Matematik for ingeniører

This monograph represents the outcome of research effort of the authors on scalable synchronization of large-scale multi-agent systems (MAS). Cooperative control of multi-agent systems has been growing in popularity and is highly interdisciplinary in recent years. The application of synchronization of MAS includes automobile systems, aerospace systems, multiple-satellite GPS, high-resolution satellite imagery, aircraft formations, highway traffic platooning, industrial process control with multiple processes, and more. Most of the proposed protocols in the literature for synchronization of MAS require some knowledge of the communication network such as bounds on the spectrum of the associated Laplacian matrix and the number of agents. These protocols suffer from scale fragility wherein stability properties are lost for large-scale networks or when the communication graph changes. In the past few years, the authors of this monograph have worked on developing scale-free protocol design for various cases of MAS problems. The key contribution of the monograph is to offer a scale-free design framework and provide scale-free protocols to achieve synchronization, delayed synchronization, and almost synchronization in the presence of input and communication delays, input saturation and external disturbances. The scale-free design framework solely is based on the knowledge of agent models and does not depend on information about the communication network such as the spectrum of the associated Laplacian matrix or size of the network. Drawing upon their extensive work in this area, the authors provide a thorough treatment of agents with higher-order dynamics, different classes of models for agents, and the underlying networks representing actions of the agents. The high technical level of their presentation and their rigorous mathematical approach make this monograph a timely and valuable resource that will fill a gap in the existing literature.

* Contains computer algebra worksheets or "recipes" designed using MAPLE (System 10); no prior knowledge of MAPLE is assumed* Effective computational science text for first- and second-year undergraduates in mathematics, physics, engineering, chemistry, economics, biology, and pre-medicine* Examples and problems provide basis for both self-study and on-line course

This book reports the developments of the Total Least Square (TLS) algorithms for parameter estimation and adaptive filtering. Specifically, this book introduces the authors¿ latest achievements in the past 20 years, including the recursive TLS algorithms, the approximate inverse power iteration TLS algorithm, the neural based MCA algorithm, the neural based SVD algorithm, the neural based TLS algorithm, the TLS algorithms under non-Gaussian noises, performance analysis methods of TLS algorithms, etc. In order to faster the understanding and mastering of the new methods provided by this book for readers, before presenting each new method in each chapter, a specialized section is provided to review the closely related several basis models. Throughout the book, large of procedure of new methods are provided, and all new algorithms or methods proposed by us are tested and verified by numerical simulations or actual engineering applications. Readers will find illustrative demonstration examples on a range of industrial processes to study. Readers will find out the present deficiency and recent developments of the TLS parameter estimation fields, and learn from the the authors¿ latest achievements or new methods around the practical industrial needs. In my opinion, this book can be assimilated by advanced undergraduates and graduate (PH.D.) students, as well as statisticians, because of the new tools in data analysis, applied mathematics experts, because of the novel theories and techniques that we propose, engineers, above all for the applications in control, system identification, computer vision, and signal processing.

Dynamic Environments Testing, Volume 7: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023, the seventh volume of ten 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 Dynamic Environments Testing including papers on:Vibration Testing Shock TestingMulti-Axis Shaker Testing Test Fixture Design Dynamic Environment Definition Specifications for Acceptance Testing

This third volume of the book series shows R-calculus is a Gentzen-typed deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. In this book, R-calculus is taken as Tableau-based/sequent-based/multisequent-based to preserve the satisfiability of the Theory/sequent/multisequent to revise, or sequent-based, to preserve the satisfiability of the sequent to revise. The R-calculi for Post and three-valued logic is given.  This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. 

Dieses Lehrbuch richtet sich an Studierende von fachfremden Studiengängen mit Informatikanteilen. Ein besonderer Schwerpunkt liegt dabei auf den sogenannten Lebenswissenschaften, wie Medizintechnik, Rettungsingenieurwesen, Biotechnologie, Umwelttechnik oder Verfahrenstechnik. Das Lehrbuch eignet sich für Leser in Studium und Praxis, die sich einen Einstieg in die Informatik verschaffen wollen. Die Besonderheit dieses Buches liegt in der problembasierten Herangehensweise, sowie der nach verschiedenen Taxonomiestufen konzipierten Übungsaufgaben.

