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"The aim of this monograph is to present a mathematical framework which makes solving problems in multiply connected domains a very natural generalization of solving them in simply connected ones"-- Whenever two or more objects or entities-be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid-interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. Solving Problems in Multiply Connected Domains is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in a diverse range of applications; is the first monograph to focus on solving applied problems in multiply connected domains; and contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. This book is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists. It provides a rich source of project material for a range of undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.

Problem solving

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Problem solving

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AN AUTHORITATIVE GUIDE TO COMPUTER SIMULATION GROUNDED IN A MULTI-DISCIPLINARY APPROACH FOR SOLVING COMPLEX PROBLEMS Simulation and Computational Red Teaming for Problem Solving offers a review of computer simulation that is grounded in a multi-disciplinary approach. The authors present the theoretical foundations of simulation and modeling paradigms from the perspective of an analyst. The book provides the fundamental background information needed for designing and developing consistent and useful simulations. In addition to this basic information, the authors explore several advanced topics. The book's advanced topics demonstrate how modern artificial intelligence and computational intelligence concepts and techniques can be combined with various simulation paradigms for solving complex and critical problems. Authors examine the concept of Computational Red Teaming to reveal how the combined fundamentals and advanced techniques are used successfully for solving and testing complex real-world problems. This important book: . Demonstrates how computer simulation and Computational Red Teaming support each other for solving complex problems. Describes the main approaches to modeling real-world phenomena and embedding these models into computer simulations. Explores how a number of advanced artificial intelligence and computational intelligence concepts are used in conjunction with the fundamental aspects of simulation Written for researchers and students in the computational modelling and data analysis fields, Simulation and Computational Red Teaming for Problem Solving covers the foundation and the standard elements of the process of building a simulation and explores the simulation topic with a modern research approach.

Problem solving. --- Simulation methods.

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This book examines the various thinking skills that leaders may need to find success in contemporary organizations and institutions, covering a wide array of skills that are held to be important by key leadership scholars. Bridging theory and practice, chapters summarize major findings with respect to a particular ability, knowledge, or skill, providing theoretical frameworks for understanding how these contribute to leader emergence and performance, and considering implications for leader selection, assessment, and development. The text appraises the existing research on the critical cognitive capabilities that underlie leader problem-solving and implications for the assessment and development of leadership potential in real-world settings. The role of creative thinking skills on leader performance is also addressed, bearing on the importance of processes such as problem definition and idea generation, but also using constraints to potentially stimulate creative thought. With contributions from some of the most eminent scholars working in the field of leadership, this book will be in invaluable resource to academics, researchers, graduate students, and professionals interested in leadership and leader skills, I/O psychology, and business management.

Leadership. --- Decision making. --- Problem solving.

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Decision making. --- Policy sciences. --- Problem solving.