Matematik for ingeniører

This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta. The authors address the development of the distinguished geometrization on dual 1-jet spaces for time-dependent Hamiltonians, in contrast with the time-independent variant on cotangent bundles. Two parts are presented to include both geometrical theory and the applicative models: Part One: Time-dependent Hamilton Geometry and Part Two: Applications to Dynamical Systems, Economy and Theoretical Physics. The authors present 1-jet spaces and their duals as appropriate fundamental ambient mathematical spaces used to model classical and quantum field theories. In addition, the authors present dual jet Hamilton geometry as a distinct metrical approach to various interdisciplinary problems.

Artificial intelligence (AI) has the potential to significantly improve efficiency, reduce costs, and increase the speed and accuracy of financial decision-making, making it an increasingly important tool for financial professionals. One way that AI can improve efficiency in finance is by automating tasks and processes that are time-consuming and repetitive for humans. For example, AI algorithms can be used to analyze and process large amounts of data, such as financial statements and market data, in a fraction of the time that it would take a human to do so. This can allow financial professionals to focus on higher-value tasks, such as interpreting data and making strategic decisions, rather than being bogged down by mundane tasks. AI can also reduce costs in finance by increasing automation and eliminating the need for certain tasks to be performed manually. This can result in cost savings for financial institutions, which can then be passed on to customers in the form of lower fees or better services. AI can be used to identify unusual patterns of activity that may indicate fraudulent behavior. This can help financial institutions reduce losses from fraud and improve customer security. AI-powered chatbots and virtual assistants can help financial institutions provide faster, more efficient customer service, particularly when it comes to answering common questions and handling routine tasks. Some financial institutions are using AI to analyze market data and make trades in real-time. AI-powered trading algorithms can potentially make faster and more accurate trading decisions than humans. In terms of speed and accuracy, AI algorithms can analyze data and make decisions much faster than humans, and can do so with a high degree of accuracy. This can be particularly useful in fast-moving financial markets, where quick and accurate decision-making can be the difference between success and failure.This book highlights how AI in finance can improve efficiency,reduce costs, and increase the speed and accuracy of financial decision-making. Moreover, the book also focuses on how to ensure the responsible and ethical use of AI in finance.This book is a valuable resource for students, scholars, academicians, researchers, professionals, executives, government agencies, and policymakers interested in exploring the role of artificial intelligence (AI) in finance. Its goal is to provide a comprehensive overview of the latest research and knowledge in this area, and to stimulate further inquiry and exploration.

This textbook provides readers a comprehensive introduction to numerical methods, using MATLAB®. The authors discuss the theory and application of the most often used numerical methods, using MATLAB as a computational tool. The book is designed to be accessible to readers of varying backgrounds, so the presentation focuses more on the description, implementation, and application of the methods and less on the mathematical details. This book not only covers the most important methods and techniques of scientific computation, but also contains a great amount of code and implementations, facilitating the process of learning and application.

This book, dedicated to Professor Georgi M. Dimirovski on his anniversary, contains new research directions, challenges, and many relevant applications related to many aspects within the broadly perceived areas of systems and control, including signal analysis and intelligent systems. The project comprises two volumes with papers written by well known and very active researchers and practitioners. The first volume is focused on more foundational aspects related to general issues in systems science and mathematical systems, various problems in control and automation, and the use of computational and artificial intelligence in the context of systems modeling and control. The second volume is concerned with a presentation of relevant applications, notably in robotics, computer networks, telecommunication, fault detection/diagnosis, as well as in biology and medicine, and economic, financial, and social systems too.

This book provides a mechanical engineering-based analysis of wave dispersion response in various structures created from different materials. Looking at materials including strengthened nanocomposites, functionally graded materials, metal foams and anisotropic materials, it uses analytical solution methods to solve typical problems.

This book introduces Multi-objective design methods to solve Multi-objective optimization problems of linear/non-linear dynamic systems under intrinsic random fluctuation and external disturbance. All proposed design methods are based on rigorous theoretical results and their applications are focused on practical engineering design example.

