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Discrete Fractional Calculus

Discrete Fractional Calculus Author Piotr Ostalczyk
ISBN-10 9789814725682
Release 2015-11-26
Pages 356
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The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing. Contents:Discrete-Variable Real FunctionsThe n-th Order Backward Difference/Sum of the Discrete-Variable FunctionFractional-Order Backward Differ-SumThe FOBD-S Graphical InterpretationThe FOBD/S Selected PropertiesThe FO Dynamic System DescriptionLinear FO System AnalysisThe Linear FO Discrete-Time Fundamental ElementsFO Discrete-Time System StructuresFractional Discrete-Time PID ControllerFOS Approximation ProblemsFractional PotentialFO Image Filtering and Edge DetectionAppendix A: Selected Linear Algebra Formulae and Discrete-Variable Special Functions Readership: Researchers, academics, professionals and graduate students in pattern recognition/image analysis, robotics and automated systems, systems engineering and mathematical modeling. Keywords:Fractional Calculus;Fractional-Order Backward-Difference;Fractional-Order Linear Difference Equation;Discrete-System;State-Space Equations



Non Integer Order Calculus and its Applications

Non Integer Order Calculus and its Applications Author Piotr Ostalczyk
ISBN-10 9783319784588
Release 2018-03-22
Pages 229
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This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that prophecy is confirmed year after year. Now this mathematical tool is successfully used in a variety of research areas, like engineering (e.g. electrical, mechanical, chemical), dynamical systems modeling, analysis and synthesis (e.g technical, biological, economical) as well as in multidisciplinary areas (e.g. biochemistry, electrochemistry).As well as the mathematical foundations the book concentrates on the technical applications of continuous-time and discrete-time fractional calculus, investigating the identification, analysis and control of electrical circuits and dynamical systems. It also presents the latest results.Although some scientific centers and scientists are skeptical and actively criticize the applicability of fractional calculus, it is worth breaking through the scientific and technological walls. Because the “fractional community” is growing rapidly there is a pressing need for the exchange of scientific results. The book includes papers presented at the 9th International Conference on Non-integer Order Calculus and Its Applications and is divided into three parts:• Mathematical foundations• Fractional systems analysis and synthesis• System modelingSeven papers discuss the mathematical foundations, twelve papers address fractional order analysis and synthesis and three focus on dynamical system modeling by the fractional order differential and difference equations. It is a useful resource for fractional calculus scientific community.



Automation 2018

Automation 2018 Author Roman Szewczyk
ISBN-10 9783319771793
Release 2018-03-07
Pages 795
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This book consists of papers presented at Automation 2018, an international conference held in Warsaw from March 21 to 23, 2018. It discusses the radical technological changes occurring due to the INDUSTRY 4.0, with a focus on offering a better understanding of the Fourth Industrial Revolution. Each chapter presents a detailed analysis of interdisciplinary knowledge, numerical modeling and simulation as well as the application of cyber-physical systems, where information technology and physical devices create synergic systems leading to unprecedented efficiency. The theoretical results, practical solutions and guidelines presented are valuable for both researchers working in the area of engineering sciences and practitioners looking for solutions to industrial problems.



Computer Vision And Robotics In Perioperative Process

Computer Vision And Robotics In Perioperative Process Author Xu Yi
ISBN-10 9789813233300
Release 2018-04-10
Pages 120
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This invaluable compendium highlights the challenges of perioperative process in hospitals today. It delves into the development of a multi-agent robotic system where a dirty-side robot that sorts instruments returned from a surgical room into different containers for easy scrubbing, a Traybot that navigates the environment and transports the instrument containers to different stations, a clean-side robot that picks up instruments and places them in surgical kits, and an orchestration software architecture that manages the cooperation between different robots. The book discusses the technical details of all the components, from system architecture to the details of the end-effector design. Readers will gain significant knowledge on how such a system was put together. Contents: Introduction Project Background Related Work Overall Robotic System Architecture Vision Based Instrument Singulation Dirty Side Robot Design Mobile Robot Architecture Clean Side Robot Design Experiments Conclusions and Future Work Readership: Researchers, academics, professionals and graduate students in machine perception /computer vision, pattern recognition/image analysis and robotics and automated systems software. Keywords: Computer Vision;Robotics;Mobile Robot;Bin-Picking;End-Effector;PerioperativeReview:0



