The present monograph defines, interprets and uses the matrix of partial derivatives of the state vector with applications for the study of some common categories of engineering. The book covers broad categories of processes that are formed by systems of partial derivative equations (PDEs), including systems of ordinary differential equations (ODEs). The work includes numerous applications specific to Systems Theory based on Mpdx, such as parallel, serial as well as feed-back connections for the processes defined by PDEs. For similar, more complex processes based on Mpdx with PDEs and ODEs as components, we have developed control schemes with PID effects for the propagation phenomena, in continuous media (spaces) or discontinuous ones (chemistry, power system, thermo-energetic) or in electro-mechanics (railway - traction) and so on. The monograph has a purely engineering focus and is intended for a target audience working in extremely diverse fields of application (propagation phenomena, diffusion, hydrodynamics, electromechanics) in which the use of PDEs and ODEs is justified.

This textbook presents a concise comparison of catalytic and biocatalytic systems outlining their catalytic properties and peculiarities. Moreover, it presents a brief introduction to the science of catalysis and attempts to unify different catalytic systems into a single, conceptually coherent structure. In fact, molecular dynamics and complexity may occur in both catalysts and biocatalysts, with many similarities in both their structural configuration and operational mechanisms. Moreover, the interactions between the different components of the catalytic system that are important in defining the overall activity, including the nature of active sites are discussed. Each chapter includes end of chapter questions supported by an online instructor solution manual. This textbook will be useful for undergraduate and graduate chemistry and biochemistry students.

Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended.

The key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin films, smart materials, and structural and topology optimization. One lecture deals with a topic important for nanomaterials: the passage from discrete to continuum problems by using nonlinear homogenization methods. Some papers reveal the role of parameterized or Young measures in description of microstructures and in optimal design. Other papers deal with recently developed methods both analytical and computational for estimating the effective behavior and field fluctuations in composites and polycrystals with nonlinear constitutive behavior.

All in all, the volume offers a cross-section of current activity in nonlinear homogenization including a broad range of physical and engineering applications. The careful reader will be able to identify challenging open problems in this still evolving field. For instance, there is the need to improve bounding techniques for nonconvex problems, as well as for solving geometrically nonlinear optimum shape-design problems, using relaxation and homogenization methods."

The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike standard approaches, it does not focus on any specific language, but aims to explain the underlying ideas. Typically, new concepts are first introduced in the particularly user-friendly Python language and then transferred and extended in various programming environments from C/C++, Julia and MATLAB to Maple and Mathematica. This includes various approaches to distributed computing. By examining and comparing different languages, the book is also helpful for mathematicians and practitioners in deciding which programming language to use for which purposes. At a more advanced level, special tools for the automated solution of partial differential equations using the finite element method are discussed. On a more experimental level, the basic methods of scientific machine learning in artificial neural networks are explained and illustrated.

Application of quantum mechanics in physics and chemistry often entails manipulation and evaluation of sums and products of coupling coefficients for the theory of angular momentum. Challenges encountered in such work can be tamed by graphical techniques that provide both the insight and analytical power. The book is the first step-by-step exposition of a graphical method grounded in established work. Copious exercises recover standard results but demonstrate the power to go beyond.

This book presents unique compendium of groundbreaking ideas where scientists from many different backgrounds are united in their interest in interdisciplinary approaches towards origins and development of cancers, innovative ways of searching for cancer treatment and the role of cancer in the evolution. Chapters give an unequivocal slice of all areas that relate to a quest for understanding cancer and its origin as many-fold nonlinear system, complexity of the cancer developments, a search for cancer treatment using artificial intelligence and evolutionary optimisation, novel modelling techniques, molecular origin of cancer, the role of cancer in evolution of species, interpretation of cancer in terms of artificial life and artificial immune systems, swarm intelligence, cellular automata, computational systems biology, genetic networks, cellular computing, validation through in vitro/vivo tumour models and tumour on chip devices. The book is an inspiring blend of theoretical and experimental results, concepts and paradigms. Distinctive features The book advances widely popular topics of cancer origin, treatment and understanding of its progress The book is comprised of unique chapters written by world top experts in theoretical and applied oncology, complexity theory, mathematics, computer science. The book illustrates attractive examples of mathematical and computer models and experimental setups.

