Rates of Convergence and Law of the Iterated Logarithm for U-Processes

We study in this paper some limit theorems for U-processes. We calculate rates of convergence in the central limit theorem of nondegenerate U-processes under metric entropy with bracketing condition. In application, we improve upon the law of the iterated logarithm of Arcones. All calculations use the Ossiander chaining procedure.     

Convergence rates for two-stage confidence intervals based on U-statistics

We consider a modified two-stage procedure for constructing a fixed-width confidence interval for the mean of a U-statistic. First, we discuss a few asymptotic results with the associated rates of convergence. The main result gives the rate of convergence for the coverage probability of our proposed confidence interval which is seen to be slower than that for the purely sequential procedure.     

A Classification of Regular p-Groups with Invariants (e, 2, 1)

The class of the regular p-groups is one of the important classes in p-groups. Not only it has many similar properties as abelian p-groups, but also many of the p-groups belong to this class. In this paper, using the algorithms for determining the isomorphic regular p-groups, we give a complete classification of the regular p-groups with e-invariants (e, 2, 1).Supported by SXYSF 991003.     

A methodology for supporting strategy implementation based on the VSM: A case study in a Latin-American multi-national

Soft OR tools have increasingly been used to support the strategic development of companies at operational and managerial levels. However, we still lack OR applications that can be useful in dealing with the “implementation gap”, understood as the scarcity of resources available to organizations seeking to align their existing processes and structures with a new strategy. In this paper we contribute to filling that gap, describing an action research case study where we supported strategy implementation in a Latin American multinational corporation through a soft OR methodology. We enhanced the ‘Methodology to support organizational self-transformation’, inspired by the Viable System Model, with substantive improvements in data collection and analyses. Those adjustments became necessary to facilitate second order learning and agreements on required structural changes among a large number of participants. This case study contributes to the soft OR and strategy literature with insights about the promise and constraints of this soft OR methodology to collectively structure complex decisions that support organizational redesign and strategy implementation.     

A Limit Result for U-Statistics of Binary Variables

Define , where is a symmetric U-type statistic, H _k() is the Hermite polynomial of degree k, and {X, X _n, n1} are independent identically distributed binary random variables with Pr(X{–1, 1}})=1. We show that according as EX=0 or EX0, respectively.     

A new method for constructing infinite families of k-tight optimal double loop networks

The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. DLN has been widely used in the designing of local area networks and distributed systems. In this paper, a new method for constructing infinite families of k-tight optimal DLN is presented. For k = 0, 1, ..., 40, the infinite families of k-tight optimal DLN can be constructed by the new method, where the number n _k (t, a) of their nodes is a polynomial of degree 2 in t and contains a parameter a. And a conjecture is proposed.     

A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number

With respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, and the attribute weight is unknown, a new decision making analysis methods are developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced. Then information entropy method is used to determine the attribute weight, and the grey relational projection method combined grey relational analysis method and projection method is proposed, and to rank the alternatives are done by the relative closeness to PIS which combines grey relational projection values from the positive ideal solution and negative ideal solution to each alternative. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

A Note on Edgeworth Expansions for <Emphasis Type="Italic">U</Emphasis>-Statistics under Minimal Conditions

A one-term Edgeworth expansion for U-statistics with kernel h(x, y) was derived by Jing and Wang [3] under optimal moment conditions. In this note, we show that one of the optimal moment conditions E| h(X ₁, X ₂|^5/3 < ∞ can be weakened to lim _t→∞ t ^5/3 P(|h(X ₁, X ₂)| > t) → 0. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 453–440, July–September, 2005.     

A value iteration method for undiscounted multichain Markov decision processes

This paper proposes a value iteration method which finds an-optimal policy of an undiscounted multichain Markov decision process in a finite number of iterations. The undiscounted multichain Markov decision process is reduced to an aggregated Markov decision process, which utilizes maximal gains of undiscounted Markov decision sub-processes and is formulated as an optimal stopping problem. As a preliminary, sufficient conditions are presented under which a policy is-optimal.

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Zusammenfassung In dieser Arbeit wird eine Wertiterationsmethode vorgeschlagen, die eine-optimale Politik für einen undiskontierten nicht-irreduziblen Markovschen Entscheidungsprozeß (MEP) in endlichen vielen Schritten liefert. Der undiskontierte nicht-irreduzible MEP wird auf einen aggregierten MEP reduziert, der maximale Gewinn eines undiskontierten Sub-MEP verwendet und als optimales Stopp-Problem formuliert wird. Zu Beginn werden hinreichende Bedingungen für die-Optimalität einer Politik angegeben.

     

Asymptotically optimal sequential estimation of regular functionals of several distributions based on generalized U-statistics

For the several sample problem, a vector of estimable parameters is considered. For a fixed total sample size, a multistage (sequential) procedure based on generalized U-statistics is developed for choosing a partition of this sample size into individual sample size for which the generalized variance of the estimator of the parameter vector is asymptotically minimized.     

