Uncertain partial differential equation is a type of partial differential equation driven by Liu processes. This paper first provides two methods for solving the first order linear uncertain partial differential equation and the inverse uncertainty distribution of solution is discussed. Moreover, on the basis of the study of uncertainty theory and the propagation process of internet public opin...

We provide a new representation for the inverse of block tridiagonal and banded matrices. The new representation is shown to be numerically stable over a variety of block tridiagonal matrices, in addition of being more computationally efficient than the previously proposed techniques. We provide two algorithms for commonly encountered problems that illustrate the usefulness of the results.

This thesis studies metaand exactly stable supersymmetry breaking mechanisms in heterotic and type IIB string theories and constructs an F-theory Grand Unified Theory model for neutrino physics in which neutrino mass is determined by the supersymmetry breaking mechanism. Focussing attention on heterotic string theory compactified on a 4-torus, stability of non-supersymmetric states is studied. ...

Solutions to the field equations generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild solution. The asymptotic form of solutions will be described, as will the lack of validity of Birkhoff’s theorem. Exact solutions are presented which ...

Abstract. We investigate the behavior of isotropic invariant subspaces of skew-Hamiltonian matrices under structured perturbations. It is shown that finding a nearby subspace is equivalent to solving a certain quadratic matrix equation. This connection is used to derive meaningful error bounds and condition numbers that can be used to judge the quality of invariant subspaces computed by strongl...

we study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. we discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. this first part introduces the main conceps and philosophies anddiscu...

The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs, which generalize the different notions ...

We model a matching market in which nonstrategic vendors sell items of different types and offer discounted prices on the bundle of all items triggered by demand volumes. Each buyer acts strategically in order to maximize her utility, given by the difference between product valuations and price paid. In a market with transferable utility, buyers might be willing to cooperate by exchanging side-...

Strange attractors – emerging out of the chaotic dynamics of the thoughts and feelings constantly swarming in the mental space of each individual – encapsulate topologies of meaning-making units and offer a key to a unified semiotic and cognitive understanding of meaning. Being dynamic constructs, Strange Attractors of Meaning have both spatial and temporal characteristics. The spatial characte...

In this note we study stability radii of positive linear discrete-time systems under real or complex parameter perturbations. A simple formula for the real stability radius is established and it is shown that the real and the complex stability radii of positive systems coincide. These results are derived for arbitrary perturbation norms induced by monotonic vector norms (e.g. p-norms, 1 p 1). N...