IAWS Newsletter April 2003

2008

In this paper we first give an elementary proof of existence of equilibrium with dividends in an economy with possibly satiated consumers. We then introduce a no-arbitrage condition and show that it is equivalent to the existence of equilibrium with dividends.

Journal of Evolution Equations, 2007

The system of equations (f (u))t − (a(u)v + b(u)) x = 0 and ut − (c(u)v + d(u)) x = 0, where the unknowns u and v are functions depending on (x, t) ∈ R × R+, arises within the study of some physical model of the flow of miscible fluids in a porous medium. We give a definition for a weak entropy solution (u, v), inspired by the Liu condition for admissible shocks and by Krushkov entropy pairs. We then prove, in the case of a natural generalization of the Riemann problem, the existence of a weak entropy solution only depending on x/t. This property results from the proof of the existence, by passing to the limit on some approximations, of a function g such that u is the classical entropy solution of ut − ((cg + d)(u))x = 0 and simultaneously w = f (u) is the entropy solution of wt − ((ag + b)(f (−1) (w)))x = 0. We then take v = g(u), and the proof that (u, v) is a weak entropy solution of the coupled problem follows from a linear combination of the weak entropy inequalities satisfied by u and f (u). We then show the existence of an entropy weak solution for a general class of data, thanks to the convergence proof of a coupled finite volume scheme. The principle of this scheme is to compute the Godunov numerical flux with some interface functions ensuring the symmetry of the finite volume scheme with respect to both conservation equations.

Parallel Processing Letters, 1992

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2009

A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions to such problems. A finite family of subspaces is said to satisfy the \emph{Inverse Best Approximation Property (IBAP)} if there exists a point that admits any selection of points from these subspaces as best approximations. We provide various characterizations of the IBAP in terms of the geometry of the subspaces. Connections between the IBAP and the linear convergence rate of the periodic projection algorithm for solving the underlying affine feasibility problem are also established. The results are applied to problems in harmonic analysis, integral equations, signal theory, and wavelet frames.

2010

In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum distinguished (d-) tensor. In that arena, we give the conservation laws and the continuity equations for multi-time plasma. The partial differential equations of the stream sheets (the equivalent of stream lines

2004

Ricerche di Matematica, 2007

We study Harnack type properties of quasiminimizers of the p-Dirichlet integral on metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality. We show that an increasing sequence of quasiminimizers converges locally uniformly to a quasiminimizer, provided the limit function is finite at some point, even if the quasiminimizing constant and the boundary values are allowed to vary in a bounded way. If the quasiminimizing constants converge to one, then the limit function is the unique minimizer of the p-Dirichlet integral. In the Euclidean case with the Lebesgue measure we obtain convergence also in the Sobolev norm.

2001

We introduce a generalization of Liu-Yang's weighted norm to linear and to nonlinear hyperbolic equations. Following an approach due to the second author for piecewise constant solutions, we establish sharp L 1 continuous dependence estimates for general solutions of bounded variation. Two different strategies are successfully investigated. On one hand, we justify passing to the limit in an L 1 estimate valid for piecewise constant wave-front tracking approximations. On the other hand, we use the technique of generalized characteristics and, following closely an approach by Dafermos, we derive the sharp L 1 estimate directly from the equation.

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is capable of dealing with an unknown weight of attributes and an unknown weight of decision-makers. Finally, a numerical example of multi-attribute group decision-making problem of investment potential is solved to show the feasibility, validity and efficiency of the proposed decision-making strategy.

TheScientificWorldJournal, 2014

Urinary Incontinence (UI) affects many older adults. Some of its deleterious consequences include stress, major depression, diminished quality of life, sexual dysfunction, and familial discord. Of the various mental health problems identified in the literature as being comorbid with UI, the most notable one continues to be depression. Despite a wealth of research contributions on this topic, the available literature is underrepresentative of ethnic minority older women. Culture has been shown to have a significant impact on a woman's perception of her own UI symptoms; this demonstrates the necessity for the recruitment of ethnically and culturally diverse samples when studying UI. In the present study, we determined the prevalence of UI among 140 community-dwelling, ethnically diverse older women (28.2%), discovered that our new UI screener is reliable, and did not find the UI-depression link to be significant. The clinical and research implications of our findings are discussed.