This book is a solid foundation of the most important formalisms used for specification and verification of reactive systems. In particular, the text presents all important results on m-calculus, w-automata, and temporal logics, shows the relationships between these formalisms and describes state-of-the-art verification procedures for them. It also discusses advantages and disadvantages of these formalisms, and shows up their strengths and weaknesses. Most results are given with detailed proofs, so that the presentation is almost self-contained. Includes all definitions without relying on other material Proves all theorems in detail Presents detailed algorithms in pseudo-code for verification as well as translations to other formalisms

Rapid development of computing power of personal computers, workstations, mainframes, super computers and integrated circuits has provided scientists and engineers with powerful tools in solving their scientific problems using computers, and is expected to continue to increase well in the future. The monograph mainly contains the following three parts: analysis of supremum of weighted pseudoinverses, study the stability of weighted pseudoinverses, weighted least squares problems and constrained weighted least squares problems, and stable methods for solving weighted least squares problems and constrained weighted least squares problems.

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

All mums are brilliant, and the mum in this story is no exception. She doesn't wear a cape or fly to earth from outer space, but she runs for the bus so fast it feels like flying, uses her super strength to carry her son's boots, coat, bag AND scooter, and can make bumps and bruises better with just a kiss. This mum really does have superpowers!