Computer Vision in Robotics and Industrial Applications

Computer Vision in Robotics and Industrial Applications Author Dominik Sankowski
ISBN-10 9789814583732
Release 2014-06-26
Pages 580
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The book presents a collection of practical applications of image processing and analysis. Different vision systems are more often used among others in the automotive industry, pharmacy, military and police equipment, automated production and measurement systems. In each of these fields of technology, digital image processing and analysis module is a critical part of the process of building this type of system. The majority of books in the market deal with theoretical issues. However, this unique publication specially highlights industrial applications, especially industrial measurement applications. Along with its wide spectrum of image processing and analysis applications, this book is an interesting reference for both students and professionals. Contents:Theoretical Introduction to Image Reconstruction and Processing:Data Set Preparation for k-NN Classifier Using the Measure of Representativeness (Marcin Raniszewski)Segmentation Methods in the Selected Industrial Computer Vision Application (Anna Fabijanska and Dominik Sankowski)Line Fractional-Order Difference/Sum, Its Properties and an Application in Image Processing (Piotr Ostalczyk)Computer Vision in Robotics:Management Software for Distributed Mobile Robot System (Maciej Łaski, Sylwester Błaszczyk, Piotr Duch, Rafał Jachowicz, Adam Wulkiewicz, Dominik Sankowski and Piotr Ostalczyk)Advanced Vision Systems in Detection and Analysis of Characteristic Features of Objects (Adam Wulkiewicz, Rafał Jachowicz, Sylwester Błaszczyk, Piotr Duch, Maciej Łaski, Dominik Sankowski and Piotr Ostalczyk)Pattern Recognition Algorithms for the Navigation of Mobile Platform (Rafał Jachowicz, Sylwester Błaszczyk, Piotr Duch, Maciej Łaski, Adam Wulkiewicz, Dominik Sankowski and Piotr Ostalczyk)Partial Fractional-Order Difference in the Edge Detection (Piotr Duch, Rafał Jachowicz, Sylwester Błaszczyk, Maciej Łaski, Adam Wulkiewicz, Piotr Ostalczyk and Dominik Sankowski)Application of Fractional-Order Derivative for Edge Detection in Mobile Robot System (Sylwester Błaszczyk, Rafał Jachowicz, Piotr Duch, Maciej Łaski, Adam Wulkiewicz, Piotr Ostalczyk and Dominik Sankowski)Vision Based Human-Machine Interfaces: Visem Recognition (Krzysztof Ślot, Agnieszka Owczarek and Maria Janczyk)Industrial Applications of Computer Vision in Process Tomography, Material Science and Temperature Control:Hybrid Boundary Element Method Applied for Diffusion Tomography Problems (Jan Sikora, Maciej Pańczyk and Paweł Wieleba)Two-phase Gas-Liquid Flow Structures and Phase Distribution Determination Based on 3D Electrical Capacitance Tomography Visualization (Robert Banasiak, Radosław Wajman, Tomasz Jaworski, Paweł Fiderek, Jacek Nowakowski and Henryk Fidos)Tomographic Visualization of Dynamic Industrial Solid Transporting and Storage Systems (Zbigniew Chaniecki, Krzysztof Grudzień and Andrzej Romanowski)Tomography Data Processing for Multiphase Industrial Process Monitoring (Krzysztof Grudzień, Zbigniew Chaniecki, Andrzej Romanowski, Jacek Nowakowski and Dominik Sankowski)Dedicated 3D Image Processing Methods for the Analysis of X-Ray Tomography Data: Case Study of Materials Science (Laurent Babout and Marcin Janaszewski)Selected Algorithms of Quantitative Image Analysis for Measurements of Properties Characterizing Interfacial Interactions at High Temperatures (Krzysztof Strzecha, Anna Fabijańska, Tomasz Koszmider and Dominik Sankowski)Theoretical Introduction to Image Reconstruction for Capacitance Process Tomography (Radosław Wajman, Krzysztof Grudzien, Robert Banasiak, Andrzej Romanowski, Zbigniew Chaniecki and Dominik Sankowski)Infra-Red Thermovision in Surface Temperature Control System (Jacek Kucharski, Tomasz Jaworski, Andrzej Frączyk and Piotr Urbanek)Medical and Other Applications of Computer Vision:The Computer Evaluation of Surface Color Changes in Cultivated Plants Influence by Different Environmental Factors (Joanna Sekulska-Nalewajko and Jarosław Gocławski)Various Approaches to Processing and Analysis of Images Obtained from Immunoenzymatic Visualization of Secretory Activity with ELISPOT Method (Wojciech Bieniecki and Szymon Grabowski)Image Processing and Analysis Algorithms for Assessment and Diagnosis of Brain Diseases (Anna Fabijanska and Tomasz Węglinski)Computer Systems for Studying Dynamic Properties of Materials at High Temperatures (Marcin Bąkała, Rafał Wojciechowski and Dominik Sankowski) Readership: Researchers, professionals and academics in image analysis, machine perception/computer vision, software engineering and fuzzy logic. Keywords:Image Processing;Computer Vision;Robotics;Pattern Recognition;Fuzzy Logic;Process Tomography;Mobile Robots



