Numerical Computation of Parametric Induced Roll Motions in Random Seas

For a vessel in open seas, the sudden appearance of roll motions due to waves from the front or rear leads to dangerous situations up to capsizing. The equations of motion used to analyze the roll motion include the righting lever curve. This curve is set up by means of hydrostatic calculations and approximated by polynomials for further analysis. The irregular waves are modeled in terms of a continuous-time ARMA process. The resulting model of stochastic differential equations is investigated numerically by Local Statistical Linearization. The necessary stochastic moments and their derivatives are computed using Itô's differential rule and Gaussian closure. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On moments of ratios of quadratic forms in normal variables

Exact expressions for moments of ratios of quadratic forms in normal variables are considered. The emphasis is on their relationship with inverse moments of such quadratic forms. Multivariate extension of work of Cressie and Borkent (1986) is briefly explored.     

Recognizing one-DOF industrial tools using invariant moments

In this paper, a simple but efficient approach is proposed to recognize one-DOF industrial tools. Since the shape is changed with the variation of the jaw angles and a feature vectorobtained by conventional approach is not unique, we use the invariant moments and the ratio of area to perimeter squared of a boundary image to construct the required feature vector for object recognition. Two statistical classifiers based on the nearest-neighbor rule and the minimum-mean-distance rule are then utilized to pattern recognition. Experimental results show the good performance of this method in the noisy environment, as well as noise-free environment are also included.     

On the Distributions of the State Sizes of Discrete Time Homogeneous Markov Systems

The evolution of a closed discrete-time homogeneous Markov system (HMS) is determined by the evolution of its state sizes in time. In order to examine the variability of the state sizes, their moments are evaluated for any time point, and recursive formulae for their computation are derived. As a consequence the asymptotic values of the moments for a convergent HMS can be evaluated. The respective recursive formula for a HMS with periodic transition matrix is given. The p.d.f.’s of the state sizes follow directly by means of the moments. The theoretical results are illustrated by a numerical example. This research was partially supported by the State Scholarships Foundation of Greece.     

Introducing Undergraduates to the Spirit of OR whilst Imparting Substantive Skills

This paper presents analytical expressions for the moments of job flow time in a job shop by computing the moments of a random number of random variables assuming that the job shop satisfies the sufficient conditions of the Jackson decomposition principle. The mathematical equivalence of the proposed method to the Laplace transform method is shown and then demonstrated in a simple example. Then, expressions for the moments of job flow time in more realistic (and more complex) job shop settings are derived by computing the moments of a random number of random variables, provided that expressions for the moments of job flow time are available for the corresponding single stage shop. It is shown that the analytical expressions developed are exact as long as the assumptions of the Jackson decomposition principle hold. Any violation of these assumptions makes the derived expressions approximations, and their accuracy should be tested by simulation.     

A distribution function whose moments are close to those of a normal law

The distance in the uniform metric between two distribution functions one of which is normal is considered in terms of the distances between their corresponding moments (in some order). This result is applied to bounds on the distance in the uniform metric of two distribution functions, the moments of whose convolutions are close to the corresponding moments (in some order) of a normal law, from the set of all normal distribution functions. Three references are given.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 627–633, December, 1967.     

An investigation of phase-distribution moment-matching algorithms for use in queueing models

Algorithms for matching moments to phase-type distributions are evaluated on the basis of their performance in their intended application, queueing models. The moment-matching algorithms under consideration match two moments to a hyperexponential distribution with balanced means and three moments to a mixture of two Erlang distributions of common order. These algorithms are used to approximate an interarrival-time distribution for a queueing model, and the accuracy of associated performance-measure approximations is then used to evaluate the moment-matching algorithms. Three performance measures are considered, and attention is focussed on the steady-state mean queue length (number in system) of theGI/M/1 queue. Performance-measure approximations are compared to three-moment bounds and performance-measure values arising from hypothetical approximated distributions.     

Moments from cumulants and vice versa

Moments and cumulants are expressed in terms of each other using Bell polynomials. Inbuilt routines for the latter make these expressions amenable to use by algebraic manipulation programs. One of the four formulas given is an explicit version of Kendall's use of Faa di Bruno's chain rule to express cumulants in terms of moments.     

具有函数纵向尺度因子的分形插值函数的分析特性

研究一类具有函数纵向尺度因子的分形插值函数的光滑性、稳定性和敏感性等分析特性.给出了这类分形插值函数的光滑性结果,证明了它们的稳定性.同时,考虑这类分形插值函数及其矩量的敏感性问题,证明了当生成这类分形插值函数的迭代函数系有小的扰动时,相应的分形插值函数及其矩量也有小的扰动,给出了相应扰动误差的上估计.     

Paramagnetic Meissner effect of highT c superconductors II

A range of powdered Bi:2 212 samples exhibiting the paramagnetic Meissner effect (PME) are systematically examined. Interpretation of the results is made in terms of a phenomenological model in which there is a concentration within the material of small local moments that can be polarized during a field cooling. Information about the magnitudes of these local m0oments and their distribution are deduced. Relations between the local moments and the particle sizes, the weak link, oxygen content and the interactions between the local moments are also discussed. Comparison of the results from small particles and bulk samples shows that conclusions obtained from small particle experiments are reliable and universal.     

Regular multigraphs and their application to the Monte Carlo evaluation of moments of non-linear functions of Gaussian random variables

This paper expands on the multigraph method for expressing moments of non-linear functions of Gaussian random variables. In particular, it includes a list of regular multigraphs that is needed for the computation of some of these moments. The multigraph method is then used to evaluate numerically the moments of non-Gaussian self-similar processes. These self-similar processes are of interest in various applications and the numerical value of their marginal moments yield qualitative information about the behavior of the probability tails of their marginal distributions.     

On a simple discrete cyclic-waiting queueing problem

On the basis of a real problem connected with the landing of airplanes, the paper investigates a queueing system with geometrically distributed interarrival and service times in which the service of a request may be started upon arrival (in the case of a free system) or (in the case of a busy server, a queue, or noncorresponding position of the request) at moments differing from it by multiples of the cycle time. For the service discipline the FIFO rule is assumed. Using the embedded-Markov-chain technique (considering the system at moments just before starting the service of a request), the generating function of ergodic probabilities is found and the condition of existence of an ergodic distribution is established. Supported by the Hungarian National Foundation for Scientific Research (grant No. OTKA 14794/95). Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part II.     

模式识别技术在机械设备故障诊断中的应用

本文从统计意义上分析了机械设备在不同运行状态下振动信号的特征;选择信号幅值的概率分布的前n阶矩作为特征向量来进行状态信息凝聚.在此,将设备的状态分为“完好”和“故障”两种,应用模式识别技术进行状态分类.最后通过对试验数据的分析,证实了特征参数的稳定性和对故障的敏感性.结果表明,分类判据是有效的.     

An efficient computational method for moments of order statistics under progressive censoring

Thomas and Wilson (Technometrics 14 (1972) 679) developed a computational method for calculating the single and product moments of order statistics from progressively censored samples by making use of the corresponding moments of the usual order statistics. The absence of an explicit representation for the marginal and joint density function of order statistics under progressive censoring makes their method extremely tedious. By deriving the required marginal and joint density functions in explicit form, we obtain an alternative, highly efficient, method for computing the desired moments.     

On the restricted Chebyshev–Boubaker polynomials

Using the language of Riordan arrays, we study a one-parameter family of orthogonal polynomials that we call the restricted Chebyshev–Boubaker polynomials. We characterize these polynomials in terms of the three term recurrences that they satisfy, and we study certain central sequences defined by their coefficient arrays. We give an integral representation for their moments, and we show that the Hankel transforms of these moments have a simple form. We show that the (sequence) Hankel transform of the row sums of the corresponding moment matrix is defined by a family of polynomials closely related to the Chebyshev polynomials of the second kind, and that these row sums are in fact the moments of another family of orthogonal polynomials.     

The possibilistic moments of fuzzy numbers and their applications

This paper, introduces the nearest weighted interval and point approximations of a fuzzy number, and then suggests weighted possibilistic moments about these points of fuzzy numbers. The possibilistic moments play an important role in fuzzy sets and systems, specifically in physics, mathematics and statistics. We provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory; some of their applications are mentioned.     

The rate of convergence to optimality of the LPT rule

The LPT rule is a heuristic method to distribute jobs among identical machines so as to minimize the makespan of the resulting schedule. If the processing times of the jobs are assumed to be independent identically distributed random variables, then (under a mild condition on the distribution) the absolute error of this heuristic is known to converge to 0 almost surely. In this note we analyse the asymptotic behaviour of the absolute error and its first and higher moments to show that under quite general assumptions the speed of convergence is proportional to appropriate powers of (log log n)/n and 1/n. Thus, we simplify, strengthen and extend earlier results obtained for the uniform and exponential distribution.     

Moment Formulas for Multitype Continuous State and Continuous Time Branching Process with Immigration

Recursions for moments of multitype continuous state and continuous time branching process with immigration are derived. It turns out that the \(k\)th (mixed) moments and the \(k\)th (mixed) central moments are polynomials of the initial value of the process, and their degree is at most \(k\) and \(\lfloor k/2 \rfloor \), respectively.     

On the Moments of Overflow and Freed Carried Traffic for the GI/M/C/0 System

In circuit-switched networks call streams are characterized by their mean and peakedness (two-moment method). The GI/M/C/0 system is used to model a single link, where the GI-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a GI/M/C/0 system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d. holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used. The main result of this paper is a numerically stable and efficient algorithm for computing the moments of freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived.     

The disteribution of a moment estimator for a parameter of the generalized poision distribution

The ratio of the sample variance to the sample mean estimates a simple function of the parameter which measures the departure of the Poisson-Poisson from the Poisson distribution. Moment series to order n²⁴ are given for related estimators. In one case, exact integral formulations are given for the first two moments, enabling a comparison to be made between their asymptotic developments and a computer-oriented extended Taylor series (COETS) algorithm. The integral approach using generating functions is sketched out for the third and fourth moments. Levin's summation algorithm is used on the divergent series and comparative simulation assessments are given.