Matematisk modellering

The fifth edition of this textbook has been completely revised and significantly extended in order to reflect the revolution of geodetic technologies, methods and applications during the last decade. The Global Geodetic Observing System established by the IAG utilizes a variety of techniques to determine the geometric shape of the earth and its kinematics, the variations of earth rotation, and the earth's gravity field. The societal importance of geodetic products was highlighted by the UN resolution on the Global Geodetic Reference Frame. In this context, both space and terrestrial techniques play a fundamental role. Recent space missions are monitoring climate-relevant processes such as mass transport in the Earth system and sea level changes. The analysis of the time variation of the geodetic products provides the link to neighboring geosciences and contributes to proper modelling of geodynamic processes. New satellite mission concepts and novel technologies such as quantum gravimetry and optical clocks show great potential to further improve the geodetic observing system in the future. The book especially addresses graduate students in the fields of geodesy, geophysics, surveying engineering, geomatics, and space navigation. It should also serve as a reference for geoscientists and engineers facing geodetic problems in their professional work. The book follows the principal directions of geodesy, providing the theoretical background as well as the principles of measurement and evaluation methods, which is enriched with numerous figures. An extensive reference list supports further studies.

The book presents select proceedings of Global meet on 'Computational Modelling and Simulation, Recent Innovations, Challenges and Perspectives, 2020. This book covers leading-edge technologies from different domains such as computation in optimization and control, multiscale and multiphysics modeling and computation analysis, environmental modeling, modeling approaches to enterprise systems and services, finite element analysis, dependability and security, high-performance computation/cloud computing applications, computational biology and chemistry and computational mechanics. The primary goal of this book is to strengthen pre-eminence in computational modeling and simulation by catalyzing the transformative use of innovative developments in a wide range of disciplines to achieve lasting societal impact. The book discusses on how to perform simulation of large complex dynamic systems in an efficient manner using advanced computational analysis. The inter-disciplinary nature of the book would be a valuable reference for academicians and research scientists, industrialists interested in modelling and simulation driven by computational technology.

Hierarchical Modeling of Energy Systems presents a detailed methodology for hierarchical modeling of large-scale complex systems with a focus on energy systems and their expansion planning and control. General methodological principles of hierarchical modeling are analyzed, and based on this analysis, a generalized technology for the hierarchical approach is presented. The mathematical foundations of decomposition and bi-level programming, as well as the possibility of using information technologies are also considered. The theoretical propositions are demonstrated by numerous hierarchical modeling examples aimed at planning the development of the energy sector and expansion of energy systems, analyzing, and optimizing these systems, and controlling their operation. In addition, codes and sample simulations are included throughout. This is an invaluable guide for researchers, engineers, and other specialists involved in the development, control and management of energy systems, while the summary of fundamental principles and concepts in energy modeling makes this an accessible learning tool for graduate students on any course involving energy systems or energy modeling.

This book investigates human-machine systems through the use of case studies such as crankshaft maintenance, liner piston maintenance, and biodiesel blend performance. Through mathematical modelling and using various case studies, the book provides an understanding of how a mathematical modelling approach can assist in working out problems in any industrial-oriented activity.Mathematical Modelling: Simulation Analysis and Industrial Applications details a data analysis approach using mathematical modelling sensitivity. This approach helps in the processing of any type of data and can predict the result so that based on the result, the activity can be controlled by knowing the most influencing variables or parameters involved in the phenomenon. This book helps to solve field and experimental problems of any research activity using a data-based modelling concept to assist in solving any type of problem.Students in manufacturing, mechanical, and industrial engineering programs will find this book very useful. This topic has continued to advance and incorporate new concepts so that the manufacturing field continues to be a dynamic and exciting field of study.

This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities.New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study. Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8. As in previous editions, end-of-chapter exercises appear for all chapters.From the reviews of the Third Edition:"e;... this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn."e; (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)

The text covers a wide range of topics such as mathematical modeling of crop pest control management, water resources management, impact of anthropogenic activities on atmospheric carbon dioxide concentrations, impact of climate changes on melting of glaciers and polar bear populations, dynamics of slow-fast predator-prey system and spread and control of HIV epidemic. It emphasizes the use of mathematical modeling to investigate the fluid flow problems including the breaking of viscoelastic jet, instability arising in nanofiber, flow in an annulus channel, and thermal instability in nano-fluids in a comprehensive manner. This book will be a readily accessible source of information for the students, researchers and policymakers interested in the application of mathematical and computational modeling techniques to investigate various biological and engineering phenomena.FeaturesFocuses on the current modeling and computational trends to investigate various ecological, epidemiological, and engineering systems.Presents the mathematical modeling of a wide range of ecological and environmental issues including crop pest control management, water resources management, the effect of anthropogenic activities on atmospheric carbon dioxide concentrations, and impact of climate changes on melting of glaciers and polar bear population.Covers a wide range of topics including the breaking of viscoelastic jet, instability arising in nanofiber, flow in an annulus channel, and thermal instability in nano-fluids.Examines evolutionary models i.e., models of time-varying processes. Highlights the recent developments in the analytical methods to investigate the nonlinear dynamical systems.Showcases diversified applications of computational techniques to solve practical biological and engineering problems.The book focuses on the recent research developments in the mathematical modeling and scientific computing of biological and engineering systems. It will serve as an ideal reference text for senior undergraduate, graduate students, and researchers in diverse fields including ecological engineering, environmental engineering, computer engineering, mechanical engineering, mathematics, and fluid dynamics.

