Characterization of integral operators with semi-separable kernels with symmetries

We characterize integral operators with semi-separable kernels in a certain class that have different symmetries. We treat the selfadjoint case, the positive case, the J-unitary case, the positive real case, the dissipative case and the contractive case.     

Non-collision periodic solutions of second order singular dynamical systems

We study the existence of non-collision periodic solutions for second order singular dynamical systems. The repulsive case and the attractive case are dealt with using a unified topological approach. The proof is based on a well-known fixed point theorem for completely continuous operators, involving a new type of cone. We do not need to consider so-called strong force conditions. Moreover, for the repulsive case, the critical case can be covered. Recent results in the literature, even in the scalar case, are complemented, generalized and improved.     

Équations du filtrage non linéaire de la prédiction et du lissage

We establish equations of non linear filtering, prediction (extrapolation) and smoothing (interpolation) in the case where the signal is a non degenerate diffusion process, and the observation is a noisy functional of the signal. We consider both the case of observation noise correlated with the signal, and the opposite case where we establish “robust” form of the equations. We study finally the case of unbounded coefficients, and the case where there is a feedback from the observation to the signal.     

Some analysis of a stochastic logistic growth model

We derive several new results on a well-known stochastic logistic equation. For the martingale case, we compute the distribution of the solution, mean passage times, and the distribution of hitting times, all in closed form. For the case of constant coefficients, we also find mean passage times and for the general equation we give the weak solution expressed in terms of stochastic quadratures. We also show how these quadratures may be considerably simplified using the results for the martingale case. As it turns out, the martingale case has a particularly elegant weak solution, and to a large degree its structure carries over to the general case.     

An approximation algorithm for the hierarchical median problem

The hierarchical median problem asks for a hierarchical sequence of solutions to the k-median problems of growing cardinality. The best algorithm known for this problem in the general metric case has competitive ratio 20.71. In the paper, the case is under study that the clients and facilities lie on the real line, as well as the case of a Euclidean space. An algorithm is proposed with competitive ratio 8 in the case of the real line, and 8 + 4√2 (approximately 13.66), in the Euclidean case.     

Interpolation error estimates of a modified 8-node serendipity finite element

Summary. Interpolation error estimates for a modified 8-node serendipity finite element are derived in both regular and degenerate cases, the latter of which includes the case when the element is of triangular shape. For defined over a quadrilateral K, the error for the interpolant is estimated as , where in the regular case and in the degenerate case, respectively. Thus, the obtained error estimate in the degenerate case is of the same quality as in the regular case at least for . Results for some related elements are also given. Received June 2, 1997 / Published online March 16, 2000     

A goal programming approach to strategic resource allocation in acute care hospitals

This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Toronto's Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.     

On the weak discontinuity surfaces and tapes of equation systems in fluid mechanics

The weak discontinuity surfaces for a system of quasi-linear differential equations of higher order are developed. The classification of equation systems in fluid mechanics is based on the propagative weak discontinuity surfaces. Types of equations for different flow models are discussed. The conclusion is as follows:(a) For incompressible nonviscous flow, incompressible viscous flow and compressible viscous flow, the types of equations are all parabolic in the unsteady case and elliptic in the steady case.(b) For compressible nonviscous flow, the type of equations is hyperbolic in the unsteady case or steady supersonic case, and the type is elliptic in the steady subsonic case.     

A note on semilinear heat equation in hyperbolic space

Bandle et al. [1] obtained a quite interesting result about a semilinear heat equation that the Fujita exponent relative to the whole hyperbolic space is just the same as that relative to bounded domain in Euclidean space, and, in addition, the properties of solutions are different in the critical exponent case. Our purpose is to answer an open problem proposed by Bandle et al. for the critical exponent case, and it, together with the one obtained by them, shows that the critical exponent case does belong to the non-blow-up case, which is completely different from the case in Euclidean space.     

Higher order invariants in the case of compact quotients

We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.     

On constructing periodic solutions of quasi-linear non-self-contained systems with one degree of freedom, when amplitude equations possess multiple roots

Construction of periodic solutions of quasilinear non-self-contained systems with one degree of freedom, was investigated in [1 and 2]. In [1] the case of simple roots of amplitude equations was considered together with the case of a double root when the solution could be expanded into a series in integral powers of μ. In [2] the case of a double root is investigated in more detail Including expansions of solutions into series in μ^1/2. In the present paper, the case of arbitrary multiple roots for non-self-contained systems is reduced to the corresponding case for self-contained systems, which simplifies computations.     

A game-theoretic formulation of joint implementation of environmental projects

The aim of this paper is to provide a game-theoretic interpretation of joint implementation in environmental projects and to assess the merit of such a strategy. More specifically, we consider a two-player game and solve it under three different cases. In the first case, countries play a non-cooperative game and optimize their welfare under an environmental constraint without having access to joint implementation. In the second case, we assume countries do have access to JI, which allows us to assess its merits by comparing the players’ welfare levels achieved with and without JI. In the last case, the players jointly optimize their welfare under a collective environmental constraint. Comparing welfare levels in this case to those in the second case allows us to assess the merits of cooperation.     

