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This book includes algorithms that illustrate the famous Monté Carlo Methods and the computer simulation of stochastic experiments in the areas of random numbers generation, the simulation of random phenomena, the computation of Pi and e (the base of logarithms), both simple and multiple integration, the computation of areas and volumes, probability and statistical distributions, in addition to an introduction to the novel Complex Probability Paradigm. As such, it will be of interest to all scholars, researchers, and undergraduate and graduate students in mathematics, computer science, and science in general.
This book covers Monté Carlo Methods and computer simulation for applications like calculating Pi, integration, areas, and volumes. It also introduces the novel Complex Probability Paradigm. For scholars and students in mathematics, computer science, and science in general.
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David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilbert’s contributions to mathematics, putting them in their historical, social and cultural context. In doing so, particular attention is paid to Hilbert’s axiomatic method and his proposal for the foundations of mathematics, the so-called Hilbert’s program. The book also discusses the development of algebraic number theory, the theory of integral equations, modern algebra and the structural image of mathematics. In addition, it considers the famous list of Mathematical Problems presented…
Explore the revolutionary work of David Hilbert, a giant of 20th-century mathematics. This book examines his axiomatic method, his famous 23 Problems, his program for the foundations of mathematics, and his crucial contributions to relativity and quantum physics.
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Game theory is an obscure area of the economic sciences. In 1995, the Nobel Prize was conferred upon John Nash, John Harsanyi and Reinhart Selton for their contribution of game theory to economics, which generated a great deal of interest in other disciplines, including the physical and material sciences. However, the beauty of game theory is its application to real world problems. This book commemorates the marriage of the theory and practice, not in heaven, but in the real world.
The beauty of game theory is its application to real world problems. This book commemorates the marriage of the theory and practice, not in heaven, but in the real world.
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The direct integration method (a general approach to analysis for boundary value problems of mathematical physics with no implications for the potential functions of higher differential order) is presented in this book as a potential tool for the analysis of the elastic response of arbitrarily nonhomogeneous solids to thermal and force loadings. This method rests upon the correct integration of the local equilibrium equations, which results in an explicit relationship between the stress-tensor components and fundamental integral conditions of equilibrium for individual stresses, which can serve to assure the correctness…
This book presents the direct integration method, a tool for analyzing the elastic response of nonhomogeneous solids to thermal and force loadings. By reducing elasticity problems to integral equations, this method provides efficient, closed-form solutions for these materials.
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This book provides insights into the dynamics of control systems with the integration of conceptions such as stability, controllability, attraction, and chain transitivity. It highlights the importance of Morse theory with its feature of describing the global dynamics of systems, presented here for the first time in control theory. The mathematical formulations are comprehensive, designed especially for students, researches, and professionals interested in qualitative studies of control systems. The reader will find the book an accessible source of basic definitions, properties, methods, examples, theorems, references, lists of problems, and open…
This book provides insights into the dynamics of control systems, highlighting the first-time use of Morse theory to describe global dynamics. It is an accessible source of definitions, examples, theorems, and open questions for students, researchers, and professionals.
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The behavior of any real system is a process to a greater or lesser degree probabilistic. As a rule, it is impossible to specify exactly which external influences and internal mechanisms of interaction of the system components will be decisive in the future. As a consequence, we cannot accurately predict the behavior of the system. We can only talk about the probability that, in the future, the system will come to a particular state. While the problem of the probabilistic description of all possible future states of the system is…
Semakov highlights some of the most important fundamental results related to crossings problems in the context of aviation. The result is a work that will appeal to engineers and scientists who are interested in the applications of random processes theory and its methods.
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This unique mathematical volume brings together geometers, analysts, differential equations specialists and graph-theorists to provide a glimpse on recent mathematical trends whose commonalities have hitherto remained, for the most part, unnoticed. The applied mathematician will be pleasantly surprised with the interpretation of a voting system in terms of the fixed points of a mapping given in the book, as much as the classical analyst will be enthusiastic to find detailed discussions on the generalization of the notion of metric space, in which the metric takes values on an abstract monoid.…
This unique mathematical volume brings together geometers, analysts, and graph-theorists to reveal unnoticed commonalities in recent trends. Classical fixed point theory is adapted to graph theory, uncovering versatile tools for mathematicians working in either area.