Before you lies the proceedings oft he NATO Advanced Study Institute/Newton Institute Workshop "Confinement, duality and non perturbative aspects of QCD." The school covered the most important techniques to study Quantum Chromodynamics (QCD) andconfinement, fromlattice gauge theory, through Wilson's renormalisation group, to electromagnetic duality. The organisingcommittee existed of: Ian Drummond (DAMTP, Cambridge), Mikhail Shifman (Minneapolis), Peter West (King's, London), and Pierrevan Baal (Leiden), who acted as director oft he school. This summer school was the concluding activity ofa six month programme on "Non perturbative Aspects of Qua ntum Field Theory" taking place at the Isaac Newton Institute for Mathematical Sciences in Ca mbridge, UK, whic h started in January 1997, organised by David Olive, Pierre van Baal, and Peter West. A large number ofthe lecturers also participated in the programme and a few programme participants were asked to present a seminar at the school. Not contained in these proceedings are the seminars by Peter Landshoff (DAMTP, Cambridge) on "The Pomeron" and Ludwig Faddeev (Steklov Math. Inst., St. Petersburg) on "Knot like solitons in 3+1 dimen sional field theory." In additiont o the lectures and seminars there were two poster sessions at which participants presented their work. Authors and titles ofthese posters are listed on a separate page. These pro ceedings address the longstanding question of understanding how quarks are confined w ithin subnuclear particles.

This volume, which coincides with the centennial anniversary of the publication of the celebrated monograph "The General Problem of the Stability Motion" by A.M. Liapunov, reviews the current state of the art of the theory and applications of the Liapunov methods. The text contains an introduction and four chapters. Chapter 2 presents some general results in stability theory. The remaining chapters deal with applications in power engineering, chemical engineering, and in non-engineering fields such as economics and in the modelling of interacting species. The diversity of mathematical tools employed, and the described approach to mathematical modelling provide considerations for applications in many other fields. The text is suitable for mathematicians and engineers whose work involves the study and applications of stability theory in systems.

This volume details state-of-the-art computational methods designed to manage, analyze, and generally leverage epigenomic and epitranscriptomic data. Chapters guide readers through fine-mapping and quantification of modifications, visual analytics, imputation methods, supervised analysis, and integrative approaches for single-cell data. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Cutting-edge and thorough, Computational Epigenomics and Epitranscriptomics aims to provide an overview of epiomic protocols, making it easier for researchers to extract impactful biological insight from their data.

Invariant Theory of Matrices; H. Aslaksen, et al. Symmetries of Elementary Particles Revisited; A.O. Barut. Perturbative SU(1,1); H. Beker. A Dual Structure for the Quantal Rotation Group, SU(2); L.C. Biedenharn, M.A. Lohe. Some Points in the Quantization of Relativistic Grassmann Dependent Interaction Systems; A. Del Sol Mesa, R.P. Martinez y Romero. q-Difference Intertwining Operators for Uq(sI(4)) and q-Conformal Invariant Equations; V.K. Dobrev. A Quantum Mechanical Evolution Equation for Mixed States from Symmetry and Kinematics; H.D. Doebner, J.D. Hennig. Quantum Mechanical Motions over the Group Manifolds and Related Potentials; I.H. Duru. Quantum Violation of Weak Equivalence Principal in the Brans-Dicke Theory; Y. Fujii. Quantum Unitary and Pseudounitary Groups and Generalized Hadron Mass Relations; A.M. Gavrilik. Linear Coxeter Groups; J. Getino. Diffeomorphism Groups, Quasiinvariant Measures, and Infinite Quantum Systems; G.A. Goldin, U. Moschella. Algebraic Shells and the Interacting Boson Model of the Nucleus; B. Gruber. Recent Developments in the Application of Vector Coherent States; K.T. Hecht. Algebraic Theory of the Threebody Problem; F. Iachello. 18 additional articles. Index.

We have considered writing the present book for a long time, since the lack of a sufficiently complete textbook about complex analysis in infinite dimensional spaces was apparent. There are, however, some separate topics on this subject covered in the mathematical literature. For instance, the elementary theory of holomorphic vector- functions.and mappings on Banach spaces is presented in the monographs of E. Hille and R. Phillips [1] and L. Schwartz [1], whereas some results on Banach algebras of holomorphic functions and holomorphic operator-functions are discussed in the books of W. Rudin [1] and T. Kato [1]. Apparently, the need to study holomorphic mappings in infinite dimensional spaces arose for the first time in connection with the development of nonlinear anal- ysis. A systematic study of integral equations with an analytic nonlinear part was started at the end ofthe 19th and the beginning ofthe 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods. The most complete presentation of these methods comes from N. Nazarov. In the forties and fifties the interest in Liapunov's and Schmidt's analytic methods diminished temporarily due to the appearence of variational calculus meth- ods (M. Golomb, A. Hammerstein and others) and also to the rapid development of the mapping degree theory (J. Leray, J. Schauder, G. Birkhoff, O. Kellog and others).

