We study a class of rational matrix differential equations that generalize the Riccati differential equations. The generalization involves replacing positive definite “weighting” matrices in the usual Riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games−both stochastic and deterministic. The purpose of this pape...

Most analyses of definiteness are based on two important notions: uniqueness and familiarity. Fundamentally, both approaches ascribe some content to the conventional meaning of definite, but not indefinite, descriptions. We explore the effect of determiner choice on listeners’ expectations about possible referents using eye-tracking in the visual world paradigm. We present listeners with tempor...

This paper gives a survey of results in the mathematical literature on positive definite kernels and their associated structures. We concentrate on properties which seem potentially relevant for Machine Learning and try to clarify some results that have been misused in the literature. Moreover we consider different lines of generalizations of positive definite kernels. Namely we deal with opera...

A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu [15] in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefini...

Spacetime is modelled by binary relations by the classes of the automorphisms GL( I C) of a complex 2-dimensional vector space with respect to the definite unitary subgroup U(2). In extension of Feynman propagators for particle quantum fields representing only the tangent spacetime structure, global spacetime representations are given, formulated as residues using energy-momentum distributions ...

For R-vector spaces U and V we consider a symmetric bilinear map B : U×U → V . This then defines a quadratic map QB : U → V by QB(u) = B(u, u). Corresponding to each λ ∈ V ∗ is a R-valued quadratic form λQB on U defined by λQB(u) = λ · QB(u). B is definite if there exists λ ∈ V ∗ so that λQB is positive-definite. B is indefinite if for each λ ∈ V ∗, λQB is neither positive nor negative-semidefi...

Multigrid methods are known for their high efficiency in the solution of definite elliptic problems. However, difficulties that appear in highly indefinite problems, such as standing wave equations, cause a total loss of efficiency in the standard multigrid solver. The aim of this paper is to isolate these difficulties, analyze them, suggest how to deal with them, and then test the suggestions ...

In this article, I argue that neither of the two main approaches to definiteness, familiarity or unique identifiability, provide necessary or sufficient conditions for the use of the definite article in English. I propose instead that the basic meaning of the article is to signal the accessibility of a discourse referent, more specifically, the availability of an access path through a configura...

Abstract Process ontology is making deep inroads into the hard sciences. For it offers a workable understanding of dynamic phenomena which sits well with inquiries that problematize traditional conception self-standing, definite, independent objects as basic stuff universe. Process-based approaches are claimed by their advocates to yield better ontological descriptions various domains physical ...