The book presents a conceptual and methodological basis for the mathematical and computational analysis of genomes.Genomes are containers of biological information, which direct the cell functions and the evolution of organisms. Combinatorial, probabilistic, and informational aspects are fundamental ingredients of any mathematical investigation of genomes aimed at providing mathematical principles for extracting the information that they contain.The topics presented in the book include research themes developed by authors in the last 15 years, and in many aspects, the book continues a preceding volume (Vincenzo Manca, Infobiotics: Information in biotic systems, Springer, 2013). The main inspiring idea of the book is an informational perspective to Genomics. Information is the most recent, among the fundamental mathematical and physical concepts developed in the last two centuries. It has revolutionized the whole science and continues, in this direction, to dominate the trends of the contemporary science. In fact, any discipline collects data from observations, by providing theories able to explain, predict, and dominate natural phenomena. But data are containers of information, whence information is essential in any scientific elaboration.Many open problems in deciphering genomes will be addressed, by showing an informational approach to the discovery of ¿genome languages¿, according to which genomic texts are written. Life strategies, at many levels of organization, are encoded in these texts, and randomness has a crucial role in the birth and in the development of biological information, where the interplay of casualty and computation is probably the most secret key of life intelligence.

Reaction to breakdowns is more expensive, by many orders of magnitude, than prevention. This again became clear during the COVID-19 pandemic and is evinced in the sustainability crisis. The dynamics of living matter transcends deterministic reaction. Embodied in machines, determinism empowered the human being, providing the path to prosperity. However, in conjunction with reductionism, it does away with complexity, in which life is couched.The living is by necessity anticipatory. Awareness of the future means preserving life not in reaction to, but in anticipation of change. Living entities, from the simplest bacteria, to plants and insects, to human beings, are adaptive, goal-oriented, and capable of self-healing. Anticipatory actions are expressed through non-deterministic processes that unfold in concert with reactions. They engage the wholeness of life, including its interactions with the environment. Awareness of consequences, together with memory of the past, informs actions that reflect the creative nature of human beings. Redefining science¿and implicitly, medicine¿is not a negation of its past, but rather an affirmation of trust in explaining life¿s capacity to renew itself. As opposed to increasingly expensive medicine as a practice of repair, to prevent and to heal is to make life sustainable. The moment of truth can no longer be postponed. At stake is the future of humankind and even of life on planet Earth. Reductionist determinism informs the obsession with progress at any cost. Awareness of the fact that the human condition transcends that of the matter in which it is embodied explains, and indeed justifies, the call to Disrupt Science in its current state. The age of the digital machine, in particular of artificial intelligence, is one of opportunities that pale when compared to its inherent risks. The record of breakdowns (including so-called natural disasters), by now global in scale, is part of the empirical premise for the call for completing the Cartesian Revolution. A ¿Second Revolution in Science¿ could unleash humanity¿s remaking, free of surrendering to want. Science has the opportunity not only to measure everything¿life included¿and accumulate data and process it for its own sake, but also to realize its meaning. The future matters. Baruch Gorkin is celebrated internationally for exquisite typefaces and for books reflecting meaning-driven design.

This book provides a comprehensive yet informal introduction to differentiating and integrating real functions with one variable. It also covers basic first-order differential equations and introduces higher-dimensional differentiation and integration. The focus is on significant theoretical proofs, accompanied by illustrative examples for clarity. A comprehensive bibliography aids deeper understanding. The concept of a function's differential is a central theme, relating to the "differential" within integrals. The discussion of indefinite integrals (collections of antiderivatives) precedes definite integrals, naturally connecting the two. The Appendix offers essential math formulas, exercise properties, and an in-depth exploration of continuity and differentiability. Select exercise solutions are provided. This book suits short introductory math courses for novice physics/engineering students. It equips them with vital differentialand integral calculus tools for real-world applications. It is also useful for first-year undergraduates, reinforcing advanced calculus foundations for better Physics comprehension.

This book presents the latest accomplishments in Novikov/conformal gearing as well as high-conformal gearing.  It is focused primarily on strength calculation of gear teeth and the manufacturing of gears for Novikov/conformal and high-conformal gearing along with a brief discussion of achievements in the modern theory of gearing. The modern theory of gearing is the foundation of all optimal designs of gears, gear-sets, and transmissions of all known designs, as well as, of all those to be developed in the future. As even a small improvement in efficiency on a single gear can represent a significant cost saving, given the millions of gears used in industry every year, this volume provides the design and manufacturing engineer in invaluable resource.

