Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of the system (its state and evolution), and relate those to the input parameters of the system and initial data.

This book is a revised and more comprehensive version of "Dynamics of Stochastic Systems." Part I provides an introduction to the topic. Part II is devoted to the general theory of statistical analysis of dynamic systems with fluctuating parameters described by differential and integral equations. Part III deals with the analysis of specific physical problems associated with coherent phenomena.
A comprehensive update of "Dynamics of Stochastic Systems"Develops mathematical tools of stochastic analysis and applies them to a wide range of physical models of particles, fluids and wavesIncludes problems for the reader to solve

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.

Praise for the First Edition

" . . . an excellent addition to an upper-level undergraduate course on environmental statistics, and . . . a 'must-have' desk reference for environmental practitioners dealing with censored datasets."
--Vadose Zone Journal

Statistical Methods for Censored Environmental Data Using Minitab(R) and R, Second Edition introduces and explains methods for analyzing and interpreting censored data in the environmental sciences. Adapting survival analysis techniques from other fields, the book translates well-established methods from other disciplines into new solutions for environmental studies.

This new edition applies methods of survival analysis, including methods for interval-censored data to the interpretation of low-level contaminants in environmental sciences and occupational health. Now incorporating the freely available R software as well as Minitab(R) into the discussed analyses, the book features newly developed and updated material including:

A new chapter on multivariate methods for censored data

Use of interval-censored methods for treating true nondetects as lower than and separate from values between the detection and quantitation limits ("remarked data")

A section on summing data with nondetects

A newly written introduction that discusses invasive data, showing why substitution methods fail

Expanded coverage of graphical methods for censored data

The author writes in a style that focuses on applications rather than derivations, with chapters organized by key objectives such as computing intervals, comparing groups, and correlation. Examples accompany each procedure, utilizing real-world data that can be analyzed using the Minitab(R) and R software macros available on the book's related website, and extensive references direct readers to authoritative literature from the environmental sciences.

Statistics for Censored Environmental Data Using Minitab(R) and R, Second Edition is an excellent book for courses on environmental statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for?environmental professionals, biologists, and ecologists who focus on the water sciences, air quality, and soil science.

Financial market modeling is a prime example of a real-life application of probability theory and stochastics. This authoritative book discusses the discrete-time approximation and other qualitative properties of models of financial markets, like the Black-Scholes model and its generalizations, offering in this way rigorous insights on one of the most interesting applications of mathematics nowadays.

This is a companion textbook for an introductory course in physics. It aims to link the theories and models that students learn in class with practical problem-solving techniques. In other words, it should address the common complaint that 'I understand the concepts but I can't do the homework or tests'. The fundamentals of introductory physics courses are addressed in simple and concise terms, with emphasis on how the fundamental concepts and equations should be used to solve physics problems.

Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry.
Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework.
Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.

The valuation of the liability structure can be determined by real options because the shares of a company can be regarded as similar to the purchase of a financial call option. Therefore, from this perspective, debt can be viewed as the sale of a financial put option. As a result, financial analysts are able to establish different valuations of a company, according to these two financing methods. Valuation of the Liability Structure by Real Options explains how the real options method works in conjunction with traditional methods. This innovative approach is particularly suited to the valuation of companies in industries where an underlying asset has high volatility (such as the mining or oil industries) or where research and development costs are high (for example, the pharmaceutical industry). Integration of the economic value of net debt (rather than the accounting value) and integration of the asset volatility are the main advantages of this approach.

The rapid developments in new communication technologies have facilitated the popularization of digital games, which has translated into an exponential growth of the game industry in recent decades. The ubiquitous presence of digital games has resulted in an expansion of the applications of these games from mere entertainment purposes to a great variety of serious purposes. In this edited volume, we narrow the scope of attention by focusing on what game theorist Ian Bogost has called 'persuasive games', that is, gaming practices that combine the dissemination of information with attempts to engage players in particular attitudes and behaviors. This volume offers a multifaceted reflection on persuasive gaming, that is, on the process of these particular games being played by players. The purpose is to better understand when and how digital games can be used for persuasion by further exploring persuasive games and some other kinds of persuasive playful interaction as well. The book critically integrates what has been accomplished in separate research traditions to offer a multidisciplinary approach to understanding persuasive gaming that is closely linked to developments in the industry by including the exploration of relevant case studies.

These materials were developed, in part, by a grant from the federally-funded Mathematics and Science Partnership through the Center for STEM Education. Some of the activities were adapted from the National Council of Teachers of Mathematics Illuminations, the National Library of Virtual Manipulatives, Hands-On Math Projects with Real Applications by Judith A. Muschla and Gary R. Muschla, Learning Math with Calculators: Activities for Grades 3-8 by Len Sparrow and Paul Swan, and Mathematical Ideas by Charles D. Miller, Vern E. Heeren and John Hornsby.