This paper is concerned with a stochastic linear–quadratic (LQ) control problem over a finite time horizon with Markovian jumps in the problem parameters. The problem is indefinite in that the cost weighting matrices for the state and control are allowed to be indefinite. A system of coupled generalized (differential) Riccati equations (CGREs) is introduced to cope with the indefiniteness of th...

The scientific community recognizes the relevance that motivational elements and students planned actions have in the process of obtaining the expected learning, however, there is no research focused on exploring the association between those variables and the learning outcomes in college students. Considering this, the aim of this research was to describe the association between school wellbei...

We set up and analyze a model of radiation damping within the framework of continuum mechanics, inspired by a model of post-Newtonian hydrodynamics due to Blanchet, Damour and Schäfer. In order to simplify the problem as much as possible we replace the gravitational field by the electromagnetic field and the fluid by kinetic theory. We prove that the resulting system has a well-posed Cauchy pro...

In this paper we investigate the regularizing properties of discretization in preimage space for linear and nonlinear ill-posed operator equations with noisy data. We propose to choose the discretization level, that acts as a regularization parameter in this context, by a discrepancy principle. While general convergence has been shown not to hold (see [17]), we provide convergence results under...

The recent Institute of Medicine report on prevention (National Research Council & Institute of Medicine, 2009) noted the substantial interrelationship among mental, emotional, and behavioral disorders and pointed out that, to a great extent, these problems stem from a set of common conditions. However, despite the evidence, current research and practice continue to deal with the prevention of ...

We consider the Lyapunov equation for the linear dynamics, which arises naturally when one seeks for a Lyapunov function with a uniform, exact decrease. In this setting, a solution to the Lyapunov equation has been characterized only for quadratic Lyapunov functions. We demonstrate that the Lyapunov equation is a well-posed equation for strictly stable dynamics and a much more general class of ...

We obtain a system for the spatial metric and extrinsic curvature of a spacelike slice that is hyperbolic non-strict in the sense of Leray and Ohya and is equivalent to the Einstein equations. Its characteristics are the light cone and the normal to the slice for any choice of lapse and shift functions, and it admits a well-posed causal Cauchy problem in a Gevrey class of index α = 2. The syste...

— We study the local existence of strong solutions for the cubic nonlinear wave equation with data in H(M), s < 1/2, where M is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct local strong solution for a large set of initial data in ...

Social relationships can have considerable influence on physical and mental well-being. AL research suggests that other residents are among the most available social contacts and that co-resident relationships can affect life satisfaction, quality of life, and well-being. Although functional status influences social relationships, research has yet to provide an in-depth understanding of how cog...

We prove that the Maxwell-Klein-Gordon system on R1þ4 relative to the Coulomb gauge is locally well-posed for initial data in H1þ" for all " > 0. This builds on previous work by Klainerman and Machedon who proved the corresponding result, with the additional restriction of small-norm data, for a model problem obtained by ignoring the elliptic features of the system, as well as cubic terms.