This textbook summarizes the course of engineering mechanics, designed for one or two semesters, at the undergraduate or graduate level for a range of academic majors. The book covers all the main components of the discipline including: Theoretical Mechanics, Theory of Mechanisms and Machines, Resistance of Materials, Machine Parts and Design Basic; and Interchangeability, Standardization, and Technical Measurements. It can also be used by students of other technical areas in to achieve competence in each of the listed disciplines. The concise presentation facilitates concentration on the most important elements of the concepts presented while also outlining the current state of mechanics, demonstrating engineering applications using various computer packages (MathCad, CosmosWorks, Inkscape, AutoCad), and updating data on engineering materials. Examples of both simple and complex engineering calculations are given at the end of each chapter along with self-assessment questions.

This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal forthe stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).

This book is aimed to provide comprehensive and systematic knowledge of kinematic synthesis as developed up to date. Modern mechanical systems require advance kinematics knowledge to support mechanism design with sound theories and methods. The book includes not only the classical foundations of kinematic synthesis, but also the latest advances developed by the authors. Moreover, many examples are included to illustrate both methods and their supporting theory.The focus is on systems of rigid bodies forming closed loops. The four-bar linkage, representing the foundations of mechanical systems,  is given due attention, in its three domains: planar, spherical, and spatial. The book contains six chapters, the first two covering fundamentals for kinematic synthesis, including qualitative synthesis. Chapters 3-5 describe, in full detail,  the function, motion, and path syntheses of single-dof linkages.  In the last chapter, the synthesis of single-dof complex linkages, including six-bar and ten-bar linkages, is introduced.The book is suitable for graduate students of mechanical engineering, researchers of mechanism and robot design, and machine design engineers.

This book, fully updated for Python version 3.6+, covers the key ideas that link probability, statistics, and machine learning illustrated using Python modules in these areas.  All the figures and numerical results are reproducible using the Python codes provided. The author develops key intuitions in machine learning by working meaningful examples using multiple analytical methods and Python codes, thereby connecting theoretical concepts to concrete implementations. Detailed proofs for certain important results are also provided. Modern Python modules like Pandas, Sympy, Scikit-learn, Tensorflow, and Keras are applied to simulate and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, and regularization. Many abstract mathematical ideas, such as convergence in probability theory, are developed and illustrated with numerical examples. This updated edition now includes the Fisher Exact Test and the Mann-Whitney-Wilcoxon Test. A new section on survival analysis has been included as well as substantial development of Generalized Linear Models. The new deep learning section for image processing includes an in-depth discussion of gradient descent methods that underpin all deep learning algorithms.   As with the prior edition, there are new and updated *Programming Tips* that the illustrate effective Python modules and methods for scientific programming and machine learning. There are 445 run-able code blocks with corresponding outputs that have been tested for accuracy.  Over 158 graphical visualizations (almost all generated using Python) illustrate the concepts that are developed both in code and in mathematics. We also discuss and use key Python modules such as Numpy, Scikit-learn, Sympy,  Scipy, Lifelines, CvxPy, Theano, Matplotlib, Pandas, Tensorflow, Statsmodels,  and Keras.This book is suitable for anyone with an undergraduate-level exposure to probability, statistics, or machine learning and with rudimentary knowledge of Python programming.

This book examines the issues of ensuring anti-terrorist security of an aviation enterprise, provides a history of terrorism in the aviation sector, and analyzes the legal regulations. This book provides mathematical and mathematical-psychological models for reducing the risk of terrorist threats, which makes it possible to objectively increase the safety of air transport facilities, reduce the likelihood of terrorist attacks, save human lives and prevent significant material losses. The solutions of general humanistic problems proposed in the book-preventing accidents and preserving the world-are an original feature of the book, which allows one to treat it with the necessary attention and interest for the reader. The concept of anti-terrorist security of an aviation enterprise presented in this book has been widely tested and introduced into the activities of leading aviation enterprises, including the Interstate Aviation Committee (IAC), and has been used in the investigation of aviation accidents.This book is written for a wide range of audience associated with ensuring aviation transport security and for the end users of airlines-passengers, in order to expand their knowledge about the reliability of using air transport. 