Redundancy allocation at component level versus system level

In this paper, we treat the problem of stochastic comparison of standby [active] redundancy at component level versus system level. In the case of standby redundancy, we present some interesting comparison results of both series systems and parallel systems in the sense of various stochastic orderings for both the matching spares case and non-matching spares case, respectively. In the case of active redundancy, a likelihood ratio ordering result of series systems is presented for the matching spares case; and for the non-matching spares case, a counterexample is provided to show that there does not exist similar result even for the hazard rate ordering. The results established here strengthen and generalize some of those known in the literature. Some numerical examples are also provided to illustrate the theoretical results.     

Asymptotic inference for AR(1) processes with (nonnormal) stable errors. IV. A note on the case of a negative unit root

In this note, we show that the limit distribution of the least-squares estimator in the case of a negative unit root is different from the limit distribution in the case of a positive unit root. Thus, the infinite-variance case is different from the finite-variance case. Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part II.     

Asymptotic behavior of dynamic equations ontime scales

As a way to unify a discussion of many kinds of problems for equations in the contionous and discrete case(but also in order to reveal discrepancies between both cases), a theory of "time scales" was proposed and developed by Sulbach and Hilger. In our paper we investigate the asymptoic behaviour of so-called dynamic equations on time scales, and sych dynamic equations are differentialequations in the continous case and difference equations in the discrete case. We offer a perturbation result that leads to a time scales version of Levinson's Fundamental Lemma. Crucial are a dichotomy condition and a growth condition on the perturbation. Also, in the case that Levinson's result cannot be applied immediately, we suggest several preliminary transformations that might lead to a situation where Levinson's lemma is applicable. Such tranformations have been suggested by Harris and Lutz in the continuous case and by Benzaid and Lutz in the discrete case. Both those cases are covered by our theory, plus cases "in between". Examples for such cases will also be discussed in this paper.     

Nonlinear three-point boundary value problems

In the present work, we investigate nonlinear three-point boundary value problems (second-order differential equations with boundary conditions imposed at three consecutive points) in an effort to understand the conditions that must be imposed upon nonlinear perturbations of a linear problem in order to obtain a solution of a three-point problem. Both the noncritical case and the critical case are considered. In the first case, existence and uniqueness results are obtained, and in the second case we deal with local bifurcation problems when the nonlinearities are quadratic and cubic.     

Placenticeras: evolution of a task

We study a sequence of concrete case examples, anchored to a single image (of a fossil shell) to explore the complexity of building mathematical models in compelling realistic situations. The case examples are drawn from work with calculus undergraduates, and also dance majors from an experimental mathematics course who built evolving spiral forms in choreographic projects. The exposition is narrative, in the sense that it emphasizes, case by case, the evolution of the authors’ thinking in the course of extended conversations and collaborations with students over several years.     

Asymptotics of the solution of an initial-boundary value problem for a singularly perturbed parabolic equation in the case of double root of the degenerate equation

For a singularly perturbed parabolic equation, we construct and justify the asymptotics of the classical solution of an initial-boundary value problem in the case of a double root of the degenerate equation. This case substantially differs from the case of a simple root in that the scales of the boundary layer variables are different.     

Hardy–Littlewoodʼs inequalities in the case of a capacity

Hardy–Littlewood?s inequalities, well known in the case of a probability measure, are extended to the case of a monotone (but not necessarily additive) set function, called a capacity. The upper inequality is established in the case of a capacity assumed to be continuous and submodular, the lower — under assumptions of continuity and supermodularity.     

Some qualitative effects in the exact solutions of the Lamé problem for large deformations

Qualitative effects in the solution of a number of radially symmetric and plane axisymmetric problems for bodies made of non-linearly elastic incompressible materials are analysed for large deformations. In the case of problems of the axisymmetric plane deformation of cylindrical bodies, the lack of uniqueness of the solution for a given follower load in the case of a Bartenev–Khazanovich material and the existence of a limiting load in the case of a Treloar (neo-Hookian) material have been studied in detail and the dependences of the limiting load on the ratio of the external and internal radii of a hollow cylinder in the undeformed state have been presented. A similar study has been carried out for constitutive relations of a special form that well describe the properties of rubber. For this material, the lack of uniqueness of the solution is revealed for fairly high loads. The axisymmetric problem of the plane stress state of a circular ring made of a Bartenev–Khazanovich material has been solved and a lack of uniqueness of the solution for a given follower load was discovered in the case when the dimensions of the ring are given in the undeformed state. Similar studies have been carried out for Chernykh and Treloar materials in the case of the problem of the radially symmetric deformation of a spherical shell. It was established that, in the case of a Chernykh material, the lack of uniqueness of the solution depends considerably on the constant characterizing the physical non-linearity. The limit case of the deformation of a spherical cavity in an infinitely extended body has been investigated. The effect of an unbounded increase in the boundary stresses is observed for finite external loads, that appears in the case of the problem of the plane axisymmetric deformation of a cylindrical cavity in an infinitely extended body made of a Bartenev–Khazanovich material and in the case of the problem of the radially symmetric deformation of an infinitely extended body made of a Chernykh material with a spherical cavity.