An adaptation of a root finding method to searching ordered disk files

Three methods for locating a record in an ordered file are considered. The keys in the files are chosen from three different statistical distributions and the methods, two of which are taken from the literature and an adapted root finding method, are compared by tabulating information relating to standard statistics for the number of probes.     

Benefits of co-operation in a production distribution environment

We model co-operation in a typical production distribution setting that contains one capacitated supplier producing and distributing a single product to many identical retailers who are facing i.i.d. end-item demands from the consumers. We consider three inventory allocation mechanisms, representing varying degrees of co-operation, at the supplier: (1) the orders from the retailers are filled in a predetermined sequence; (2) the orders from the retailers are filled after taking into account their current inventories; and (3) the orders from the retailers are filled assuming that the product can also be shipped from one retailer to another. We estimate the benefits due to co-operation in this supply chain and study the effect of various system parameters on these benefits. An extensive computational study indicated that the benefits of co-operation in this production distribution environment decrease with increase in the supplier capacity, increase in the number of retailers, decrease in penalty cost, and decrease in consumer demand variance.     

On the Distribution of Random Samples from Finite Populations of Random Variables

This article deals with probability distributions of sums of simple random sample and Bernoulli sample when samples are selected from finite population of independent random variables. Random variables are quasi-lattice. Probability distributions from class ? and Poisson distribution are used for approximation. Analogue of Cornish-Fisher transformation is obtained in case of limit distributions from class ?.     

An inventory control model with stochastic review interval and special sale offer

Periodic review inventory models are widely used in practice, especially for inventory systems in which many different items are purchased from the same supplier. However, most of periodic review models have assumed a fixed length of the review periods. In practice, it is possible that the review periods are of a random (stochastic) length. This paper presents an inventory control model in the case of random review intervals and special sale offer from the supplier. The replenishment interval is assumed to obey from two different distributions, namely, exponential and uniform distributions. Also, shortages are allowed in the term of partial backordering. For this model, its convexity condition is discussed and closed form solutions are proposed.     

Symbolic evaluation of coefficients in Airy-type asymptotic expansions

Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from integration by parts. An application is given for the Weber parabolic cylinder function.     

Mixtures of Global and Local Edgeworth Expansions and Their Applications

Edgeworth expansions which are local in one coordinate and global in the rest of the coordinates are obtained for sums of independent but not identically distributed random vectors. Expansions for conditional probabilities are deduced from these. Both lattice and continuous conditioning variables are considered. The results are then applied to derive Edgeworth expansions for bootstrap distributions, for Bayesian bootstrap distribution, and for the distributions of statistics based on samples from finite populations. This results in a unified theory of Edgeworth expansions for resampling procedures. The Bayesian bootstrap is shown to be second order correct for smooth positive “priors,” whenever the third cumulant of the “prior” is equal to the third power of its standard deviation. Similar results are established for weighted bootstrap when the weights are constructed from random variables with a lattice distribution.     

Parallel assimilation of observed data in the hydrodynamic model of the ocean circulation

The parallel use of the Kalman ensemble filter technique for assimilating data from observations in theHYCOMmodel of theWorldOcean is described. Data from satellite observations of the sea’s surface temperature and the sea’s surface height are assimilated both separately and conjointly. Numerical experiments on correcting model calculations using data from observations are performed. The results from the corrections are compared to model calculations without assimilation. The effectiveness of the employed parallelization algorithm is confirmed.     

On the strength of Gomory mixed-integer cuts as group cuts

Gomory mixed-integer (GMI) cuts generated from optimal simplex tableaus are known to be useful in solving mixed-integer programs. Further, it is well-known that GMI cuts can be derived from facets of Gomory’s master cyclic group polyhedron and its mixed-integer extension studied by Gomory and Johnson. In this paper we examine why cutting planes derived from other facets of master cyclic group polyhedra (group cuts) do not seem to be as useful when used in conjunction with GMI cuts. For many practical problem instances, we numerically show that once GMI cuts from different rows of the optimal simplex tableau are added to the formulation, all other group cuts from the same tableau rows are satisfied.     

Simulating Multivariate Extreme Value Distributions of Logistic Type

Methods are given for simulating from symmetric and asymmetric versions of the multivariate logistic distribution, and from other multivariate extreme value distributions based on the well known logistic model. We consider two general approaches. The first approach uses transformations to derive random variables with a joint distribution function from which it is easy to simulate. The second approach derives from a specification of conditionally independent marginal components, conditioning on positive stable random variables. This specification extends to models of nested or hierarchical type and leads to an efficient way of incorporating marginal censoring. The algorithms presented in Sections 2 and 3 are available on request from the author. They are also included in the R (Ihaka and Gentleman, 1996) package evd (Stephenson, 2002), which is available from http://www.maths.lancs.ac.uk/~stephena/.     

Homogeneous and rank bases in spaces of metric configurations

Two families of sets of metric configurations are considered. The conditions are established under which sets from these families are bases for a special linear vector space. It is shown that the transition from the representation of a metric configuration in the trivial basis to its representation in any of the considered bases and back can be effectively calculated. It is shown that the nonnegativity of the decomposition of a metric configuration in the considered bases is a sufficient condition for the semi-metric axioms to hold for this configuration, while the nonnegativity of the decomposition in a rank basis is a necessary and sufficient condition for the metric configuration to have a given rank. The transition coefficients and decomposition components are interpreted in the case of homogeneous bases. Sets from the considered families are indicated that characterize largest-volume cones of metric configurations.     

An assessment of two approaches to variable metric methods

Two recent suggestions in the field of variable metric methods for function minimization are reviewed: the self-scaling method, first introduced by Oren and Luenberger, and the method of Biggs. The two proposals are considered both from a theoretical and computational aspect. They are compared with methods which use correction formulae from the Broyden one-parameter family, in particular the BFGS formula and the Fletcher switching strategy.     

