Canonizing ordering theorems for hales Jewett structures

The natural linear orderings of an n-dimensional cube over a finite set A are investigated. We obtain a characterization theorem for these orderings extending earlier result, e.g., for natural orderings on finite Boolean lattices, as given in [5.], 193–197.     

Some partial orderings of exchangeable random variables by positive dependence

Some partial orderings of positively dependent exchangeable random variables are introduced. The interrelations among them, the inequalities which follow from them and two models which yield such partial orderings are then discussed. Particular examples include ordering multivariate normal, t, χ², Cauchy, exponential, binomial, Poisson, gamma and Farlie-Gumbel-Morgenstern random vectors. Applications to genetic selection and choice of sampling procedures are given.     

On Some Analytic Methods for Calculating of Cusped Prismatic Shells

Cusped plates, on the one hand, are very important details from the practical point of view, such plates and beams are often encountered in spatial structures with partly fixed edges, e.g., stadium ceilings, aircraft wings, submarine wings etc., in machine-tool design, as in cutting-machines, planning-machines, in astronautics, turbines, and in many other areas of engineering (e.g., dams); on the other hand, their theoretical analysis and calculation are mathematically connected with the study of the problems for degenerate partial differential equations which are not covered by the general theory for degenerate partial differential equations (see, e.g., [3]). Some satisfactory results are achieved in this direction in the case of Lipschitz domains but in the case of non-Lipschitz domains there are a lot of open problems. To investigate such problems are the main part of the the present paper. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

IDENTIFICATION OF EXTRAPOLATION SPACES FOR UNBOUNDED OPERATORS

Abstract

Abstract extrapolation spaces for strongly continuous semigroups of linear operators on Banach spaces have been constructed by various methods (see, e.g., [Am (1988)], [DaP-Gr (1984)], [Na (1983)], [Ne (1992)], [Wa (1986)]). Usually they appear as “artefacts” used in some intermediate step in order to solve the Cauchy problem on the original space. Only in a few cases (see the papers by the Dutch school on X ^⊙*, e.g., [Ne (1992)]), and in sharp contrast to the situation for interpolation spaces (see, e.g., [Gr (1969)], [DiB (1991)], [Lu (1985)], [Ac-Te (1987)]), the extrapolation spaces have been identified in a concrete way. It is our intention to fill this gap and subsequently to give an application of the extrapolation method to a perturbation problem.     

Approximations for Multi-Class Departure Processes

The exact analysis of a network of queues with multiple products is, in general, prohibited because of the non-renewal structure of the arrival and departure processes. Two-moment approximations (decomposition methods, Whitt [9] ) have been successfully used to study these systems. The performance of these methods, however, strongly depends on the quality of the approximations used to compute the squared coefficient variation (CV) of the different streams of products.In this paper, an approximation method for computing the squared coefficient of variation of the departure stream from a multi-class queueing system is presented. In particular, we generalize the results of Bitran and Tirupati [3] and Whitt [11] related to the interference effect.     

Hausdorff-Besicovitch Dimension of Graphs and <Emphasis Type="Italic">p</Emphasis>-Variation

A relationship between Hausdorff-Besicovitch dimension of graphs of trajectories and p-variation index is well known for many real-valued Levy processes (see, e.g., [10]). Here this relationship is extended to a class of subordinated processes used in econometrics. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 359–366, July–September, 2005.     

Fluid-structure interaction in porous media for loaded filter pleats

Currently, the known simulation efforts with respect to fluid-structure interaction (FSI) are mainly restricted to the study of flow interacting with deformable solid bodies. On the other hand, there is extensive literature on simulation of flow through porous media. In particular, algorithms and software for CFD simulations of filtration processes in the case of rigid filtration medium were presented earlier by Fraunhofer ITWM, see, e.g., [1, 2]. In these papers the deformation of the solid skeleton is neglected. In many cases of water filtration, filtration for hydraulic applications, and even in certain air filtration regimes, the fluid pressure can be quite high, and the deformation of the pleats can be an issue. The deflection of pleats and its effect on the filtration process merits examination because under operating conditions (and especially after a partial loading of the media) the pleats often cannot be anymore considered as rigid porous media. Therefore, in this paper, the deflection is considered for clean media, as well as for partially loaded media. A new model describing the coupled flow and deformation, and corresponding numerical results are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the asymptotics of locally dependent point processes

