Using a quasilinear representation for unitarily invariant norms, we prove a basic inequality: Let A = L X X M be positive semideenite, where X 2 M m;n. Then k jX j p k 2 kL p k kM p k for all p > 0 and all unitarily invariant norms k k. We show how several inequalities of Cauchy-Schwarz type follow from this bound and obtain a partial analog of our results for l p norms.

The Cauchy problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodynamically perfect and polytropic. A corresponding initial-boundary value problem has a unique strong solution on ]0, 1[×]0, T [, for each T > 0. By using this result we construct a sequence of approximate solutions which converges to a sol...

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat’s principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a class...

There are several sections. The goal is to link complex analysis and imbeddings of graphs so that graph imbeddings can be performed systematically using identification spaces based on group actions in the complex plane. We give a short primer of basic calculus and then explain some of the finer aspects that obfuscate a complete solution to the Riemann Hypothesis. This is not central to our main...

In the present paper, a new characterization of orthogonality monic polynomials sequence $\left\{ Q_{n}\right\} _{n\geq 0}$ is obtained. This defined as linear combination another orthogonal P_{n}\right\} such as% \begin{equation*} Q_{n}(x)+r_{n}Q_{n-1}(x)=P_{n}(x)+s_{n}P_{n-1}(x)+t_{n}P_{n-2}\left( x\right) +v_{n}P_{n-3}\left( +w_{n}P_{n-4}(x),\ n\geq 0 \end{equation*}% where $w_{n}r_{n}\neq 0...

Abstract In this paper we prove that, after an appropriate rescaling, the sum of moments E <mml...

By a ‘completion’ on a 2-category K we mean here an idempotent pseudomonad on K . We are particularly interested in pseudomonads that arise from KZdoctrines. Motivated by a question of Lawvere, we compare the Cauchy completion [23], defined in the setting of V-Cat for V a symmetric monoidal closed category, with the Grothendieck completion [7], defined in the setting of S-Indexed Cat for S a to...

If A is a Lipschitz function, i.e., || A |L < °°, then %A makes a very significant example of non-convolution type singular integral operators. The problem of L -boundedness of the Cauchy transform was raised and solved when || A |L is small by A. P. Calderόn in relation to the Dirichlet problem on Lipschitz domains [Call, Cal2]. Since then, it has been a central problem in the theory of singul...

Contents Preface v 1 Continuous-time stochastic processes 1 1.1 Measurability and stopping times. . Bibliography 133 iv CONTENTS Preface This monograph concerns itself with the theory of continuous-time martingales with continuous paths and the theory of stochastic integration with respect to continuous semimartingales. To set the scene for the theory to be developed, we consider an example. As...