This book focuses on open issues of Society 5.0, a new paradigm of a society, that balances a human-centred approach and technologies based on cyber-physical systems and artificial intelligence. The book contains results of how intelligent or cyber-solutions help to improve the quality of life in society despite new challenges. This book includes five sections. Section Society 5.0: Biomedicine and Healthcare present how cyber-physical systems help in healthcare, e.g. analysis of clinical data in pregnant women with hypertension, breast cancer diagnostics, healthy diet design and others. In the chapter, the problem of data analysis and optimization is considered. The second Section, Society 5.0: Human-centric Cyber-Solutions highlight new findings on constructing virtual reality simulators, training of workers on the basis of equipment's digital twins, development of human capital. Society 5.0: Socio-Economic Systems Modelling includes chapters concerning the application of quantum-like mathematical models for the analysis of socio-economic systems, indicative planning models for agriculture, approaches of assessing and monitoring competitiveness risks of regions. A section, Society 5.0: Industrial Cyber-Solutions provides new results on cyber-physical systems of Russian oil market, railway joint diagnostics, and information support for maintenance and repair of a machine-building cyber-physical system. The last section, Society 5.0: Cyber-Solutions Security consider interoperability issues of security, the video conferencing, and scaling networks.This book is directed to researchers, practitioners, engineers, software developers, professors and students. We do hope the book will be useful for them.

This book summarizes new discoveries on fracturing in chalk. Based on studies on the Danish North Sea, this book shows how observations from outcrop analogues, core and seismic data can be used to characterize the density, distribution and geometry of natural fractures in chalk and marl. Laboratory experiments on chalk samples reveal the controls on the geomechanical properties of chalk and thus on the growth of natural fractures. Finally, various modeling techniques are employed to investigate the mechanical deformation in the chalk structures of the Danish North Sea and to predict fracture distribution and geometry in the subsurface. An understanding of fracture density, distribution and geometry is essential for planning efficient fluid extraction or injection strategies and CO2 sequestration. This book provides the necessary knowledge.

This book examines how the rapid acceleration and interconnection of globalization comes with the need for more flexible and adaptable solutions to complex problems and solutions. It describes and demonstrates possible combinations of methods and methodologies to address the complex problems that the world offers us today. Sharing meaningful experiences of the application of workshops in mixed public private companies and with vulnerable communities and peacebuilding communities. The text offers readers, who are looking for tools to face complexity and enhance their projects, real-world examples and accessible methods. The book is based on advanced engineering tools however it is understandable and accessible to a broad audience.This book is for decision makers involved with social complex systems who are uncertain about how they should start and proceed. Discussions on new methodologies to support engineering interventions with communities are being shown. A new multi-methodology proposal called ¿Complexity Funnel Methodology¿ (CFM) dissected in ¿Social Transformation Workshops¿ (STW) is provided and discussed. It is used with combinations of different methods and methodologies of critical Systems thinking. The implementation of this methodology is described using a case study approach.

This book contains high-quality refereed research papers presented at the 6th International Conference on Computer Science, Engineering, and Education Applications (ICCSEEA2023), which took place in Warsaw, Poland, on March 17¿19, 2023, and was organized by the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute¿, the National Aviation University, Lviv Polytechnic National University, the Polish Operational and Systems Society, Warsaw University of Technology, and the International Research Association of Modern Education and Computer Science. The book covers a variety of topics, including cutting-edge research in computer science, artificial intelligence, engineering techniques, smart logistics, and knowledge representation with educational applications. The book is an invaluable resource for academics, graduate students, engineers, management professionals, and undergraduate students who are interested in computer science and its applications in engineering and education.

