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Small Viscosity and Boundary Layer Methods
* Metivier is an expert in the field of pdes/math physics, with a particular emphasis on shock waves. * New monograph focuses on mathematical methods, models, and applications of boundary layers, present in many problems of physics, engineering, fluid mechanics. * Metivier has good Birkhauser track record: one of the main authors of "Advances in the Theory of Shock Waves" (Freistuehler/Szepessy, eds, 4187-4). * Manuscript endorsed by N. Bellomo, MSSET series editor...should be a good sell to members of MSSET community, who by-in-large are based in Europe. * Included are self-contained introductions to different topics such as hyperbolic boundary value problems, parabolic systems, WKB methods, construction of profiles, introduction to the theory of Evans’ functions, and energy methods with Kreiss’ symmetrizers.
Resolving Markov Chains onto Bernoulli Shifts via Positive Polynomials
The two parts of this monograph contain two separate but related papers. The longer paper in Part A obtains necessary and sufficient conditions for several types of codings of Markov chains onto Bernoulli shifts. It proceeds by replacing the defining stochastic matrix of each Markov chain by a matrix whose entries are polynomials with positive coefficients in several variables; a Bernoulli shift is represented by a single polynomial with positive coefficients, $p$. This transforms jointly topological and measure-theoretic coding problems into combinatorial ones. In solving the combinatorial problems in Part A, the work states and makes use of facts from Part B concerning $p DEGREESn$ and its coefficients. Part B contains the shorter paper on $p DEGREESn$ and its coefficients, and is independ
Existence of the Sectional Capacity
In the case where the norms are induced by metrics on the fibres of ${\mathcal L}$, we establish the functoriality of the sectional capacity under base change, pullbacks by finite surjective morphisms, and products. We study the continuity of $S Gamma(\overline{\mathcal L})$ under variation of the metric and line bundle, and we apply this to show that the notion of $v$-adic sets in $X(\mathbb C v)$ of capacity $0$ is well-defined. Finally, we show that sectional capacities for arbitrary norms can be well-approximated using objects of finite type.
Layer Potentials, the Hodge Laplacian, and Global Boundary Problems in Nonsmooth Riemannian Manifolds
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds. In the first part (ss1-4), we develop a theory for Cauchy type operators on Lipschitz submanifolds of co dimension one (focused on boundedness properties and jump relations) and solve the $Lp$-Dirichlet problem, with $p$ close to $2$, for general second-order strongly elliptic systems. The solution is represented in the form of layer potentials and optimal non tangential maximal function estimates are established.This analysis is carried out under smoothness assumptions (for the coefficients of the operator, metric tensor and the u...
Gorenstein Liaison, Complete Intersection Liaison Invariants and Unobstructedness
This paper contributes to the liaison and obstruction theory of subschemes in $\mathbb{P}^n$ having codimension at least three. The first part establishes several basic results on Gorenstein liaison. A classical result of Gaeta on liaison classes of projectively normal curves in $\mathbb{P}^3$ is generalized to the statement that every codimension $c$ ``standard determinantal scheme'' (i.e. a scheme defined by the maximal minors of a $t\times (t+c-1)$ homogeneous matrix), is in the Gorenstein liaison class of a complete intersection. Then Gorenstein liaison (G-liaison) theory is developed as a theory of generalized divisors on arithmetically Cohen-Macaulay schemes. In particular, a rather ge...
Equivariant Analytic Localization of Group Representations
This book is intended for graduate students and research mathematicians interested in topological groups, Lie groups, category theory, and homological algebra.
Cocycles of CCR Flows
We study the partially ordered set of quantum dynamical semigroups dominated by a given semigroup on the algebra of all bounded operators on a Hilbert space. For semigroups of *-endomorphisms this set can be described through cocycles. This helps us to prove a factorization theorem for dilations and to show that minimal dilations of quantum dynamical semigroups with bounded generators can be got through Hudson-Parthasarathy cocycles.
Tilings of the Plane, Hyperbolic Groups and Small Cancellation Conditions
This book is intended for graduate students and research mathematicians interested in group theory and generalizations.
Black Box Classical Groups
If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. The proof relies on the geometry of the classical groups rather than on difficult group-theoretic background. This algorithm has applications to matrix group questions and to nearly linear time algorithms for permutation groups. In particular, we upgrade all known nearly linear time Monte Carlo permutation group algorithms to nearly linear Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3-dimensional unitary group.
Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations
This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the intro...