A Minimal-Automaton-Based Algorithm for the Reliability of Con(d,k, n) Systems

A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's algorithm published in 1997, where . In this paper we use automata theory to reduce to . For d small or close to k, we have reduced from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is , where .     

Algorithms for the single-source uncapacitated minimum concave-cost network flow problem

We investigate algorithms, applications, and complexity issues for the single-source uncapacitated (SSU) version of the minimum concave-cost network flow problem (MCNFP). We present applications arising from production planning, and prove complexity results for both global and local search. We formally state the local search algorithm of Gallo and Sodini [5], and present alternative local search algorithms. Computational results are provided to compare the various local search algorithms proposed and the effects of initial solution techniques.     

A queueing theoretic methodology for the analysis of separable conflict resolution algorithms with variable length elementary events

We describe a queueing theoretic approach to the delay analysis for the class of synchronous random-access protocols consisting of a Capetanakis-type Tree Algorithm for conflict resolution and a window algorithm for channel access. Our method features a stochastic decomposition, in which a major component of the delay is viewed as a discrete time queueing problem, where each window (selected by the channel access algorithm) becomes a customer requiring service in the form of conflict resolution. This technique is sufficiently powerful to give us the distribution of the packet delay in steady state. In this paper, we extend our method to allow the durations of elementary algorithmic steps to take on a general distribution (rather than being constants), which allows us to provide a unified treatment of channels with shared errors, some types of explicit reservation systems, and Local Area Networks with carrier sensing and/or collision detection, possibly in combination with variable size packets.     

A method for group decision-making based on determining weights of decision makers using TOPSIS

In general, weights of decision makers (DMs) play a very important role in multiple attribute group decision-making (MAGDM), how to measure the weights of DMs is an interesting research topic. This paper presents a new approach for determining weights of DMs in group decision environment based on an extended TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method. We define the positive ideal solution as the average of group decision. The negative ideal solution includes two parts: left and right negative ideal solution, which are the minimum and maximum matrixes of group decision, respectively. We give an example to illustrate the developed approach. Finally, the advantages and disadvantages of this study are also compared.     

New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.     

A polynomial method for the pos/neg weighted 3-median problem on a tree

Let a connected undirected graph G  =  (V, E) be given. In the classical p-median problem we want to find a set X containing p points in G such that the sum of weighted distances from X to all vertices in V is minimized. We consider the semi-obnoxious case where every vertex has either a positive or negative weight. In this case we have two different objective functions: the sum of the minimum weighted distances from X to all vertices and the sum of the weighted minimum distances. In this paper we show that for the case p = 3 an optimal solution for the second model in a tree can be found in O(n ⁵) time. If the 3-median is restricted to vertices or if the tree is a path then the complexity can be reduced to O(n ³). This research has partially been supported by the Spezialforschungsbereich F 003 “Optimierung und Kontrolle”, Projektbereich Diskrete Optimierung.     

A note on the optimality of the N- and D-policies for the M/G/1 queue

This note considers the N- and D-policies for the M/G/1 queue. We concentrate on the true relationship between the optimal N- and D-policies when the cost function is based on the expected number of customers in the system.     

A sufficient condition for self-concordance,with application to some classes of structured convex programming problems

Recently a number of papers were written that present low-complexity interior-point methods for different classes of convex programs. The goal of this article is to show that the logarithmic barrier function associated with these programs is self-concordant. Hence the polynomial complexity results for these convex programs can be derived from the theory of Nesterov and Nemirovsky on self-concordant barrier functions. We also show that the approach can be applied to some other known classes of convex programs.This author's research was supported by a research grant from SHELL.On leave from the Eötvös University, Budapest, Hungary. This author's research was partially supported by OTKA No. 2116.     

Bessel generalized translations and some problems of approximation theory for functions on the half-line

Approximation problems for functions on the half-line [0,+∞) in a weighted L _p -metric are studied with the use of Bessel generalized translation. A direct theorem of Jackson type is proven for the modulus of smoothness of arbitrary order which is constructed on the basis of Bessel generalized translation. Equivalence is stated between the modulus of smoothness and the K-functional constructed by the Sobolev space corresponding to the Bessel differential operator. A particular class of entire functions of exponential type is used for approximation. The problems under consideration are studied mostly by means of Fourier-Bessel harmonic analysis.     

Toward a unified theory for third R-order iterative methods for operators with unbounded second derivative

In this paper, we provide a semilocal convergence analysis for a family of Newton-like methods, which contains the best-known third-order iterative methods for solving a nonlinear equation F(x)=0 in Banach spaces. It is assumed that the operator F is twice Fréchet differentiable and F^″ satisfies a Lipschitz type condition but it is unbounded. By using majorant sequences, we provide sufficient convergence conditions to obtain cubic semilocal convergence. Results on existence and uniqueness of solutions, and error estimates are also given. Finally, a numerical example is provided.