We investigate a family of approximating processes that can capture the asymptotic behaviour of locally dependent point processes. We prove two theorems presented to accommodate respectively the positively and negatively related dependent structures. Three examples are given to illustrate that our approximating processes can circumvent the technical difficulties encountered in compound Poisson process approximation (see Barbour and Månsson (2002) [10]) and our approximation error bound decreases when the mean number of the random events increases, in contrast to the increasing of bounds for compound Poisson process approximation.     

Discrete Ingham type inequalities and simultaneous observability of strings or beams

Harmonic analysis has been an efficient tool in control theory for a long time, see, e.g., Russell [D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions, SIAM Rev. 20 (1978) 639-739] and its numerous references. Here we establish discrete Ingham type and Haraux type inequalities for exponential sums satisfying a weakened gap condition. They enable us to obtain discrete simultaneous observability theorems for systems of vibrating strings or beams.     

Two inequalities on stop-loss premiums and some of its applications

The present study is motivated by the following practical problem in collective risk theory. Besides the problem of determining the distribution of the total amount of claims and its concrete by-products (reinsurance premiums, refund formulae for example), what is the influence of negative risk sums (e.g., in group life insurance: include or not include annuitants in a group contract). This note gives some qualitative answers by giving criteria for deciding this question in the form of inequalities. The quantitative aspect could be made effective for insurance models having numerically computable distributions [e.g., Compound Poisson distribution [Bertram (1981, 1983). Hürlimann (1985)] negative binomial distribution and others [Bertram (1981)]].     

SOME NEW PARTIAL ORDERINGSDESCRIBING AGING PROPERTY

The concept of aging, which is very users in relability describes the adverse orbeneficial effects of age on the lifetime of systems. Several partial orderings of life distributionshave been introduced. In this article,some more partial orderings of life distributions are imtroduced mainly by means of the equilibrium distribution. And conversely, a group of new aging clasps oflife distrbutions can be derived from these orderings.     

Large Deviations Approximations to Distributions of the Total Distance of Compound Random Walks with von Mises Directions

This article considers the planar random walk where the direction taken by each consecutive step follows the von Mises distribution and where the number of steps of the random walk is determined by the class of inhomogeneous birth processes. Saddlepoint approximations to the distribution of the total distance covered by the random walk, i.e. of the length of the resultant vector of the individual steps, are proposed. Specific formulae are derived for the inhomogeneous Poisson process and for processes with linear contagion, which are the binomial and the negative binomial processes. A numerical example confirms the high accuracy of the proposed saddlepoint approximations.     

Wavelet expansion of functions on a differentiable manifold

A wavelet expansion involving uniform meshes is accounted in many of the references (see, e.g., [1–4] and references therein); results on wavelets on nonuniform meshes may be found in [5–8]. Numerical flows associated with a smooth manifold may be processed using local functions (see [9]). However, development of efficient algorithms involves the resources of wavelet expansions.     

The intersection theorem for orderings of higher level in rings

This short note is ment as a supplement to the paper “On Rings admitting Orderings and 2-primary Orderings of Higher Level” by E. Becker and D. Gondard ([4]), where an intersection theorem for 2-primary orderings of higher level has been proved ([4]), Proposition 2.6). We will show that the same characterization holds for orderings of arbitrary level. This result finds several applications. For example, it is useful for the continuous representation of sums of 2n-th powers in function fields (see [8]) and it can be applied to derive several Null- and Positivstellensätze for generalized real closed fields (see [5]). As a further example we will prove a strict “Positivstellensatz of higher level” for a certain class of formally real fields. For unexplained notions we refer the reader to [4].     