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

A new method is presented for Fourier decomposition of the Helmholtz Green function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Green function are split into their half advanced + half retarded and half advanced–half retarded components, and closed form solutions for these components are then obtained in terms of a Horn function and a Kampé de Fériet function respectively. Series solutions for the Fourier coefficients are given in terms of associated Legendre functions, Bessel and Hankel functions and a hypergeometric function. These series are derived either from the closed form 2-dimensional hypergeometric solutions or from an integral representation, or from both. A simple closed form far-field solution for the general Fourier coefficient is derived from the Hankel series. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented. Fourth order ordinary differential equations for the Fourier coefficients are also given and discussed briefly.     

ON AVOIDANCE ACTIVITIES IN FISHERY ENFORCEMENT MODELS

Compliance and enforcement in fisheries are important issues from an economic point of view since management measures are useless without a certain level of enforcement. These conclusions come from the well‐established theoretical literature on compliance and enforcement problems within fisheries and a common result is that, it is efficient to set fines as high as possible and monitoring as low as possible, when fines are costless and offenders are risk neutral. However, this result is sensitive to the assumption that fishermen cannot engage in avoidance activities, e.g., activities to reduce the likelihood of being detected when noncomplying. The paper presents a model of fisheries that allows the fishermen to engage in avoidance activities. The conclusions from the model are that, under certain circumstances, fines are costly transfers to society since they not only have a direct positive effect on the level of deterrence, but also an indirect negative effect in the form of increased avoidance activities to reduce the probability of detection. The paper contributes to the literature on avoidance activities by introducing the externality from the illegal behavior as an endogenous effect on other offenders. For an externality, that has an exogenous effect on other actors, Malik shows that fines are only costly transfers for conditional deterrence (when one actor is deterred while another actor is not). For fisheries, we show that fines are also costly transfers under no deterrence (when no agents are deterred).     

Frechet-valued martingales and stochastic integrals

Stochastic processes with values in a separable Frechet space whose a itinuous linear functional are real-valued square integrable martingales are investigated. The coordinate measures on the Fréchet space are obtained from cylinder set measures on a Hilbert space that is dense in the Fréchet space. Real-valued stochastic integrals are defined from the Fréchet-valued martingales using integrands from the topological dual of the aforementioned Hilbert space. An increasing process with values in the self adjoint operators on the Hilbert space plays a fundamental role in the definition of stochastic integrals. For Banach-valued Brownian motion the change of variables formula of K. Itô is generalized. A converse to the construction of the measures on the Fréchet space from cylinder set measures on a Hilbert space is also obtained.     

A new heuristic for learning Bayesian networks from limited datasets: a real-time recommendation system application with RFID systems in grocery stores

Bayesian networks (BNs) are a useful tool for applications where dynamic decision-making is involved. However, it is not easy to learn the structure and conditional probability tables of BNs from small datasets. There are many algorithms and heuristics for learning BNs from sparse datasets, but most of these are not concerned with the quality of the learned network in the context of a specific application. In this research, we develop a new heuristic on how to build BNs from sparse datasets in the context of its performance in a real-time recommendation system. This new heuristic is demonstrated using a market basket dataset and a real-time recommendation model where all items in the grocery store are RFID tagged and the carts are equipped with an RFID scanner. With this recommendation model, retailers are able to do real-time recommendations to customers based on the products placed in cart during a shopping event.     

Singularity among selfsimilar Gaussian random fields with different scaling parameters and others

Abstract

It is shown in this paper that the probability measures generated by selfsimilar Gaussian random fields are mutually singular, whenever they have different scaling parameters. So are those generated from a selfsimilar Gaussian random field and a stationary Gaussian random field. Certain conditions are also given for the singularity of the probability measures generated from two Gaussian random fields whose covariance functions are Schoenberg–Lévy kernels, and for those from stationary Gaussian random fields with spectral densities.     

CONSTRUCTION OF SOLUTIONS TO M-D RIEMANN PROBLEMS FOR A2×2 QUASILINEAR HYPERBOLIC SYSTEM

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CONSTRUCTION OF SOLUTIONS TO M-D RIEMANN PROBLEMS FOR A 2*2 QUASILINEAR HYPERBOLIC SYSTEM

The author studies M-D Riemann problems for a quasilinear nonstrictly byperbolic system.The initial date are taken as three different constants in three sections divided by three rays starting from the origin.From each direction of these rays two waves coming from infinity are allowed.All possible local singularity structures are carefully studied and classified.Then based on such analysis,existence and global singularity structure of the solution are obtained under some assumptions.     

Authentication codes and bipartite graphs

In this paper, a characterization of authentication codes in terms of bipartite graphs is given. By using such a characterization, two necessary and sufficient conditions for a minimal authentication code with perfect secrecy are derived. The probabilities of a successful impersonation and of a successful substitution attack are discussed. As a result, some (optimal) minimal authentication codes with perfect secrecy are constructed from association schemes, from finite groups or from known authentication codes no matter whether the known ones are with or without secrecy.     

重建极性连续统理论的基本定律和原理(Ⅳ)——表面守恒定律

从普遍均衡定律的平移和转动的不变性出发来重新建立较为完整的微极热力连续统的表面守恒定律,提出了广义的能量动量和能量动量矩张量.给出了Piola型、Cauchy型和Kirchhoff型微极热力连续统的表面守恒定律的具体形式.现有的结果都可以当做是特殊情形从该结果自然地推导出来,并可从归结过程中清楚地看出现有理论的不完整性程度.非局部微极热力连续统的表面守恒定律可通过局部化得到.