With approximately 2500 problems, this book provides a collection of practical problems on the basic and advanced data structures, design, and analysis of algorithms. To make this book suitable for self-instruction, about one-third of the algorithms are supported by solutions, and some others are supported by hints and comments. This book is intended for students wishing to deepen their knowledge of algorithm design in an undergraduate or beginning graduate class on algorithms, for those teaching courses in this area, for use by practicing programmers who wish to hone and expand their skills, and as a self-study text for graduate students who are preparing for the qualifying examination on algorithms for a Ph.D. program in Computer Science or Computer Engineering. About all, it is a good source for exam problems for those who teach algorithms and data structure. The format of each chapter is just a little bit of instruction followed by lots of problems. This book is intended to augment the problem sets found in any standard algorithms textbook. This book * begins with four chapters on background material that most algorithms instructors would like their students to have mastered before setting foot in an algorithms class. The introductory chapters include mathematical induction, complexity notations, recurrence relations, and basic algorithm analysis methods. * provides many problems on basic and advanced data structures including basic data structures (arrays, stack, queue, and linked list), hash, tree, search, and sorting algorithms. * provides many problems on algorithm design techniques: divide and conquer, dynamic programming, greedy algorithms, graph algorithms, and backtracking algorithms. * is rounded out with a chapter on NP-completeness.

In this book, we delve into the fascinating world of managing data using the relational model, a widely adopted approach in the field of database management.As technology continues to advance at an unprecedented pace, the need for efficient and reliable data storage and retrieval has become paramount. Relational database management systems (RDBMS) have emerged as the backbone of modern data management, providing a structured and organized approach to handling vast amounts of information. Its a compiled materials from various sources of books and journals which will help for the students who wanted to learn RDBMS.

This book provides two new optimization algorithms to address real optimization problems. Optimization is a fundamental concept in engineering and science, and its applications are needed in many fields. From designing products and systems to developing algorithms and models, optimization plays a critical role in achieving efficient and effective solutions to complex problems. Optimization algorithms inspired by nature have proven effective in solving a wide range of problems, including those in engineering, finance, and machine learning. These algorithms are often used when traditional optimization techniques are impractical due to the size or complexity of the problem. In this book, we are presenting two new optimization algorithms inspired by plant roots and the Mycorrhiza Network. The first algorithm is called the Continuous Mycorrhiza Optimization Algorithm (CMOA), which was proposed based on the model of the Continuous Lotka-Volterra System Equations. The second algorithm is called the Discrete Mycorrhiza Optimization Algorithm (DMOA), which design based on the model of Discrete Lotka-Volterra System Equations. By mastering the proposed algorithms, the readers able to develop innovative solutions that improve efficiency, reduce costs, and improve performance in the corresponding field of work.

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

This book investigates two types of static multi-fidelity surrogates modeling approaches, sequential multi-fidelity surrogates modeling approaches, the multi-fidelity surrogates-assisted efficient global optimization, reliability analysis, robust design optimization, and evolutionary optimization. Multi-fidelity surrogates have attracted a significant amount of attention in simulation-based design and optimization in recent years. Some real-life engineering design problems, such as prediction of angular distortion in the laser welding, optimization design of micro-aerial vehicle fuselage, and optimization design of metamaterial vibration isolator, are also provided to illustrate the ability and merits of multi-fidelity surrogates in support of engineering design. Specifically, lots of illustrative examples are adopted throughout the book to help explain the approaches in a more "e;hands-on"e; manner. This book is a useful reference for postgraduates and researchers of mechanical engineering, as well as engineers of enterprises in related fields.

This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The ¿Problems and Complements¿ sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students.Partial Differential Equations: Third Edition is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.

This book aims to strengthen programming skills and foster creative thinking by presenting and solving 90 challenging problems. The book is intended for individuals with elementary, intermediate, and advanced Python programming skills who aspire to take their abilities to the next level. Additionally, the book is valuable for individuals interested in enhancing their creative thinking and logical reasoning skills. It is a self-instructional book meant to provide readers with the ability to solve challenging problems independently. The presented challenges are lucidly and succinctly expressed, facilitating readers to follow along and comprehend the problem-solving process. The challenges cover various fields, making it suitable for a wide range of individuals. The book is divided into eight chapters, beginning with an introduction in chapter one. The second chapter presents essential Python basics for programming challenging problems, while the subsequent chapters focuson specific types of challenges. These include math-based challenges in chapter three, number-based challenges in chapter four, string-based challenges in chapter five, game-based challenges in chapter six, count-based challenges in chapter seven, and miscellaneous challenges in chapter eight. Each chapter comprises a set of challenges with examples, hints, algorithms, and Python code solutions. The target audience of the book includes computer science and engineering students, teachers, software developers, and participants in programming competitions.

