Clifford拟正则半群

作为Ｃｌｉｆｆｏｒｄ半群在拟正则半群范围内的推广，本文定义了Ｃｌｉｆｆｏｒｄ拟正则半群，给出了它的若干特征，建立了它的θ－积结构，同时，又给出了它为拟群的强半格的充要条件．     

事后分层方法及其在交通运输抽样调查中的应用

本文介绍事后分层技术，说明了它不仅可用于简单随机抽样，而且可以用于放回ＰＰＳ抽样。给出了事后分层估计量的形式，证明了它的无编性，并给出了它在交通运输抽样调查中的应用。     

“精确度”是什么？

《黑龙江珠算》近几年来，笔者一直订阅着，并且还是它的一位热心的读者。可去年由于工作的繁忙，遂对它有一点冷落，但成了它的一位忠实的收藏者。     

四元数中的真半范数

讨论了四元数中的真半范数，并给出了它的一般形式，它适合核维数分别为1，2，3的情形，推广了复数域中的真半范数的一般形式，给出了一个较好的结果．     

关于对称R—循环分块矩阵

给出了对称Ｒ－循环分块矩阵的概念，讨论了它的一些性质，当Ｒ＝Ｉｎ时，得到了它的分解定理及标准形。     

Excess函数的应用

在本文中，我们研究了曲率有下界的开流形的拓扑，并推广了文[7]中的结果，证明了截曲率有下界的开流形如果它的excess函数被它的临界半径的某个函数所界定时，它就具有有限拓扑型或者微分同胚于R^n．     

也谈复利率的连续计算方法——析连续复利计算公式的科学性及实用性

本文分析了连续复利公式形成的经济背景，论述了它的科学性、实用性，并举例说明了它在经济决策中的重要作用     

“渐近线”——双曲线的特殊成员

我们在初中阶段学过函数y=1/x的图象，知道它的图象是双曲线，但对它的一些性质知道得不多，通过学习解析几何之后，我们对它的了解可以算是有了一个比较完整的轮廓．双曲线与椭圆、抛物线有许多共同的性质，但也有独一无二的个性，其中最重要的是它具有其它曲线所不具有的“渐近线”这一特殊的成员，可以说渐近线是双曲线的“影子”，它始终陪伴双曲线的左右．我们在学习双曲线时，与椭圆、     

另一形式的多元Γ分布及其性质

本文基于开关参数可变，尺度参数不变的思路，提出了一种新形式的多元Γ分布，并研究了它的性质以及它与多元正态分布的关系。     

狗的笑话

一男养一狗，特烦它，就想把它给扔了，但是此狗认得回家的路，扔了好多次都没有成功。某日，此人驾车弃狗，当晚打电话给他的妻子：“快让狗来接电话，我迷路了。”     

Determination of Stackelberg–Nash equilibria using a sensitivity based approach

A sensitivity based approach is presented to determine Nash solution(s) in multiobjective problems modeled as a non-cooperative game. The proposed approach provides an approximation to the rational reaction set (RRS) for each player. An intersection of these sets yields the Nash solution for the game. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. The two approaches for generating the RRS are compared on three example problems to find Nash and Stackelberg solutions. For the examples presented, it is seen that the proposed sensitivity based approach (i) requires less computational effort than a RSM-DOE approach, (ii) is less prone to numerical errors than the RSM-DOE approach, (iii) has the ability to find multiple Nash solutions when the Nash solution is not a singleton, (iv) is able to approximate nonlinear RRS, and (v) on one example problem, found a Nash solution better than the one reported in the literature.     

Determination of the relaxation and retardation spectra – a view from the up-to-date signal processing perspective

The problem of determination of relaxation and retardation spectra (RRS) is considered from the viewpoint of up-to-date signal processing. It is shown that the recovery of RRS represents the Mellin deconvolution problem, which transforms into the Fourier deconvolution problem for data on a logarithmic time or frequency scale, where it can also be treated as the inverse filtering problem. On this basis, discrete deconvolution (inverse) filters operating with geometrically sampled data are proposed to use as RRS estimators. Appropriate frequency responses and algorithms are derived for estimating RRS from eight different material functions. The noise amplification coefficient is suggested to use as a measure for quantifying the degree of ill-posedness and illconditioness of the RRS recovery problem and algorithms. A methodology is developed for designing RRS estimators with a desired noise amplification, producing maximum accurate spectra for available limited input data. Practical algorithms for determining RRS are proposed, and their performance is studied. The algorithms suggested are compared with the so-called moving-average formulae. It is demonstrated that the minimum frequency range for recovering the point estimate of a relaxation spectrum depends on the allowable noise amplification (the degree of ill-conditioness) and is in no way limited by 1.36 decades, as it is stated by the sampling localization theorem.     

Skew linear recurring sequences of maximal period over galois rings

Let p be a prime number, and R = GR(q ^d , p ^d ) be a Galois ring of q ^d = p ^rd elements and of characteristic p ^d . Denote by S = GR(q ^nd , p ^d ) a Galois extension of the ring R of dimension n and by ? the ring of all linear transformations of the module _R S. We call a sequence v over the ring S with the law of recursion $$ {\mathrm{for}\ \mathrm{all}\ }i \in {\mathbb{N}_0}:v\left( {i + m} \right) = {\psi_{m - 1}}\left( {v\left( {i + m - 1} \right)} \right) + \cdots + {\psi_0}\left( {v(i)} \right),\quad {\psi_0}, \ldots, {\psi_{m - 1}} \in \textit{\v{S}} $$ (i.e., a linear recurring sequence of order m over the module _? S) a skew LRS over S. It is known that the period T(v) of such a sequence satisfies the inequality T(v) ?? ?? = (q ^nm ?1)p ^d?1. If T(v) = ?? , then we call v a skew LRS of maximal period (a skew MP LRS) over S. A new general characterization of skew MP LRS in terms of coordinate sequences corresponding to some basis of a free module _R S is given. A simple constructive method of building a big enough class of skew MP LRS is stated, and it is proved that the linear complexity of some of them (the rank of the linear recurring sequence) over the module _S S is equal to mn, i.e., to the linear complexity over the module _R S.     

