Jost Functions and Jost Solutions for Jacobi Matrices, II. Decay and Analyticity

We present necessary and sufficient conditions on the Jost function for the corresponding Jacobi parameters $a_n -1$ and $b_n$ to have a given degree of exponential decay.Comment: 28 page

Introduction

Husserl’s philosophy, by the usual account, evolved through three stages: 1. development of an anti-psychologistic, objective foundation of logic and mathematics, rooted in Brentanian descriptive psychology; 2. development of a new discipline of "phenomenology" founded on a metaphysical position dubbed "transcendental idealism"; transformation of phenomenology from a form of methodological solipsism into a phenomenology of intersubjectivity and ultimately (in his Crisis of 1936) into an ontology of the life-world, embracing the social worlds of culture and history. We show that this story of three revolutions can provide at best a preliminary orientation, and that Husserl was constantly expanding and revising his philosophical system, integrating views in phenomenology, ontology, epistemology and logic with views on the nature and tasks of philosophy and science as well as on the nature of culture and the world in ways that reveal more common elements than violent shifts of direction. We argue further that Husserl is a seminal figure in the evolution from traditional philosophy to the characteristic philosophical concerns of the late twentieth century: concerns with representation and intentionality and with problems at the borderlines of the philosophy of mind, ontology, and cognitive science

Warranted Diagnosis

A diagnostic process is an investigative process that takes a clinical picture as input and outputs a diagnosis. We propose a method for distinguishing diagnoses that are warranted from those that are not, based on the cognitive processes of which they are the outputs. Processes designed and vetted to reliably produce correct diagnoses will output what we shall call ‘warranted diagnoses’. The latter are diagnoses that should be trusted even if they later turn out to have been wrong. Our work is based on the recently developed Cognitive Process Ontology and further develops the Ontology of General Medical Science. It also has applications in fields such as intelligence, forensics, and predictive maintenance, all of which rely on vetted processes designed to secure the reliability of their outputs

Do ‘Fat Tails’ Matter in GARCH Estimation? Stock Market Efficiency in Romania and the Czech Republic

The use of the GARCH-class of models is commonplace when examining stock market returns. In this paper we use data on stock markets in two transition economies to demonstrate the importance of using the correct GARCH specification. When returns are characterised by ‘fat tails’ or kurtosis the use of a GARCH-t specification is appropriate. Returns in Romania are symmetric, but characterised by kurtosis. Returns in the Czech Republic are normally distributed. Using a standard GARCH specification leads to rejection of the null hypothesis of market efficiency in Romania, whereas this null hypothesis cannot be rejected using the GARCH-t specification. The null hypothesis of efficiency cannot be rejected in the Czech Republic using either specification. Thus, we find that the presence of ‘fat tails’ can have important implications for inference in the analysis of stock market returns.GARCH, transition, stock market efficiency

Fostering Chinese firms through entrepreneurship, globalisation and international finance

The success of ventures that have pursued non traditional marketing approaches may be attributed to a range of forward thinking practices which it is argued here, should be the starting and finishing points for Chinese companies. Chinese multinationals need to develop entrepreneurial ability more compatible with their growth in the international markets. Chinas educational framework is still largely based on rote learning, which is a method typically seen as ill suited to modern needs. Many Chinese high tech sectors are still dominated by overseas know-how and the ongoing strength of wholly foreign- owned enterprises

Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients

We extend the results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and Killip-Simon from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations.Comment: 64 pages, to appear in Ann. of Mat

The Analytic Theory of Matrix Orthogonal Polynomials

We give a survey of the analytic theory of matrix orthogonal polynomials.Comment: 85 page