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years."

"Biomedical Engineering: Health Care Systems, Technology and Techniques" is an edited volume with contributions from world experts. It provides readers with unique contributions related to current research and future healthcare systems. Practitioners and researchers focused on computer science, bioinformatics, engineering and medicine will find this book a valuable reference.

Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

This updated and enlarged Second Edition provides in-depth, progressive studies of kinematic mechanisms and offers novel, simplified methods of solving typical problems that arise in mechanisms synthesis and analysis - concentrating on the use of algebra and trigonometry and minimizing the need for calculus.;It continues to furnish complete coverage of: key concepts, including kinematic terminology, uniformly accelerated motion, and the properties of vectors; graphical techniques for both velocity and acceleration analysis; analytical techniques; and ready-to-use computer and calculator programmes for analyzing basic classes of mechanisms.;This edition supplies detailed explications of such new topics as: gears, gear trains, and cams; velocity and acceleration analyses of rolling elements; acceleration analysis of sliding contact mechanisms by the effective component method; four-bar analysis by the parallelogram method; and centre of curvature determination methods.

This book explores a different pragmatic approach to algorithmic complexity rooted or motivated by the theoretical foundations of algorithmic probability and explores the relaxation of necessary and sufficient conditions in the pursuit of numerical applicability, with some of these approaches entailing greater risks than others in exchange for greater relevance and applicability. Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently coexist for the first time, ranging from the dominant ones based upon popular statistical lossless compression algorithms (such as LZW) to newer approaches that advance, complement, and also pose their own limitations. Evidence suggesting that these different methods complement each other for different regimes is presented, and despite their many challenges, some of these methods are better grounded in or motivated by the principles of algorithmic information. The authors propose that the field can make greater contributions to science, causation, scientific discovery, networks, and cognition, to mention a few among many fields, instead of remaining either as a technical curiosity of mathematical interest only or as a statistical tool when collapsed into an application of popular lossless compression algorithms. This book goes, thus, beyond popular statistical lossless compression and introduces a different methodological approach to dealing with algorithmic complexity. For example, graph theory and network science are classic subjects in mathematics widely investigated in the twentieth century, transforming research in many fields of science from economy to medicine. However, it has become increasingly clear that the challenge of analyzing these networks cannot be addressed by tools relying solely on statistical methods. Therefore, model-driven approaches are needed. Recent advances in network science suggest that algorithmic information theory could play an increasingly important role in breaking those limits imposed by traditional statistical analysis (entropy or statistical compression) in modeling evolving complex networks or interacting networks. Further progress on this front calls for new techniques for an improved mechanistic understanding of complex systems, thereby calling out for increased interaction between systems science, network theory, and algorithmic information theory, to which this book contributes.

Important developments in the progress of the theory of rock mechanics during recent years are based on fractals and damage mechanics. The concept of fractals has proved to be a useful way of describing the statistics of naturally occurring geometrics. Natural objects, from mountains and coastlines to clouds and forests, are found to have boundaries best described as fractals. Fluid flow through jointed rock masses and clusterings of earthquakes are found to follow fractal patterns in time and space. Fracturing in rocks at all scales, from the microscale (microcracks) to the continental scale (megafaults), can lead to fractal structures. The process of diagenesis and pore geometry of sedimentary rock can be quantitatively described by fractals, etc. The book is mainly concerned with these developments, as related to fractal descriptions of fragmentations, damage and fracture of rocks, rock burst, joint roughness, rock porosity and permeability, rock grain growth, rock and soil particles, shear slips, fluid flow through jointed rocks, faults, earthquake clustering, and so on. The prime concerns of the book are to give a simple account of the basic concepts, methods of fractal geometry, and their applications to rock mechanics, geology, and seismology, and also to discuss damage mechanics of rocks and its application to mining engineering. The book can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.