Theory and Applications of Fractional Differential Equations

Theory and Applications of Fractional Differential Equations Author Anatoliĭ Aleksandrovich Kilbas
ISBN-10 0444518320
Release 2006
Pages 523
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This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.



Discrete Fractional Calculus

Discrete Fractional Calculus Author Christopher Goodrich
ISBN-10 9783319255620
Release 2016-02-09
Pages 556
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This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject. Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1—2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1—2 may be covered quickly and readers may then skip to Chapters 6—7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6—7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1—5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.



Computer Vision

Computer Vision Author Richard Szeliski
ISBN-10 1848829469
Release 2010-11-05
Pages 812
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Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.



Local Fractional Integral Transforms and Their Applications

Local Fractional Integral Transforms and Their Applications Author Xiao Jun Yang
ISBN-10 9780128040324
Release 2015-10-22
Pages 262
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Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. Provides applications of local fractional Fourier Series Discusses definitions for local fractional Laplace transforms Explains local fractional Laplace transforms coupled with analytical methods



New Trends in Nanotechnology and Fractional Calculus Applications

New Trends in Nanotechnology and Fractional Calculus Applications Author Dumitru Baleanu
ISBN-10 9048132932
Release 2010-03-14
Pages 531
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In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.



Fractional Calculus

Fractional Calculus Author Varsha Daftardar-Gejji
ISBN-10 8184873336
Release 2013-08-31
Pages 222
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FRACTIONAL CALCULUS: Theory and Applications deals with differentiation and integration of arbitrary order. The origin of this subject can be traced back to the end of seventeenth century, the time when Newton and Leibniz developed foundations of differential and integral calculus. Nonetheless, utility and applicability of FC to various branches of science and engineering have been realized only in last few decades. Recent years have witnessed tremendous upsurge in research activities related to the applications of FC in modeling of real-world systems. Unlike the derivatives of integral order, the non-local nature of fractional derivatives correctly models many natural phenomena containing long memory and give more accurate description than their integer counterparts. The present book comprises of contributions from academicians and leading researchers and gives a panoramic overview of various aspects of this subject: * Introduction to Fractional Calculus * Fractional Differential Equations * Fractional Ordered Dynamical Systems * Fractional Operators on Fractals * Local Fractional Derivatives * Fractional Control Systems * Fractional Operators and Statistical Distributions * Applications to Engineering