High dimensional reference architectures presented here allows confronting and prevailing over the growing complexity of polytopic projects implementations.Such projects should be envisaged giving that conventional systems operations, equipments, methodologies or organizations will reach their limits for self-evolvability in high complexity conditions. Self-evolvable high complexity systems are based on high dimensional polytopic reference architectures.Polytope is the general term of the sequence: point, line, polygon, polyhedron and so on.The polytopic projects are targeting the artificiality, not only for materials where it is well known and applied, but also for biological, cognitive, intelligent and mathematical systems. The book highlights the polytopic projects basic similarity despite the noticeable difference as domains of application. The roads to follow and the algebra of changing roads are emphasized.The book is divided in 9 chapters. Chapter 1 introduces the Polytopic Roadmap to 4D and beyond. The role for the dialogue of processes in duality of the non-Aristotelian Logic of Contradiction and of Included Middle is emphasized for different domains. Chapter 2 refers to chemical systems. Supramolecular chemistry, metal organic frameworks, MOF, and reaction networks, are the examples considered in the frame of polytopic chemistry. Chapter 3 refers to biological systems. Biological dynamical hierarchies and quasi-species are the considered case studies. Technological and scientific projects targeting artificiality for cells and viruses are considered. Chapter 4 refers to cognitive systems. Developmental stages, formal and relational concepts analysis, and neural coding are considered here. The roles of the 4D systems of systems of systems and of conceptual 4D-cube are emphasized. Artificiality for cognitive systems is the object of study.Chapter 5 refers to mathematical systems. Modeling levels and the 4D digital twins are discussed. Hopf monoids as tools for the study of combinations and separations, dual graded graphs and V-models are informally presented. Chapter 6 refers to application of formal concept analysis, FCA, for high dimensional separations, nesting and drug delivery. Chapter 7 refers to polytopic engineering systems as multiscale transfer, distributors-collectors, cyclic operations, middle vessel columns, mixing, assembly and designs. Equipments have been characterized using Polytopic Roadmaps and classified by Periodic Tables. Chapter 8 introduces polytopic industry, economy, society and sustainability. Chapter 9 outlines new domains of interest as arts and architecture, transdisciplinarity, complex systems and unity of sciences and engineering.Polytopic Roadmaps are proposed as Method for experts from various fields to synthesize their thinking and capabilities into new projects implementation to face and surpass high complexity. A repetitive finding of this book is that self-evolvability observed in physical systems is based on the same directed sequence of reference architectures as the self-evolvability of concepts in our mind. Continuing to develop the field of self-evolvable systems and presenting the polytopic roadmaps for 4D and beyond advances in ever growing complexity domains, the book will be useful to engineers, researchers, entrepreneurs and students in different branches of production, complex systems sciences and engineering, ecology and applied mathematics.

This monograph is focused on control law design methods for asymptotic tracking and disturbance rejection in the presence of uncertainties. The methods are based on adaptive implementation of the Internal Model Principle (IMP). The monograph shows how this principle can be applied to the problems of asymptotic rejection/tracking of a priori uncertain exogenous signals for linear and nonlinear plants with known and unknown parameters. The book begins by introducing the problems of adaptive control, the challenges that are faced, modern methods and an overview of the IMP. It then introduces special observers for uncertain exogeneous signals affecting linear and nonlinear systems with known and unknown parameters. The basic algorithms of adaptation applied to the canonical closed-loop error models are presented. The authors then address the systematic design of adaptive systems for asymptotic rejection/tracking of a priori uncertain exosignals. The monograph also discusses the adaptive rejection/tracking of a priori uncertain exogenous signals in systems with input delay, the problems of performance improvement in disturbance rejection and reference tracking and the issue of robustness of closed-loop systems. Adaptive Regulation provides a systematic discussion of the IMP applied to a variety of control problems, making it of interest to researchers and industrial practitioners.

This book introduces analytic solution methods for viscous flow problems, which is important in fluid mechanics. The author, after many years of experience in teaching and research, has refined useful analytic methods to treat fluid mechanics problems. This book is written in concise and understandable terms and is beneficial to practicing scientists and engineers who would like to understand and solve laminar fluid mechanics problems. The author provides new materials and insights and presents examples that are succinct to illustrate the methodology.

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 featuresThe book advances widely popular topics of  cancer origin, treatment and understanding of its progressThe 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.

