A Discrete Hilbert Transform with Circle Packings

Mathematics

A Discrete Hilbert Transform with Circle Packings By Dominik Volland
D. F. Andrews, J. E. Stafford, “Symbolic Computation for Statistical Inference”
Nonabsolute Integration On Measure Spaces
Advanced Algebra, Second Edition by Anthony W. Knapp
College Algebra by Carl Stitz

A Discrete Hilbert Transform with Circle Packings By Dominik Volland

English | PDF | 2017 | 110 Pages | ISBN : 3658204567 | 2.61 MB

Dominik Volland studies the construction of a discrete counterpart to the Hilbert transform in the realm of a nonlinear discrete complex analysis given by circle packings. The Hilbert transform is closely related to Riemann-Hilbert problems which have been studied in the framework of circle packings by E. Wegert and co-workers since 2009. The author demonstrates that the discrete Hilbert transform is well-defined in this framework by proving a conjecture on discrete problems formulated by Wegert. Moreover, he illustrates its properties by carefully chosen numerical examples.

D. F. Andrews, J. E. Stafford, “Symbolic Computation for Statistical Inference”

2000 | ISBN-10: 0198507054 | 172 pages | PDF scan | 5 MB

Over recent years, developments in statistical computing have freed statisticians from the burden of calculation and have made possible new methods of analysis that previously would have been too difficult or time-consuming. Up till now these developments have been primarily in numerical computation and graphical display, but equal steps forward are now being made in the area of symbolic computing, or in other words the use of computer languages and procedures to manipulate expressions. This allows researchers to compute an algebraic expression, rather than evaluate the expression numerically over a given range. This book summarizes a decade of research into the use of symbolic computation applied to statistical inference problems. It shows the considerable potential of the subject to automate statistical calculation, leaving researchers free to concentrate on new concepts. Starting with the development of algorithms applied to standard undergraduate problems, the book then goes on to develop increasingly more powerful tools. Later chapters then discuss the application of these algorithms to different areas of statistical methodology.

Nonabsolute Integration On Measure Spaces

World Scientific | English | 2018 | ISBN-10: 9813221968 | 160 pages | PDF | 2.70 mb

by Wee Leng Ng (Author)
This book offers to the reader a self-contained treatment and systematic exposition of the real-valued theory of a nonabsolute integral on measure spaces. It is an introductory textbook to Henstock-Kurzweil type integrals defined on abstract spaces. It contains both classical and original results that are accessible to a large class of readers.
It is widely acknowledged that the biggest difficulty in defining a Henstock-Kurzweil integral beyond Euclidean spaces is the definition of a set of measurable sets which will play the role of “intervals” in the abstract setting. In this book the author shows a creative and innovative way of defining “intervals” in measure spaces, and prove many interesting and important results including the well-known Radon-NikodYm theorem.

Advanced Algebra, Second Edition by Anthony W. Knapp

English | 2016 | ISBN: NA | 758 Pages | PDF | 9.97 MB

Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems.

College Algebra by Carl Stitz

English | 2013 | ISBN: NA | 716 Pages | PDF | 5.82 MB

An introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes.