This book explains how the partial differential equations (pdes) in electroanalytical chemistry can be solved numerically. It guides the reader through the topic in a very didactic way, by first introducing and discussing the basic equations along with some model systems as test cases systematically. Then it outlines basic numerical approximations for derivatives and techniques for the numerical solution of ordinary differential equations. Finally, more complicated methods for approaching the pdes are derived. The authors describe major implicit methods in detail and show how to handle homogeneous chemical reactions, even including coupled and nonlinear cases. On this basis, more advanced techniques are briefly sketched and some of the commercially available programs are discussed. In this way the reader is systematically guided and can learn the tools for approaching his own electrochemical simulation problems. This new fourth edition has been carefully revised, updated and extended compared to the previous edition (Lecture Notes in Physics Vol. 666). It contains new material describing migration effects, as well as arrays of ultramicroelectrodes. It is thus the most comprehensive and didactic introduction to the topic of electrochemical simulation.

This book presents the current trends, technologies, and challenges in Big Data in the diversified field of engineering and sciences. It covers the applications of Big Data ranging from conventional fields of mechanical engineering, civil engineering to electronics, electrical, and computer science to areas in pharmaceutical and biological sciences. This book consists of contributions from various authors from all sectors of academia and industries, demonstrating the imperative application of Big Data for the decision-making process in sectors where the volume, variety, and velocity of information keep increasing. The book is a useful reference for graduate students, researchers and scientists interested in exploring the potential of Big Data in the application of engineering areas.

This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000). Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems. The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view. The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.

1) Provides analytical solutions based on a three-phase model for composites of various structures 2) Identifies computational models to solve problems within all applications of composite materials 3) Constructs higher approximations of the Maxwell formula 4) Proposes efficient analytical algorithms ensuring reliable computational analysis

This book presents an exciting collection of contributions based on the workshop "Bringing Maths to Life" held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content useful as it addresses existing challenges in identifying the gaps between mathematical modeling and biological research. The shared solutions will aid and promote further collaboration between life sciences and mathematics.

This book presents the proceedings of the 10th International Parallel Tools Workshop, held October 4-5, 2016 in Stuttgart, Germany - a forum to discuss the latest advances in parallel tools. High-performance computing plays an increasingly important role for numerical simulation and modelling in academic and industrial research. At the same time, using large-scale parallel systems efficiently is becoming more difficult. A number of tools addressing parallel program development and analysis have emerged from the high-performance computing community over the last decade, and what may have started as collection of small helper script has now matured to production-grade frameworks. Powerful user interfaces and an extensive body of documentation allow easy usage by non-specialists.

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs which model real-life situations. Due to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. The book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. The book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. The book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences. useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering. .

This book opens up new ways to develop mathematical models and optimization methods for interdependent energy infrastructures, ranging from the electricity network, natural gas network, district heating network, and electrified transportation network. The authors provide methods to help analyze, design, and operate the integrated energy system more efficiently and reliably, and constitute a foundational basis for decision support tools for the next-generation energy network. Chapters present new operation models of the coupled energy infrastructure and the application of new methodologies including convex optimization, robust optimization, and equilibrium constrained optimization. Four appendices provide students and researchers with helpful tutorials on advanced optimization methods: Basics of Linear and Conic Programs; Formulation Tricks in Integer Programming; Basics of Robust Optimization; Equilibrium Problems. This book provides theoretical foundation and technical applications for energy system integration, and the the interdisciplinary research presented will be useful to readers in many fields including electrical engineering, civil engineering, and industrial engineering.

A nonsimple (complex) system indicates a mix of crucial and non-crucial events, with very different statistical properties. It is the crucial events that determine the efficiency of information exchange between complex networks. For a large class of nonsimple systems, crucial events determine catastrophic failures - from heart attacks to stock market crashes.This interesting book outlines a data processing technique that separates the effects of the crucial from those of the non-crucial events in nonsimple time series extracted from physical, social and living systems. Adopting an informal conversational style, without sacrificing the clarity necessary to explain, the contents will lead the reader through concepts such as fractals, complexity and randomness, self-organized criticality, fractional-order differential equations of motion, and crucial events, always with an eye to helping to interpret what mathematics usually does in the development of new scientific knowledge.Both researchers and novitiate will find Crucial Events useful in learning more about the science of nonsimplicity.

Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.

This contributed volume presents an overview of concepts, methods, and applications used in several quantitative areas of drug research, development, and marketing. Chapters bring together the theories and applications of various disciplines, allowing readers to learn more about quantitative fields, and to better recognize the differences between them. Because it provides a thorough overview, this will serve as a self-contained resource for readers interested in the pharmaceutical industry, and the quantitative methods that serve as its foundation. Specific disciplines covered include: Biostatistics Pharmacometrics Genomics Bioinformatics Pharmacoepidemiology Commercial analytics Operational analytics Quantitative Methods in Pharmaceutical Research and Development is ideal for undergraduate students interested in learning about real-world applications of quantitative methods, and the potential career options open to them. It will also be of interest to experts working in these areas.

This book covers all the relevant dictionary learning algorithms, presenting them in full detail and showing their distinct characteristics while also revealing the similarities. It gives implementation tricks that are often ignored but that are crucial for a successful program. Besides MOD, K-SVD, and other standard algorithms, it provides the significant dictionary learning problem variations, such as regularization, incoherence enforcing, finding an economical size, or learning adapted to specific problems like classification. Several types of dictionary structures are treated, including shift invariant; orthogonal blocks or factored dictionaries; and separable dictionaries for multidimensional signals. Nonlinear extensions such as kernel dictionary learning can also be found in the book. The discussion of all these dictionary types and algorithms is enriched with a thorough numerical comparison on several classic problems, thus showing the strengths and weaknesses of each algorithm. A few selected applications, related to classification, denoising and compression, complete the view on the capabilities of the presented dictionary learning algorithms. The book is accompanied by code for all algorithms and for reproducing most tables and figures. Presents all relevant dictionary learning algorithms - for the standard problem and its main variations - in detail and ready for implementation; Covers all dictionary structures that are meaningful in applications; Examines the numerical properties of the algorithms and shows how to choose the appropriate dictionary learning algorithm.

This book presents cutting-edge research on the use of physical and mathematical formalisms to model and quantitatively analyze biological phenomena ranging from microscopic to macroscopic systems. The systems discussed in this compilation cover protein folding pathways, gene regulation in prostate cancer, quorum sensing in bacteria to mathematical and physical descriptions to analyze anomalous diffusion in patchy environments and the physical mechanisms that drive active motion in large sets of particles, both fundamental descriptions that can be applied to different phenomena in biology. All chapters are written by well-known experts on their respective research fields with a vast amount of scientific discussion and references in order the interested reader can pursue a further reading. Given these features, we consider Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues as an excellent and up-to-date resource and reference for advanced undergraduate students, graduate students and junior researchers interested in the latest developments at the intersection of physics, mathematics, molecular biology, and computational sciences. Such research field, without hesitation, is one of the most interesting, challenging and active of this century and the next.

This book introduces readers to numerous multiplicative inverse functional equations and their stability results in various spaces. This type of functional equation can be of use in solving many physical problems and also has significant relevance in various scientific fields of research and study. In particular, multiplicative inverse functional equations have applications in electric circuit theory, physics, and relations connecting the harmonic mean and arithmetic mean of several values. Providing a wealth of essential insights and new concepts in the field of functional equations, the book is chiefly intended for researchers, graduate schools, graduate students, and educators, and can also used for seminars in analysis covering topics of functional equations.

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer's series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA's first funding phase, and provides an overview of SPPEXA's contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.

This book discusses the problems of complexity in industrial data, including the problems of data sources, causes and types of data uncertainty, and methods of data preparation for further reasoning in engineering practice. Each data source has its own specificity, and a characteristic property of industrial data is its high degree of uncertainty. The book also explores a wide spectrum of soft modeling methods with illustrations pertaining to specific cases from diverse industrial processes. In soft modeling the physical nature of phenomena may not be known and may not be taken into consideration. Soft models usually employ simplified mathematical equations derived directly from the data obtained as observations or measurements of the given system. Although soft models may not explain the nature of the phenomenon or system under study, they usually point to its significant features or properties.

This book, for biochemists and molecular biologists, presents the best and most recent computational tools and approaches for recognizing and analysing biological patterns such as those that occur in DNA, RNA, amino-acid sequences, molecular structural motifs, gene and protein families, and so on. These tools have largely been developed by computer scientists working in such areas as machine learning, computer vision, neural networks, graphics, data compression, statistics, and parallel computing, and a sizable proportion of the biological community needs help and guidance in biological informatics approaches to the rapidly growing databases of molecular and genetic information.

This book discusses the semantic foundations of concurrent systems with nondeterministic and probabilistic behaviour. Particular attention is given to clarifying the relationship between testing and simulation semantics and characterising bisimulations from metric, logical, and algorithmic perspectives. Besides presenting recent research outcomes in probabilistic concurrency theory, the book exemplifies the use of many mathematical techniques to solve problems in computer science, which is intended to be accessible to postgraduate students in Computer Science and Mathematics. It can also be used by researchers and practitioners either for advanced study or for technical reference.

The contributions included in the volume are drawn from presentations at ODS2019 - International Conference on Optimization and Decision Science, which was the 49th annual meeting of the Italian Operations Research Society (AIRO) held at Genoa, Italy, on 4-7 September 2019. This book presents very recent results in the field of Optimization and Decision Science. While the book is addressed primarily to the Operations Research (OR) community, the interdisciplinary contents ensure that it will also be of very high interest for scholars and researchers from many scientific disciplines, including computer sciences, economics, mathematics, and engineering. Operations Research is known as the discipline of optimization applied to real-world problems and to complex decision-making fields. The focus is on mathematical and quantitative methods aimed at determining optimal or near-optimal solutions in acceptable computation times. This volume not only presents theoretical results but also covers real industrial applications, making it interesting for practitioners facing decision problems in logistics, manufacturing production, and services. Readers will accordingly find innovative ideas from both a methodological and an applied perspective.

From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism." After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software.

Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering:
-General papers (survey of specific aspects of optimization and inverse problems in electromagnetism),
-Methodologies,
-Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer science, applied mathematics (PhD level) and to researchers interested in the topic.

This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introductory textbook on fuzzy logic, presenting theory together with examples and not always following the typical mathematical style of theorem-corollaries. Primarily intended to support engineers during their university studies, and to spark their curiosity about fuzzy logic and its applications, the book is also suitable for self-study, providing a valuable resource for engineers and professionals who deal with imprecision and non-random uncertainty in real-world applications.

This book provides engineers with focused treatment of the mathematics needed to understand probability, random variables, and stochastic processes, which are essential mathematical disciplines used in communications engineering. The author explains the basic concepts of these topics as plainly as possible so that people with no in-depth knowledge of these mathematical topics can better appreciate their applications in real problems. Applications examples are drawn from various areas of communications. If a reader is interested in understanding probability and stochastic processes that are specifically important for communications networks and systems, this book serves his/her need.

The primary focus of this book is an examination of longitudinal team communication and its impact on team performance. This theoretically-grounded, holistic examination of team communication includes cross-condition comparisons of team (i.e., distributed/in person, unrestricted/time pressured, two performance episodes) and employs multiple quantitative methodological approaches to examine the phenomena of interest. This book simultaneously provides practical content for researchers and practitioners in the social sciences and humanities. Included are step-by-step instructions for the methodologies employed, and distillations of findings via Managerial Minutes that highlight best practices and/or examples to help enhance team communication in practice.

This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous : insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book.