The book is devoted to the solution of one general problem of the theory of a three-dimensional quasi-stationary sinusoidal and pulse electromagnetic field. These studies, unlike many well-known works, are based on obtained exact analytical solution of the problem for the field, generated by external current sources near the conducting body with plane surface. The solution for the vector and scalar potentials, electric and magnetic intensities in the dielectric and conducting media is found without restrictions on the configuration of current sources,properties of the media and field frequency. Some general properties of field formation for arbitrary field in the considered system are obtained (in particular, full compensation by the field of the electric charge distributed on the interface between the media, the normal component of the induced external electric field and, accordingly, the equality to zero the components both of the current density and the electric field intensity perpendicular to the interface; the non-uniform electromagnetic field decreases in depth of conducting medium faster than uniform field). It is shown that the exact analytical solution depends on the values of the parameter proportional to the ratio of the field penetration depth to the distance between the external field sources and the body. The concept of strong skin effect is extended to the case of small value of the introduced parameter. A significant simplification of theexpressions was obtained as an asymptotic expansion on this small parameter. In the case of pulsed fields approximate method gives the highest accuracy during important initial period of pulse time. For asymptotic expansion the approximate impedance boundary condition is generalized to the diffusion of non-uniform field into conducting medium. The book is intended for the researchers, postgraduate students and students specialized in theory and calculations of electromagnetic fields.

This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach.The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature.This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.

In this book, we study decision trees for fault diagnosis in circuits and switching networks, which are among the most fundamental models for computing Boolean functions. We consider two main cases: when the scheme (circuit or switching network) has the same mode of operation for both calculation and diagnostics, and when the scheme has two modes of operation¿normal for calculation and special for diagnostics. In the former case, we get mostly negative results, including superpolynomial lower bounds on the minimum depth of diagnostic decision trees depending on scheme complexity and the NP-hardness of construction diagnostic decision trees. In the latter case, we describe classes of schemes and types of faults for which decision trees can be effectively used to diagnose schemes, when they are transformed into so-called iteration-free schemes.The tools and results discussed in this book help to understand both the possibilities and challenges of using decision trees to diagnosefaults in various schemes. The book is useful to specialists both in the field of theoretical and technical diagnostics.It can also be used for the creation of courses for graduate students.

The book includes papers about various problems of dependable operation of computer systems and networks, which were presented during the 18th DepCoS-RELCOMEX conference. Their collection can be an interesting source material for scientists, researchers, practitioners, and students who are dealing with design, analysis, and engineering of computer systems and networks and must ensure their dependable operation.The increasing role of artificial intelligence algorithms and tools in modern information technology and computer engineering, especially rapid expansion of tools based on deep learning methods, calls for extending our view on system dependability. Selection of papers in these proceedings not only illustrates a wide-ranging variety of multidisciplinary topics which should be considered in this context but also proves that virtually all areas of contemporary computer systems and networks musttake into account an aspect of dependability.

The book consists of 8 parts: Energy Informatics, Electric Power Engineering, Heat Power Engineering, Nuclear Power Engineering, Renewable Power Engineering, Fuels, Transport, and Environmental Safety. The results presented in this book are aimed at solving some of the technical issues proposed by the Ukraine Recovery Plan and other important scientific and applied problems in the field of energy. Scientists from leading Ukrainian academic institutions and universities are working on this book.This book is for scientists, researchers, engineers, as well as lecturers and postgraduates of higher education institutions dealing with energy sector, power systems, ecological safety, etc.

Special Topics in Structural Dynamics & Experimental Techniques, Volume 5: Proceedings of the 40th MAC, A Conference and Exposition on Structural Dynamics, 2022, the fifth volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on:Analytical MethodsEmerging Technologies for Structural DynamicsEngineering ExtremesExperimental TechniquesFinite Element Techniques

Process Control details the core knowledge and practical skills that a successful process control practitioner needs. It explains the essential technologies that are in use in current industrial practice or which may be wanting for the future. The book focuses on practical considerations, not only on those that make a control solution work, but also on those that prevent it from failing, especially for complex control loops and plant-wide control solutions.After discussing the indispensable role of control in modern process industries, the authors concentrate on the skills required for process analysis, control design, and troubleshooting. One of the first books to provide a systematic approach and structured methodology for process analysis and control design, Process Control illustrates that methodology with many practical examples that cover process control, equipment control, and control calculations derived from real projects and applications. The book uses 229 drawings and 83 tables to make the concepts it presents more intuitive and its methodology easy to follow.Process Control will help the practising control engineer to benefit from a wealth of practical experience and good ideas on how to make control work in the real world and students training to take up roles in process control are shown the applied relevance of control theory in the efficient functioning of industrial plant and the considerations needed to make it work.Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