Classification of locally rotationally symmetric Bianchi-I space–times using conformal Ricci collineations

We present a complete classification of locally rotationally symmetric (LRS) Bianchi-I space–times in accordance with their conformal Ricci collineations (CRCs). In the case where the Ricci tensor is nondegenerate, we find a general form of the vector field generating CRCs subject to some integrability conditions. Solving the integrability conditions in different cases, we find that the LRS Bianchi-I space–times admit 7-, 10-, 11-, or 15-dimensional Lie algebras of CRCs in the case where the Ricci tensor is nondegenerate. Moreover, we find that these space–times admit an infinite number of CRCs if the Ricci tensor is degenerate. We give some examples of LRS Bianchi-I space–times that admit nontrivial CRCs and are models of a perfect fluid.     

The evaluation and application of some modified moments

Recurrence formulas for the calculation of the modified moments $$\int\limits_{ - 1}^{ + 1} {(1 - x)^\alpha (1 + x)^\beta T_n (x)dx} $$ and $$\int\limits_{ - 1}^{ + 1} {(1 - x)^\alpha (1 + x)^\beta \ln \left( {\frac{{1 + x}}{2}} \right)T_n (x)dx} $$ are presented. Some applications of these modified moments are discussed, such as the numerical calculation of integrals of functions having branch points, the computation of Chebyshev series coefficients and the construction of Gaussian quadrature formulas for integrals with logarithmic singularity.     

Applying Local Rescheduling in response to schedule disruptions

In realistic scenarios of disruption management the high number of potential options makes the provision of decision support—on how to get back on track—complex. It is thus desirable to reduce the size of the regarded problems by applying methods of partial rescheduling. As existing approaches (such as Affected Operations Rescheduling or Matchup Scheduling) mainly focus on production-specific problems, we propose Local Rescheduling (LRS) as a generic approach to partial rescheduling in this paper. It integrates previous research on partial rescheduling and local search in the context of complex project scheduling problems. LRS is based on the bidirectional incremental extension of a time window regarded for potential schedule modifications. Experiments show that LRS outperforms previous approaches.     

The Relation Reflection Scheme

We introduce a new axiom scheme for constructive set theory, the Relation Reflection Scheme (RRS). Each instance of this scheme is a theorem of the classical set theory ZF. In the constructive set theory CZF^–, when the axiom scheme is combined with the axiom of Dependent Choices (DC), the result is equivalent to the scheme of Relative Dependent Choices (RDC). In contrast to RDC, the scheme RRS is preserved in Heyting‐valued models of CZF^– using set‐generated frames. We give an application of the scheme to coinductive definitions of classes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The dispersion of the Hammersley Sequence in the unit square

The notion of dispersion, a measure of denseness of sequences, plays an important role in quasi-Monte Carlo optimization. In this paper, we obtain an explicit formula for the dispersion of an important low dispersion sequence, namely the Hammersley Sequence in the unit square. The dispersiond _M of theM points of this sequence, whereM=2^N withN a positive integer is given by $$d_M = \frac{{\sqrt {2M - 2\sqrt M + 1} }}{M},if N is even, d_M = \frac{{\sqrt {\left( {5/2} \right)M - \sqrt {8M} + 1} }}{M},if N is odd.$$ .     

Recurrence relations for a Newton-like method in Banach spaces

The convergence of iterative methods for solving nonlinear operator equations in Banach spaces is established from the convergence of majorizing sequences. An alternative approach is developed to establish this convergence by using recurrence relations. For example, the recurrence relations are used in establishing the convergence of Newton's method [L.B. Rall, Computational Solution of Nonlinear Operator Equations, Robert E. Krieger, New York, 1979] and the third order methods such as Halley's, Chebyshev's and super Halley's [V. Candela, A. Marquina, Recurrence relations for rational cubic methods I: the Halley method, Computing 44 (1990) 169–184; V. Candela, A. Marquina, Recurrence relations for rational cubic methods II: the Halley method, Computing 45 (1990) 355–367; J.A. Ezquerro, M.A. Hernández, Recurrence relations for Chebyshev-type methods, Appl. Math. Optim. 41 (2000) 227–236; J.M. Gutiérrez, M.A. Hernández, Third-order iterative methods for operators with bounded second derivative, J. Comput. Appl. Math. 82 (1997) 171–183; J.M. Gutiérrez, M.A. Hernández, Recurrence relations for the Super–Halley method, Comput. Math. Appl. 7(36) (1998) 1–8; M.A. Hernández, Chebyshev's approximation algorithms and applications, Comput. Math. Appl. 41 (2001) 433–445 [10]].     

Asymptotic distributions in the testing and estimation of the missing-data multivariate normal linear patterned mean and correlation matrix

Techniques used by Szatrowski (1979, 1983) to solve the testing and estimation problem for linear patterned covariance are used to obtain results for the linear patterned correlation problem in the presence of missing data. Iterative algorithms are given for finding the maximum-likelihood estimates (MLE). Asymptotic distributions of the MLE and likelihood-ratio statistics (LRS) are obtained using the delta method.