Gaussian linear modelling cannot address current signal processing demands. In moderncontexts, suchasIndependentComponentAnalysis(ICA), progresshasbeen made speci?cally by imposing non-Gaussian and/or non-linear assumptions. Hence, standard Wiener and Kalman theories no longer enjoy their traditional hegemony in the ?eld, revealing the standard computational engines for these problems. In their place, diverse principles have been explored, leading to a consequent diversity in the implied computational algorithms. The traditional on-line and data-intensive pre- cupations of signal processing continue to demand that these algorithms be tractable. Increasingly, full probability modelling (the so-called Bayesian approach)-or partial probability modelling using the likelihood function-is the pathway for - sign of these algorithms. However, the results are often intractable, and so the area of distributional approximation is of increasing relevance in signal processing. The Expectation-Maximization (EM) algorithm and Laplace approximation, for ex- ple, are standard approaches to handling dif?cult models, but these approximations (certainty equivalence, and Gaussian, respectively) are often too drastic to handle the high-dimensional, multi-modal and/or strongly correlated problems that are - countered. Since the 1990s, stochastic simulation methods have come to dominate Bayesian signal processing. Markov Chain Monte Carlo (MCMC) sampling, and - lated methods, are appreciated for their ability to simulate possibly high-dimensional distributions to arbitrary levels of accuracy. More recently, the particle ?ltering - proach has addressed on-line stochastic simulation. Nevertheless, the wider acce- ability of these methods-and, to some extent, Bayesian signal processing itself- has been undermined by the large computational demands they typically mak

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers.

Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design.

This book provides a comprehensive overview of various aspects of the development of smart cities from a secure, trusted, and reliable data transmission perspective. It presents theoretical concepts and empirical studies, as well as examples of smart city programs and their capacity to create value for citizens. The contributions offer a panorama of the most important aspects of smart city evolution and implementation within various frameworks, such as healthcare, education, and transportation. Comparing current advanced applications and best practices, the book subsequently explores how smart environments and programs could help improve the quality of life in urban spaces and promote cultural and economic development.

This book addresses a range of aging intensity functions, which make it possible to measure and compare aging trends for lifetime random variables. Moreover, they can be used for the characterization of lifetime distributions, also with bounded support. Stochastic orders based on the aging intensities, and their connections with some other orders, are also discussed. To demonstrate the applicability of aging intensity in reliability practice, the book analyzes both real and generated data. The estimated, properly chosen, aging intensity function is mainly recommended to identify data's lifetime distribution, and secondly, to estimate some of the parameters of the identified distribution. Both reliability researchers and practitioners will find the book a valuable guide and source of inspiration.

This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Symposium on the Theory and Applications of Integral Methods in Science and Engineering, held virtually in July 2021, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

Within the Smart Grid, the combination of automation equipment, communication technology and IT is crucial. Interoperability of devices and systems can be seen as the key enabler of smart grids. Therefore, international initiatives have been started in order to identify interoperability core standards for Smart Grids. IEC 62357, the so called Seamless Integration Architecture, is one of these very core standards, which has been identified by recent Smart Grid initiatives and roadmaps to be essential for building and managing intelligent power systems. The Seamless Integration Architecture provides an overview of the interoperability and relations between further standards from IEC TC 57 like the IEC 61970/61968: Common Information Model - CIM. CIM has proven to be a mature standard for interoperability and engineering; consequently, it is a cornerstone of the IEC Smart Grid Standardization Roadmap. This book provides an overview on how the CIM developed, in which international projects and roadmaps is has already been covered and describes the basic use cases for CIM. This book has been written for both Power Engineers trying to get to know the EMS and business IT part of Smart Grid and for Computer Scientist finding out where ICT technology is applied in EMS and DMS Systems. The book is divided into two parts dealing with the theoretical foundations and a practical part describing tools and use cases for CIM.

Leyton's Process Grammar has been applied by scientists and engineers in many disciplines including medical diagnosis, geology, computer-aided design, meteorology, biological anatomy, neuroscience, chemical engineering, etc. This book demonstrates the following:

The Process Grammar invents several entirely new concepts in biological morphology and manufacturing design, and shows that these concepts are fundamentally important.

The Process Grammar has process-inference rules that give, to morphological transitions, powerful new "causal explanations."

Remarkably, the book gives a profound "unification" of "biological morphology" and "vehicle design."

The book invents over 30 new CAD operations that realize fundamentally important functions of a product.

A crucial fact is that the Process Grammar is an example of the laws in Leyton's Generative Theory of Shape which give the ability to recover the "design intents "for which the shape features of a CAD model were created. The book demonstrates that the Process Grammar recovers important design intents in biological morphology and manufacturing design. In large-scale manufacturing systems, the recovery of design intents is important for solving the interoperability problem and product lifecycle management.

This book is one of a series of books in Springer that elaborates Leyton's Generative Theory of Shape.