Nowhere-Zero 4-Flows,Simultaneous Edge-Colorings,And Critical Partial Latin Squares

It is proved in this paper that every bipartite graphic sequence with the minimum degree 2 has a realization that admits a nowhere-zero 4-flow. This result implies a conjecture originally proposed by Keedwell (1993) and reproposed by Cameron (1999) about simultaneous edge-colorings and critical partial Latin squares.* Partially supported by RGC grant HKU7054/03P. Partially supported by the National Security Agency under Grants MDA904-00-1-00614 and MDA904-01-1-0022.     

Quasi sure version of a theorem of littlewood

Let (c _n) _nZ be a double-sided sequence of complex numbers; if, for quasi-all (i.e. in the Baire sense) choices of signs ( _n) _nZ , ( _n c _n) _nZ is a Fourier-Stieltjes sequence, then we prove that (c _n) _nZ l ² (Z); this extends a result of Littlewood and at the same time provides a very simple proof of this result.     

The limiting behaviour of the last exit time for sequences of independent,identically distributed random variables

Summary Let {X _k , k0} be i.i.d. random variables with EX ⁺< and define t =max{k0: X _k > k} if such a k exists and =0 else, the last exit time of the sequence X _k for fixed >0. We discuss weak limit laws for t as 0; in particular the limit distributions, the stability and the relative stability.This work is partially supported by a grant of the Schweizerischer Nationalfonds zur Förderung der wissenschaftlichen Forschung, while the author was at the University of Pittsburgh, USAHerrn Prof. L. Schmetterer zu seinem 60. Geburtstag gewidmet     

Peculiarities of relativistic particle evolution in classical scalar field theory

The interaction of particles in the model of a scalar field linearly coupled with the source is demonstrated to have the following peculiarities. First, the particles are attracted to one another at large interparticle distances and are repelled at small. Second, in the process of evolution of the system of particles, its components gain the maximum possible velocity, the velocity of light. Third, after the head-on collision of two identical particles, the pumping effect may probably arise. This effect consists of the fact that after experiencing a few oscillations between the walls of a squeezing potential well, the particles fly out of the finite motion region to the region of infinite motion. Fourth, on the trajectory of the interacting particles, a plateau region of motion with a high and relatively constant velocity appears.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 464–473, December, 1996.     

Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

Reiter’s Condition <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript> and Approximate Identities for Polynomial Hypergroups

Let K be a commutative hypergroup with the Haar measure . In the present paper we investigate whether the maximal ideals in L¹(K,) have bounded approximate identities. We will show that the existence of a bounded approximate identity is equivalent to the existence of certain functionals on the space L(K,). Finally we apply the results to polynomial hypergroups and obtain a rather complete solution for this class.The third author was partially supported by KBN (Poland) under grant 5 P03A 034 20 and by Research Training Network Harmonic Analysis and Related Problems Contract HPRN-CT-2001-00273.     

Posterior Sensitivity to the Sampling Distribution and the Prior: More than One Observation

Sensitivity of a posterior quantity (f, P) to the choice of the sampling distribution f and prior P is considered. Sensitivity is measured by the range of (f, P) when f and P vary in nonparametric classes ^f and ^P respectively. Direct and iterative methods are described which obtain the range of (f, P) over f ^f when prior P is fixed, and also the overall range over f ^f and P ^P . When multiple i.i.d. observations X ₁,...,X _k are observed from f, the posterior quantity (f, P) is not a ratio-linear function of f. A method of steepest descent is proposed to obtain the range of (f, P). Several examples illustrate applications of these methods.     

On the number of non conjugate subgroups

We shall prove that every group of cardinality ₁ has at least ₁ non conjugate subgroups, and we shall generalize this theorem to many more uncountable cardinalities. For example underGCH for every uncountable cardinal and every groupG of cardinality ,G has at least non conjugate subgroups.Presented by W. Taylor.I would like to thank Rami Grossberg for writing and rewriting this paper, and Wilfrid Hodges for removing many errors and suggesting improvements in presentation; many facts are proved only due to his explicit request.This research was supported by grant (No. 1110) from the United States-Israel Binational Science Foundation.     

On the Number of Subgraphs of a Specified Form Embedded in a Random Graph

Let U ₁, U ₂,... be a sequence of i.i.d. random elements in R^d. For x>0, a graph G _n (x) may be formed by connecting with an edge each pair of points in that are separated by a distance no greater than x. The points of G _n (x) could represent the stations in a telecommunications network and the edge set the lines of communication that exist among them. Let be a collection of graphs on mn points having a specified form or structure, and let denote the number of subgraphs embedded in G _n (x) and contained in . It is shown that a SLLN, CLT and LIL for follow easily from the theory of U-statistics. In addition, a uniform (in x) SLLN is proved for collections that satisfy a certain monotonicity condition. Some applications are mentioned and the results of some simulations presented. The scaling constants appearing in the CLT are usually hard to obtain. These are worked out for some special cases.     

Zero-One Law for Symmetric Convolution Semigroups of Measures on Groups

Let ( _t ) _t>0 be a symmetric weakly continuous semigroup of probability measures on a nonabelien complete separable group G and let v be its Lévy measure. The purpose of this paper is to provide a relatively simple proof of the zero-one law for semigroups with the Lévy measure satisfying either v(H ^c) = or v(H ^c) = 0.     