Fractional order Modeling and Control of Dynamic Systems

Fractional order Modeling and Control of Dynamic Systems Author Aleksei Tepljakov
ISBN-10 9783319529509
Release 2017-02-08
Pages 173
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This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional-order calculus. It describes the development of model-based control design methods for systems described by fractional dynamic models. More than 300 years had passed since Newton and Leibniz developed a set of mathematical tools we now know as calculus. Ever since then the idea of non-integer derivatives and integrals, universally referred to as fractional calculus, has been of interest to many researchers. However, due to various issues, the usage of fractional-order models in real-life applications was limited. Advances in modern computer science made it possible to apply efficient numerical methods to the computation of fractional derivatives and integrals. This book describes novel methods developed by the author for fractional modeling and control, together with their successful application in real-world process control scenarios.



Mathematical Techniques of Fractional Order Systems

Mathematical Techniques of Fractional Order Systems Author Ahmad Taher Azar
ISBN-10 9780128135938
Release 2018-06-11
Pages 700
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Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes circuits and systems based on new nonlinear elements Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers Closes the gap between theoretical approaches and real-world applications Provides MATLAB® and Simulink code for many applications in the book



Fractional Dynamics

Fractional Dynamics Author Vasily E. Tarasov
ISBN-10 9783642140037
Release 2011-01-04
Pages 505
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"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.



The Essential Guide to Image Processing

The Essential Guide to Image Processing Author Alan C. Bovik
ISBN-10 0080922511
Release 2009-07-08
Pages 672
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A complete introduction to the basic and intermediate concepts of image processing from the leading people in the field Up-to-date content, including statistical modeling of natural, anistropic diffusion, image quality and the latest developments in JPEG 2000 This comprehensive and state-of-the art approach to image processing gives engineers and students a thorough introduction, and includes full coverage of key applications: image watermarking, fingerprint recognition, face recognition and iris recognition and medical imaging. "This book combines basic image processing techniques with some of the most advanced procedures. Introductory chapters dedicated to general principles are presented alongside detailed application-orientated ones. As a result it is suitably adapted for different classes of readers, ranging from Master to PhD students and beyond." – Prof. Jean-Philippe Thiran, EPFL, Lausanne, Switzerland "Al Bovik’s compendium proceeds systematically from fundamentals to today’s research frontiers. Professor Bovik, himself a highly respected leader in the field, has invited an all-star team of contributors. Students, researchers, and practitioners of image processing alike should benefit from the Essential Guide." – Prof. Bernd Girod, Stanford University, USA "This book is informative, easy to read with plenty of examples, and allows great flexibility in tailoring a course on image processing or analysis." – Prof. Pamela Cosman, University of California, San Diego, USA A complete and modern introduction to the basic and intermediate concepts of image processing – edited and written by the leading people in the field An essential reference for all types of engineers working on image processing applications Up-to-date content, including statistical modelling of natural, anisotropic diffusion, image quality and the latest developments in JPEG 2000



Advanced Synchronization Control and Bifurcation of Chaotic Fractional Order Systems

Advanced Synchronization Control and Bifurcation of Chaotic Fractional Order Systems Author Boulkroune, Abdesselem
ISBN-10 9781522554196
Release 2018-05-11
Pages 539
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In the recent years, fractional-order systems have been studied by many researchers in the engineering field. It was found that many systems can be described more accurately by fractional differential equations than by integer-order models. Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems is a scholarly publication that explores new developments related to novel chaotic fractional-order systems, control schemes, and their applications. Featuring coverage on a wide range of topics including chaos synchronization, nonlinear control, and cryptography, this publication is geared toward engineers, IT professionals, researchers, and upper-level graduate students seeking current research on chaotic fractional-order systems and their applications in engineering and computer science.



The Analysis of Fractional Differential Equations

The Analysis of Fractional Differential Equations Author Kai Diethelm
ISBN-10 9783642145742
Release 2010-08-18
Pages 247
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Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.