Optimal sampling design for global approximation of jump diffusion stochastic differential equations

The paper deals with strong global approximation of stochastic differential equations (SDEs) driven by two independent processes: a nonhomogeneous Poisson process and a Wiener process. We assume that the jump and diffusion coefficients of the underlying SDE satisfy jump commutativity condition (see Chapter 6.3 in [21]). We establish the exact convergence rate of minimal errors that can be achieved by arbitrary algorithms based on a finite number of observations of the Poisson and Wiener processes. We consider classes of methods that use equidistant or nonequidistant sampling of the Poisson and Wiener processes. We provide a construction of optimal methods, based on the classical Milstein scheme, which asymptotically attain the established minimal errors. The analysis implies that methods based on nonequidistant mesh are more efficient, with respect to asymptotic constants, than those based on the equidistant mesh.     

An effective boundary element method for inhomogeneous partial differential equations

A method for removing the domain or volume integral arising in boundary integral formulations for linear inhomogeneous partial differential equations is presented. The technique removes the integral by considering a particular solution to the homogeneous partial differential equation which approximates the inhomogeneity in terms of radial basis functions. The remainder of the solution will then satisfy a homogeneous partial differential equation and hence lead to an integral equation with only boundary contributions. Some results for the inhomogeneous Poisson equation and for linear elastostatics with known body forces are presented.     

Orderings of higher level on noetherian rings

The noncommutative algebraic geometry has found fruitful applications in quantum geometry. Similar applications are expected to be found for its younger sister the noncommutative real algebraic geometry

One of the basic results in real algebraic geometry is the Positivestellensatz. The original results of Dubois and Risler (see section 3.3 of [13]) have been extended in many directions. We refer to [14], [1], [2], [3] for commutative rings and [9], [4] for associative rings. The aim of this paper is to prove the higher level Posit ivstellensatz for noncommutative Noetherian rings. Our proof depends on the intersection theorem for orderings of higher level on skew fields ([11], Theorem 3.13). The general case of orderings of higher level on associative rings remains open.     

Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

We consider a flexible class of space-time point process models—inhomogeneous shot-noise Cox point processes. They are suitable for modelling clustering phenomena, e.g. in epidemiology, seismology, etc. The particular structure of the model enables the use of projections to the spatial and temporal domain. They are used to formulate a stepwise estimation method to estimate different parts of the model separately. In the first step, the Poisson likelihood approach is used to estimate the inhomogeneity parameters. In the second and third steps, the minimum contrast estimation based on K-functions of the projected processes is used to estimate the interaction parameters. We study the asymptotic properties of the resulting estimators and formulate a set of conditions sufficient for establishing consistency and asymptotic normality of the estimators under the increasing domain asymptotics.     

A hybrid approach to 3-level FETI

Finite Element Tearing and Interconnecting (FETI) methods are nonoverlapping domain decomposition methods which have been proven to be very robust and parallel scalable for a class of elliptic partial differential equations. These methods are also called dual domain decomposition methods since the continuity accross the subdomain boundaries is enforced by Lagrange multipliers and, after elimination of the primal variables, the remaining Schur complement system is solved iteratively in the Lagrange multiplier space using a Krylov space method. Domain decomposition methods iterating on the primal variables are called primal substructuring methods. FETI and FETI–DP methods are different members of the family of dual domain decomposition methods. Their standard versions have in common that the local subproblems and a small global problem are solved exactly by a direct method, essentially representing two different levels within the algorithm. Several extensions of dual and primal iterative substructuring beyond two levels have been proposed in the past, see, e.g., [7] for FETI–DP, and, e.g., Tu [13,12,11] or [9] and [1] for BDDC. In the present article, a hybrid FETI/FETI–DP method is considered and some numerical results are presented. It is noted that independently, there is ongoing research on hybrid FETI methods by Jungho Lee of the Courant Institute. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Poisson source localization on the plane: change-point case

We present a detection problem where several spatially distributed sensors observe Poisson signals emitted from a single radioactive source of unknown position. The measurements at each sensor are modeled by independent inhomogeneous Poisson processes. A method based on Bayesian change-point estimation is proposed to identify the location of the source’s coordinates. The asymptotic behavior of the Bayesian estimator is studied. In particular, the consistency and the asymptotic efficiency of the estimator are analyzed. The limit distribution and the convergence of the moments are also described. The similar statistical model could be used in GPS localization problems.