There are several textbooks and monographs on dislocations and the mechanical and physical properties of metals, but most of them discuss the topics in terms of more or less one-dimensional or scalar quantities. However, actual metallic materials are often three-dimensionally heterogeneous in their microstructure, and this heterogeneity has a significant impact on the macroscopic mechanical properties. With advances in computational technology, the complexity introduced by spatial heterogeneity in the microstructure of metals can now be explored using numerical methods. This book explains in simple terms the idea of extending the continuum mechanics theory of plastic deformation of crystals to three-dimensional analysis and applying it to the analysis of more realistic models of metal microstructures. This book links solid mechanics and materials science by providing clear physical pictures and mathematical models of plastic slip deformation and the accumulation of dislocations and atomic vacancies in metallic materials. Both monotonic and cyclic loading cases are considered.

This book presents select, recent developments in nonlinear and complex systems reported at the 1st Online Conference on Nonlinear Dynamics and Complexity, held on November 23-25, 2020. It provides an exchange recent developments, discoveries, and progresses in Nonlinear Dynamics and Complexity. The collection presents fundamental and frontier theories and techniques for modern science and technology, stimulates more research interest for exploration of nonlinear science and complexity; and passes along new knowledge and insight to the next generation of engineers and technologists in a range of fields. 

Sensors and Instrumentation, Aircraft/Aerospace and Energy Harvesting, Volume 7:  Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2020, the seventh volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Shock & Vibration, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing including papers on:Alternative Sensing & AcquisitionActive ControlsInstrumentationAircraft/Aerospace & Aerospace Testing Techniques Energy Harvesting

Lisa Schneider entwickelt und implementiert ein Untersuchungsinstrument zur Analyse von Lösungsprozessen beim mathematischen Modellieren, das Modelling-Activity-Interaction-Tool (MAI-Tool). Das MAI-Tool zeichnet sich durch eine digitale Erfassung sowie eine automatisierte Darstellung und algorithmische Auswertung der Daten aus. Im Rahmen einer empirischen Studie wird das MAI-Tool angewendet, in der Modellierungsprozesse von Lernenden beim Lösen einer mathematischen Modellierungsaufgabe untersucht werden: Die Hälfte der Lernenden erhielt eine Unterweisung in idealtypische Modellierungsprozesse, die andere Hälfte nicht. Der Einfluss der Unterweisung auf die Struktur individueller Lösungsprozesse kann nachgewiesen werden und daraus ableitend Hürden während des Modellierens identifiziert werden. Außerdem werden Ergebnisse hinsichtlich des Zusammenhangs von Interaktionen und der Gruppenstruktur präsentiert. Die in der Studie erhobenen Daten werden zur Entwicklung eines Algorithmus mitMachine Learning verwendet, der individuelle Lösungsprozesse anhand von Strukturmerkmalen klassifiziert. Insgesamt leistet diese Forschungsarbeit einen Beitrag zur Grundlagenforschung in mathematischer Modellierung auf technologischer, empirischer und algorithmischer Ebene.

This book comprises chapters authored by experts who are professors and researchers in internationally recognized universities and research institutions. The book presents the results of research and descriptions of real-world systems, services, and technologies. Reading this book, researchers, professional practitioners, and graduate students will gain a clear vision on the state of the art of the research and real-world practice on system dependability and analytics.The book is published in honor of Professor Ravishankar K. Iyer, the George and Ann Fisher Distinguished Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign (UIUC), Urbana, Illinois. Professor Iyer is ACM Fellow, IEEE Fellow, AAAS Fellow, and served as Interim Vice Chancellor of UIUC for research during 2008-2011. The book contains chapters written by many of his former students.