Assessment of approximate algorithms: The error measure's crucial role

Initially, the distinction between exact and approximate algorithms is accounted for. We then consider a broad class of decision problems including the so-called account location ork-plant location problem (kPLP), and show that the choice of an appropriate reference value is critical; even an apparent plausible choice may lead to disputable conclusions.A family of data instances forkPLP is presented for which the relative duality gap approaches one. Consequently, for this class of optimization problems, no error measure on the upper bound should permit a characterization of the strong linear programming relaxation as good.     

基于Jeffreys验前的Bayes方差估计修正

分析了基于Jeffreys验前的经典Bayes方差估计以及考虑验前信息可信度情况下Bayes方差估计存在的问题,在一般情况下,其方差估计要大于验前子样和验后子样的方差,这显然是不合理的.这是采用Jeffreys验前和正态共轭分布假设时存在的固有问题.为了解决这一问题,提出了方差估计的修正公式,经过计算验证,其值在验前子样和验后子样方差之间,说明修正公式是合理的.     

A counter-example to the boundary regularity of solutions to elliptic quasilinear systems

It is shown that solutions to the Dirichlet problem for quasilinear elliptic systems in a domain ofR ⁿ n3 with smooth boundary datum can be singular at the boundary.     

An approximation theorem for second-order evolution equations

Summary A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos for 0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.Research supported by ONR grant N00014-57-A-0298-0015Research supported by USARO grant DAAG 29-278-C-0024     

Error estimates for the finite element solution of variational inequalities

Summary We study the mixed finite element approximation of variational inequalities, taking as model problems the so called obstacle problem and unilateral problem. Optimal error bounds are obtained in both cases.Supported in part by National Science Foundation grant MCS 75-09457, and by Office of Naval Research grant N00014-76-C-0369     

Asymptotic analysis of the exponential penalty trajectory in linear programming

We consider the linear program min{cx: Axb} and the associated exponential penalty functionf _r(x) = cx + rexp[(A _ix – b_i)/r]. Forr close to 0, the unconstrained minimizerx(r) off _r admits an asymptotic expansion of the formx(r) = x ^* + rd^* + (r) wherex ^* is a particular optimal solution of the linear program and the error term(r) has an exponentially fast decay. Using duality theory we exhibit an associated dual trajectory(r) which converges exponentially fast to a particular dual optimal solution. These results are completed by an asymptotic analysis whenr tends to : the primal trajectory has an asymptotic ray and the dual trajectory converges to an interior dual feasible solution.Corresponding author. Both authors partially supported by FONDECYT.     

On Hankel Transform and Hankel Convolution of Beurling Type Distributions Having Upper Bounded Support

In this paper we study Beurling type distributions in the Hankel setting. We consider the space of Beurling type distributions on (0, ) having upper bounded support. The Hankel transform and the Hankel convolution are studied on the space . We also establish Paley Wiener type theorems for Hankel transformations of distributions in .     

Entropy maximisation and queueing network models

Over recent years it has become increasingly evident that classical queueing theory cannot easily handle complex queueing systems and networks with many interacting elements. As a consequence, alternative ideas and tools, analogous to those applied in the field of Statistical Mechanics, have been proposed in the literature. In this context, the principles of Maximum Entropy (ME) and Minimum Relative Entropy (MRE), a generalisation, provide consistent methods of inference for characterising the form of an unknown but true probability distribution, based on information expressed in terms of known to exist true expected values or when, in addition, there exists a prior estimate of the unknown distribution. This paper traces the progress achieved so far towards the creation of ME and MRE product-form approximations and related algorithms for the performance analysis of general Queueing Network Models (QNMs) and indicates potential research extensions in the area.Earlier research on entropy maximisation and QNMs was sponsored by the UK Science and Engineering Research Council (SERC) with grant GR/D/12422, while recent and current work is supported by SERC grants GR/F/29271 and GR/H/18609. Research on Complex I/O subsystems was funded by Metron Technology Ltd., UK, under grant JJCA415.     

On a transformation operator for a system of Sturm-Liouville equations

We prove the existence of a transformation operator with a condition at infinity that sends a solution of the matrix equation^–y + My=²y (M is a constant Hermitian matrix) into a solution of the matrix equation^–y+Q(x)y+My=²y (the matrix function Q(x) is continuously differentiable for 0 x< and it is Hermitian for each x belonging to [0, )); we study some properties of the kernel of the transformation operator.Translated from Matematicheskii Zametki, Vol. 11, No. 5, pp. 559–567, May, 1972.The authors express their thanks to B. M. Levitan for a discussion.     

A bayesian approach to nonparametric test problems

We propose an alternative approach to the classical nonparametric test problems, such as the goodness of fit test and the two-sample nonparametric test. In this approach, those problems are reviewed from the viewpoint of the estimation of the underlying population distributions and are formulated as the problem of model selection between Bayesian models which were recently proposed by the present authors. The model selection can be easily realized by choosing a model with the smallest ABIC, Akaike Bayesian information criterion. The approach provides the estimates of the density of the underlying population distribution(s) of any shape as well as the evaluation of the goodness of fit or the check of homogeneity of distributions. The practical utility of the present procedure is demonstrated by numerical examples. The difference in behavior between the present procedure and a density estimator GALTHY proposed by Akaike and Arahata is also briefly discussed.This paper was originally read at the Conference on Graphical Models to Analyze Structures (Organizer: N. Wermuth, Johannes Gutenberg University), June 30-July 2, 1986, Wiesbaden, West Germany.