This book, following the three published volumes of the book, provides the main purpose to collect research papers and review papers to provide an overview of the main issues, results, and open questions in the cutting-edge research on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of this book is to collect papers of the world experts in mathematics, economics, and other applied sciences that is seminal to the future research developments. The majority of the papers presented in this book is authored by the participants in The Joint Meeting 6th International Conference on Dynamics, Games, and Science - DGSVI - JOLATE and in the 21st ICABR Conference.  The scientific scope of the conferences is focused on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology, and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of the conference is to bring together some of the world experts in mathematics, economics, and other applied sciences that reinforce ongoing projects and establish future works and collaborations.

This book provides readers with a comprehensive and recent exposition in deep learning and its multidisciplinary applications, with a concentration on advances of deep learning architectures. The book discusses various artificial intelligence (AI) techniques based on deep learning architecture with applications in natural language processing, semantic knowledge, forecasting and many more.  The authors shed light on various applications that can benefit from the use of deep learning in pattern recognition, person re-identification in surveillance videos, action recognition in videos, image and video captioning. The book also highlights how deep learning concepts can be interwoven with more modern concepts to yield applications in multidisciplinary fields.Presents a comprehensive look at deep learning and its multidisciplinary applications, concentrating on advances of deep learning architectures;Includes a survey of deep learning problems and solutions, identifying the main open issues, innovations and latest technologies;Shows industrial deep learning in practice with examples/cases, efforts, challenges, and strategic approaches.

This proceedings volume contains selected revised and extended research articles written by researchers who participated in the World Congress on Engineering and Computer Science 2015, held in San Francisco, USA, 21-23 October 2015. Topics covered include engineering mathematics, electrical engineering, circuits, communications systems, computer science, chemical engineering, systems engineering, manufacturing engineering, and industrial applications.The book offers the reader an overview of the state of the art in engineering technologies, computer science, systems engineering and applications, and will serve as an excellent reference work for researchers and graduate students working in these fields.

This edited volume is a collection of selected research articles discussing the analysis of infectious diseases by using mathematical modelling in recent times. Divided into two parts, the book gives a general and country-wise analysis of Covid-19. Analytical and numerical techniques for virus models are presented along with the application of mathematical modelling in the analysis of their spreading rates and treatments. The book also includes applications of fractional differential equations as well as ordinary, partial and integrodifferential equations with optimization methods. Probability distribution and their bio-mathematical applications have also been studied. This book is a valuable resource for researchers, scholars, biomathematicians and medical experts.

Unsichtbar und zugleich omnipräsent, erobern sich Computermodelle ständig neue Anwendungsfelder. Ihre Macht verdanken sie den immensen Kapazitäten moderner Rechnersysteme, und sie wird zusätzlich befeuert durch das maschinelle Lernen aus riesigen Datenbergen. Digitale Patienten, Szenarien zum Klimawandel, Missionen zu fernen Planeten, das Jonglieren an den Finanzmärkten, die Entwicklung nuklearer Waffensysteme ¿ anhand vielfältiger Episoden und persönlicher Erlebnisse des Autors bietet Ihnen dieses Buch Einblick in eine faszinierende Welt, die zu einer wesentlichen Quelle des Erkenntnisgewinns geworden ist. Doch die unaufhaltsame Mathematisierung schürt auch Ängste: Sind wir, wie Goethes Zauberlehrling, schon tief im Netz der Algorithmen und Computermodelle verstrickt und verlieren die Kontrolle über ihre Macht? Wie ein modernes Orakel stillen Computermodelle unsere Sehnsucht nach einer berechenbaren Zukunft. Doch es lauern Fallstricke, aufgrund derer ihre Prognosen gravierend danebenliegen können. Blindes Vertrauen beim Laien wie auch starre Modellgläubigkeit beim Experten resultieren dann in Fehlentscheidungen, dem Versagen technischer Systeme oder ökonomischem Desaster. Kann man diesen Fallstricken entgehen?Zum Lesen dieses Buches benötigen Sie Neugierde sowie Offenheit für Überraschendes, aber keine Fachkenntnisse. Eine Fülle von Abbildungen veranschaulicht die wesentlichen Zusammenhänge, ergänzt um spannende Anekdoten aus Wissenschaft und Technik. Wollen Sie mehr erfahren? Dann kommen Sie mit auf diesen Streifzug durch den Kosmos der Computermodelle.