This book highlights recent advances in nonlinear dynamics and control with applications in mechanics and physics. The book includes selected articles from the 5th Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD 2023) and presents recent theoretical, experimental and numerical findings covering various topics in nonlinear structural dynamics and diagnosis. The main topics includes multiple scales dynamics, energy harvesting, dynamics of MEMS, NEMS and AFM, systems with time delay, quasi-periodic oscillations and synchronization, stochastic dynamics, analytical and semi-analytical methods, time series analysis, control and analysis of switching systems, structural health monitoring, nonlinear vibrations of structures, nonsmouth dynamics, nonlinear phenomena in discrete and continuum systems, dynamic modeling and fault diagnosis, constrained multi-catenary systems, conservative chaotic system, hysteretic structures, and nonlinear PDEs and their dynamics.

This book investigates in detail model-based fault diagnosis methods, including observer-based residual generation, residual evaluation based on threshold computation, observer-based fault isolation strategies, observer-based fault estimation, Kalman filter-based fault diagnosis methods, and parity space approach. Studies on model-based fault diagnosis have attracted engineers and scientists from various disciplines, such as electrical, aerospace, mechanical, and chemical engineering. Pursuing a holistic approach, the book establishes a fundamental framework for this topic, while emphasizing the importance of state-space approach. The methods introduced in the book are systemic and easy to follow. The book is intended for undergraduate and graduate students who are interested in fault diagnosis and state estimation, researchers investigating fault diagnosis and fault-tolerant control, and control system design engineers working on safety-critical systems.

This book deals with several types of multi-dimensional control problems in the face of data uncertainty for vector cases-multi-dimensional multi-objective control problem with uncertain objective functionals, uncertain constraint functionals, and uncertain objective as well as constraint functionals, uncertain multi-dimensional multi-objective control problem with semi-infinite constraints, uncertain dual multi-dimensional multi-objective variational control problem, and second-order PDE&PDI constrained robust optimization problem. The book provides the solution approaches-an exact l1 penalty function approach, modified objective approach, robust approach-in the simplest way to solve the recent developing optimization problems in the sense of uncertainty. 

This book focuses on fault diagnosis for linear discrete time-varying (LDTV) systems and its applications in modern engineering processes, with more weighting placed on the development of theory and methodologies. A comprehensive and systematic study on fault diagnosis for LDTV systems is provided, covering Hinfinity-optimization-based fault diagnosis, Hinfinity-filtering-based fault diagnosis, parity space-based fault diagnosis, Krein space technique-aided fault detection and fault estimation, and their typical applications in linear/nonlinear processes such as satellite attitude control systems and INS/GPS systems. This book benefits researchers, engineers, and graduate students in the fields of control engineering, electrical and electronic engineering, instrumentation science, and optoelectronic engineering.

The book is devoted to the solution of the problem of determining the presence of corona discharge on electrical equipment with acoustic radiation. It is shown that corona discharge leads not only to irreversible losses of electrical energy, but also interferes with the transmission of high-frequency signals, deteriorates insulating elements, can become a source of conditions for the occurrence of a destructive arc discharge and is one of the factors of changing the continuity of the electrical system as a whole. The book describes the processes in a corona discharge that lead to the occurrence of acoustic waves. The authors analyzed acoustic radiation from a corona discharge reproduced in laboratory conditions. The received acoustic signals were processed by Fourier transform. Thus, the features of the spectral function, which belong specifically to the corona discharge in electrical networks with industrial frequency current, were determined. Based on the inverse Fourier transform, a simplified model of the acoustic radiation of the corona discharge was constructed. The authors proposed a method for detecting the presence of a corona discharge based on the spectral characteristics of acoustic radiation. Techniques were developed to determine the presence of a corona discharge for the creation of stationary and mobile devices. The advantages of the method of detecting the presence of corona discharge by the acoustic spectrum are shown. The method makes it possible to determine the presence of a corona discharge remotely, even out of direct sight, regardless of the time of day and regardless of the season. The book states that determining the presence of a corona discharge is not enough, it is still necessary to determine its location. The method of finding the coordinates of the corona discharge as a source of sound was described. Methods of searching for corona discharge coordinates with a fixed scanning device and a moving scanning device are proposed. A UAV is proposed as a mobile platform for the scanning system. The influence of the Doppler effect on acoustic measurements when the UAV speed changes was taken into account. The authors have shown that the use of coronal discharge detection with UAVs will not only enable the prevention of coronal discharge, but also increase the frequency of surface inspections. This will allow timely measures to be taken to improve the reliability of the power system operation. The book is intended for the researchers, postgraduate students and students specialized in theory and calculations of electrical systems.