.     

Amenability,locally finite spaces,and bi-lipschitz embeddings

We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, clearly extends amenability to any locally finite space. Therefore, we start making a comparison between this property and other notions of amenability for locally finite metric spaces that have been proposed by Gromov, Lafontaine and Pansu, by Ceccherini-Silberstein, Grigorchuk and de la Harpe and by Block and Weinberger. We discuss possible applications of the property SN in the study of embedding a metric space into another one. In particular, we propose three results: we prove that a certain class of metric graphs that are isometrically embeddable into Hilbert spaces must have the property SN. We also show, by a simple example, that this result is not true replacing property SN with amenability. As a second result, we prove that many spaces with uniform bounded geometry having a bi-lipschitz embedding into Euclidean spaces must have the property SN. Finally, we prove a Bourgain-like theorem for metric trees: a metric tree with uniform bounded geometry and without property SN does not have bi-lipschitz embeddings into finite-dimensional Hilbert spaces.     

Some quantum mechanical problems in Lobachevsky space

Quantum mechanical problems are considered for potentials satisfying Bertrand's problem in Lobachevsky space. The self-adjointness of the corresponding Schrödinger operators is proved. The energy levels are calculated both from the Schrödinger equation and by means of the Bohr-Sommerfeld method. The effect of the quantum binding of classically infinite motion was discovered and is presented for the first time. It is shown that the quasi-classical limit is equivalent, in a sense, to the Euclidean limit.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 395–405, December, 1996.     

更新过程中的几个随机比较结果

本文研究了更新过程中的几个随机比较结果.通过对不同时刻之前的最后一次更新发生时刻变量在失效率序、反向失效率序和似然比序意义下的随机比较,获得了若底分布F是IFR,则t之前最后一次更新的发生时刻变量SN(t)在失效率序和反向失效率序意义下关于t单调递增;若底分布F是IFR且绝对连续,则SN(t)在似然比序意义下关于t单调递增.     

供应链组织的复杂适应特征及其推论

供应链网络是一个复杂适应系统，具有涌现、自组织、动态、非线性和演化等特征。在供应链网络中，任何一个环节上的细微变化都可能在另外的环节上产生重大的震颤。复杂系统理论的出现和发展不但大大扩展了传统系统理论范围，而且也有助于我们用新的观点观察供应链网络中发生的各种变化，如企业之间相互关系的变化、市场的变化、以及环境的变化等。这些复杂的变化，以及企业为了响应这些变化的表现出适应能力导致了供应链网络中的自组织和涌现的发生。供应链网络中的秩序和控制是自组织和涌现的宏观表现，是不同企业根据各自的局部信息和行为规则而采取行动的结果。     

Hellinger distance estimation of SSAR models

The present paper deals with the statistical inference of the simultaneous switching autoregressive (SSAR) model. This model has been introduced by Kunitomo and Sato (Jpn. Econ. Rev. 50 (2) (1996) 161) in order to take into account the asymmetry in financial and economical time series modelling. Under some conditions which ensure some probabilistic properties of the model, we establish, under other mild assumptions, the asymptotic properties of the minimum Hellinger distance estimates of the parameters. An application to a true data is also given.     

中国碳强度的影响因素解析——基于LMDI分解方法

基于1996-2009年我国碳强度分析,采用对数平均权重分解法(LMDI)进行因素分解.结果显示1996-2009年中国碳强度总体降低了2.9078吨/万元,其中能源强度效应最大,贡献率为85.64%,能源结构效应偏小,为26.78%,而产业结构效应表现出小幅正负波动,总体为-12.0975%,这说明能源结构效应和产业结构效应的潜力还没有充分发挥出来.因此,降低高耗能产业的能源强度是短期内降低碳强度的关键措施,但长远来看改善能源结构以及优化产业结构是降低碳强度的根本途径.     

Supernova survey system in beijing astronomical Observatory (I)

The robotic supernova survey system of Beijing Astronomical Observatory (BAO) is based on the 60-cm telescope of BAO, which includes a CCD camera attached to the prime focus and a software system for facility control and image reduction.     

Interior and exterior functions of positive Boolean functions

The interior and exterior functions of a Boolean function f were introduced in Makino and Ibaraki (Discrete Appl. Math. 69 (1996) 209–231), as stability (or robustness) measures of the f. In this paper, we investigate the complexity of two problems -INTERIOR and -EXTERIOR, introduced therein. We first answer the question about the complexity of -INTERIOR left open in Makino and Ibaraki (Discrete Appl. Math. 69 (1996) 209–231); it has no polynomial total time algorithm even if is bounded by a constant, unless P=NP. However, for positive h-term DNF functions with h bounded by a constant, problems -INTERIOR and -EXTERIOR can be solved in (input) polynomial time and polynomial delay, respectively. Furthermore, for positive k-DNF functions, -INTERIOR for two cases in which k=1, and and k are both bounded by a constant, can be solved in polynomial delay and in polynomial time, respectively.     

Simplification of joint confidence regions for the parameters of the Pareto distribution

The Pareto distribution is an important distribution in statistics, which has been widely used in economics to model the distribution of incomes. Separate interval estimations for parameters of the Pareto distribution have been well established in the literature. For a type-II right censored sample, Chen (Metrika 44:191–197, 1996) proposed a joint confidence region for the parameters. Wu (Comput Stat Data Anal 52:3779–3788, 2008) derived a joint confidence region for any type-II censored sample, but its computation is difficult. Both Wu’s and Chen’s results are simplified in this paper, and some errors are corrected. The methodology used in this article can be applied to other distributions, as long as the underlying distribution can be transformed to the standard exponential distribution in a simple way.     

A solving method of an mdp with a constraint by genetic algorithms

We consider a discrete time Markov decision process (MDP) with a finite state space, a finite action space, and two kinds of immediate rewards. The problem is to maximize the time average reward generated by one reward stream, subject to the other reward not being smaller than a prescribed value. An MDP with a reward constraint can be solved by linear programming in the range of mixed policies. On the other hand, when we restrict ourselves to pure policies, the problem is a combinatorial problem, for which a solution has not been discovered. In this paper, we propose an approach by Genetic Algorithms (GAs) in order to obtain an effective search process and to obtain a near optimal, possibly optimal pure stationary policy. A numerical example is given to examine the efficiency of the approach proposed.     

Primeness of the enveloping algebra of a Cartan type Lie superalgebra

We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras , even. Other algebras are considered but there are no definitive answers in these cases.

     

Rook theory and cycle-counting permutation statistics

A statistic is found to combinatorially generate the cycle-counting q-hit numbers, defined algebraically by Haglund [Adv. in Appl. Math. 17 (1996) 408–459]. We then define the notion of a cycle-Mahonian pair of statistics (generalizing that of a Mahonian statistic), and show that our newly discovered statistic is part of such a pair. Finally, we note a second example of a cycle-Mahonian pair of statistics which leads us to define the stronger property of being a cycle-Euler–Mahonian pair.