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Signal Processing
Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics-including familiarity with Fourier series, matrices, probab
Birational Algebraic Geometry
Ten research reports illustrate the many directions the field is taking, and feature problems on special models such as Fanos and their fibrations, adjunctions and subadjunction formuli, and projectivity and projective embeddings. Also included are a eulogy and bibliography for the mathematician Chow, who was at Johns Hopkins since the 1940s. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Set Theoretical Aspects of Real Analysis
Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary between fundamental concepts of measurability and nonmeasurability for point sets and functions. The remainder of the book deals with more specialized material on set theoretical real analysis. The book focuses on certain logical and set theoretical aspects of real analysis. It is expected that the first eleven chapters can be used in a course on Le...
Modeling and Inverse Problems in the Presence of Uncertainty
Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation i
Birational Geometry, Rational Curves, and Arithmetic
This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the...
Cohomological and Geometric Approaches to Rationality Problems
Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
The Planar Cubic Cayley Graphs
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Absolute Continuity Under Time Shift of Trajectories and Related Stochastic Calculus
The text is concerned with a class of two-sided stochastic processes of the form . Here is a two-sided Brownian motion with random initial data at time zero and is a function of . Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when is a jump process. Absolute continuity of under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, , and on with we verify i.e. where the product is taken over all coordinates. Here is the divergence of with respect to the initial position. Crucial for this is the temporal homogeneity of in the sense that , , where is the trajectory taking the constant value . By means of such a density, partial integration relative to a generator type operator of the process is established. Relative compactness of sequences of such processes is established.