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Experiences in the Biocontinuum
A New Foundation for Living Systems
The central question in the biological sciences for the past 100 years has concerned an understanding of how living systems differ from other general physical phenomena and what makes these systems unique. With new developments in the fields of nonequilibrium thermodynamics, systems theory, chaos, and information theory over the past few decades, there has been growing interest in finally answering the question first posed by Erwin Schrödinger in the 1940s concerning the true scientific nature of living systems. Similarly, there is also increasing interest within the biologic community for a…
This book addresses the central question of what makes living systems unique. Building on information theory, thermodynamics, and systems theory, it forms a singular unifying concept and develops a dynamic mathematical framework for the study of life’s fundamental processes.
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Computational Modeling by Case Study
All Models Are Uncertain
Mathematical models power the modern world; they allow us to design safe buildings, investigate changes to the climate, and study the transmission of diseases through a population. However, all models are uncertain: building contractors deviate from the planned design, humans impact the climate unpredictably, and diseases mutate and change. Modern advances in mathematics and statistics provide us with techniques to understand and quantify these sources of uncertainty, allowing us to predict and design with confidence. This book presents a comprehensive treatment of uncertainty: its conceptual nature, techniques to quantify uncertainty,…
Mathematical models power the modern world, but they are all uncertain. This book provides techniques to quantify uncertainty, allowing you to predict and design with confidence. Learn through case studies and reproducible examples in Python adapted for your own problems.
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This book tackles some modern trends and methods in the modelling of extreme data. Usually such data arise from random phenomena such as floods, hurricanes, air and water pollutants, extreme claim sizes, life spans, and maximum sizes of ecological populations. It provides the latest statistical methods to model these random phenomena to understand and predict them, thus allowing the avoidance of damage or at least minimizing it. In addition, this book sheds light on the mathematical and statistical theories on which applied modelling methods were built. Therefore, it has both…
This book tackles modern methods in the modelling of extreme data, such as floods and hurricanes. It provides the latest statistical methods to predict these random phenomena and minimize damage, offering both an applied and theoretical orientation.
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Disruption Recovery in Air Traffic
An Airport Perspective
Disruptions to commercial airline schedules are frequent and can inflict significant costs. This is the first book to treat the optimisation of disruption management (irregular operations) in air traffic from a common good perspective that addresses the concerns of airlines, airports, air traffic service providers and, most importantly of all, the travelling public. It describes a number of disruption management systems which are already in place at air traffic service (ATC) providers such as Airservices Australia. As such, the book will be of immense value to ATC providers, and will…
This is the first book to treat the optimisation of air traffic disruption management from a common good perspective, addressing airlines, airports, ATC providers, and the public. It describes optimisation techniques of immense value to industry professionals and academics.
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This book considers a number of research topics in graph theory and its applications, including ideas devoted to alpha-discrepancy, strongly perfect graphs, reconstruction conjectures, graph invariants, hereditary classes of graphs, and embedding graphs on topological surfaces. It also discusses applications of graph theory, such as transport networks and hazard assessments based on unified networks. The book is ideal for developers of grant proposals and researchers interested in exploring new areas of graph theory and its applications.
This book explores research topics in graph theory and its applications, from strongly perfect graphs and reconstruction conjectures to transport networks. It is ideal for researchers interested in exploring new areas of graph theory and its applications.
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The Mysteries of Mystery Snails
Facts and Myths
This book offers a comprehensive review of the literature on Chinese and Japanese mystery snails around the globe, providing details of their distribution in 10 continents and more than 130 countries. It discusses several fascinating facts on dispersal mechanisms, biology, ecology, impacts, and control, revealed from more than 900 peer-reviewed articles. The Chinese Mystery Snail has been in North America now for more than 130 years, and is the second oldest introduced freshwater mollusc species from Eurasia, the oldest being the Faucet Snail, Bithynia tentaculata, introduced in 1870. The scientific…
This book is a comprehensive review of Chinese and Japanese mystery snails around the globe. It discusses fascinating facts on their dispersal, biology, ecology, impacts, and control, drawing from more than 900 peer-reviewed articles. For anyone interested in invasive molluscs.
