Variation And Convergence

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches.

Contemporary accounts of welfare state change have produced conflicting findings and incompatible theoretical explanations. By discussing the most salient aspects of the 'dependent variable problem', this work offers suggestions as to how the problem might be tackled within empirical cross-national analyses of modern welfare states.

This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.

Become a fabulous quilt artist - the fun, easy way! Popular quilting expert Ricky Tims presents an imaginative, new piecing technique that quilters will adore! Convergence quilts feature two or more fabrics cut into strips, sewn together, then cut and pieced again. Nothing could be simpler - or more magical! Ricky offers lots of creative guidelines but no hard-and-fast rules, so every Convergence quilt is a unique work of art. • 4 projects walk you through the steps of making Convergence quilts • Quilts look complex but are fun, easy, and, best of all, creative to make • Use any fabric from commercial prints to hand-dyed • Add decorative touches such as appliqué to dress up your projects • An infinite number of looks from one ingenious technique