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This book takes readers on a fascinating journey through various mathematical concepts, including geometry, calculus, probability, and topics that students have never seen in the classroom. Unlike traditional textbooks that focus on “how” to solve problems, this book challenges readers to think deeply about the “why” and “why not” of math concepts. It is accessible, enjoyable, and engaging. Featuring relatable student characters engaging in conversations about math, this book brings complex topics to life. Through interesting stories and real-world problems, readers will learn about the best ways to approach and…
Go on a mathematical adventure that challenges you to think about the “why,” not just the “how.” Featuring relatable characters and real-world problems, this book brings complex topics to life. A fun and engaging read that trains your mind to think mathematically.
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This book presents an exploration of the wave and vibration equation in one, two and three dimensions, with emphasis on singular solutions. The distinction between the wave treatment and the vibration treatment is particularly discussed with the causality principle being the leading principle for waves in this context. The necessity of regularization of the singular solutions is presented whilst the scattered waves are differentiated from the reflected (and refracted) waves, according to Huygens principle. The physical content of the wave equation is underlined. Relevant applications are included and some more…
Explore the wave and vibration equation, emphasizing singular solutions and physical content. This book covers applications from tsunamis and storm breakers to the ringing of bells and collapsing towers. For students, researchers, and engineers in physics and applied mathematics.
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This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented,…
This historical account traces the discovery of a singular wave in 1834 to the development of modern soliton theory. It describes deep connections between soliton theory and nonlinear continuum mechanics, with wide applications for research scientists and advanced students.
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One major problem of contemporary physics is posed by the incompatibility of the two greatest theories of the 20th century: quantum mechanics (QM) and general relativity (GR). Joining them gives rise to a perturbatively non-renormalizable quantum gravity theory. The two theories, on their own, have been amazingly successful, and quantum mechanics, in particular, gave rise to many of the recent technical advances that have revolutionized our lives. Today, however, there is a lack of an over-arching theoretical framework within which both QM and GR successes could be accommodated. This book…
A major problem of contemporary physics is the incompatibility of its two greatest theories: quantum mechanics and general relativity. There is a lack of an over-arching framework to unite them. This book provides an accessible guideline to a possible framework.
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Semirings as an algebraic structure have been known since 1934, but remained unapplied for mathematical purposes for a long time. It has only been in the past decade that they have been used in cryptography. The advantage of (additively) idempotent semirings is that the additive operation does not have an inverse, which can help in preventing the breakage of a cryptosystem. This book describes a number of cryptographic protocols, as well as the hard mathematical problems on which their security is based. It will appeal to cryptographers and specialists in…
Semirings are used in cryptography as their additive operation lacks an inverse, preventing cryptosystem breakage. This book describes such protocols and the hard math their security is based on, appealing to cryptographers and specialists in applied algebra.
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This book provides a comprehensive background for analysis of the finite deformation of materials. It is intended for engineering scientists, applied mathematicians, and advanced students beginning their studies in the field. The book begins with the geometry of deformation and motion in finite straining. This is followed by the general theory of stress and stress measures (corresponding to each strain measure) and balance laws of continuum physics. Rotating reference frames and related issues of invariance, objective stress-rates, and material spin are then covered. Simple shearing examples illustrate and clarify stress…
This book provides a comprehensive background for analysis of the finite deformation of materials. It covers deformation geometry, stress measures, and balance laws, with applications in rubber elasticity and metal plasticity, including experiments and illustrations.
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The Origin of Geometry in India
A Study in the Śulbasūtras
This book is the first complete study of the origin of geometry in India. In Ancient India, brick-built fire-altars (citi-s) were ordained for the Soma sacrifice, a Vedic rite, which led to the compilation of rule-books for making and arranging bricks. These volumes, called Śulbasūtra-s, represent the first available texts of both geometry and mensuration, and were composed from 600 BCE, although the actual practice goes back to c. 1500 BCE. This book begins by detailing the history of geometry in Egypt, Mesopotamia, and Greece, and shows that geometry everywhere…
The ancient Śulbasūtras, composed from 600BCE, were rule-books for making and arranging bricks, and represent the first available texts of both geometry and mensuration. This publication uses them as a lens to view the origin of geometry in India and elsewhere.
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