Pekka Neittaanmäki

Amir Z. Averbuch

Valery A. Zheludev

This book presents various contributions of splines to signal and image processing from a unified perspective that is based on the Zak transform (ZT). It expands the methodology from periodic splines, which were presented in the first volume, to non-periodic splines. Together, these books provide a universal toolbox accompanied by MATLAB software for manipulating polynomial and discrete splines, spline-based wavelets, wavelet packets and wavelet frames for signal/ image processing applications. In this volume, we see that the ZT provides an integral representation of discrete and polynomial splines, which, to some extent, is similar to Fourier integral. The authors explore elements of spline theory and design, and consider different types of polynomial and discrete splines. They describe applications of spline-based wavelets to data compression. These splines are useful for real-time signal processing and, in particular, real-time wavelet and frame transforms. Further topics addressed in this volume include: "global" splines, such as interpolating, self-dual and smoothing, whose supports are infinite; the compactly supported quasi-interpolating and smoothing splines including quasi-interpolating splines on non-uniform grids; and cubic Hermite splines as a source for the design of multiwavelets and multiwavelet frames. Readers from various disciplines including engineering, computer science and mathematical information technology will find the descriptions of algorithms, applications and software in this book especially useful.

Volume II: Non-Periodic Splines

Spline and Spline Wavelet Methods with Applications to Signal and Image Processing

N.V. Banichuk

Structural optimization is currently attracting considerable attention. Interest in - search in optimal design has grown in connection with the rapid development of aeronautical and space technologies, shipbuilding, and design of precision mach- ery. A special ?eld in these investigations is devoted to structural optimization with incomplete information (incomplete data). The importance of these investigations is explained as follows. The conventional theory of optimal structural design - sumes precise knowledge of material parameters, including damage characteristics and loadings applied to the structure. In practice such precise knowledge is seldom available. Thus, it is important to be able to predict the sensitivity of a designed structure to random ?uctuations in the environment and to variations in the material properties. To design reliable structures it is necessary to apply the so-called gu- anteed approach, based on a “worst case scenario” or a more optimistic probabilistic approach, if we have additional statistical data. Problems of optimal design with incomplete information also have consid- able theoretical importance. The introduction and investigations into new types of mathematical problems are interesting in themselves. Note that some ga- theoretical optimization problems arise for which there are no systematic techniques of investigation. This monograph is devoted to the exposition of new ways of formulating and solving problems of structural optimization with incomplete information. We recall some research results concerning the optimum shape and structural properties of bodies subjected to external loadings.

Structural Optimization with Uncertainties

Martti Lehto

The book, in addition to the cyber threats and technology, processes cyber security from many sides as a social phenomenon and how the implementation of the cyber security strategy is carried out. The book gives a profound idea of the most spoken phenomenon of this time. The book is suitable for a wide-ranging audience from graduate to professionals/practitioners and researchers. Relevant disciplines for the book are Telecommunications / Network security, Applied mathematics / Data analysis, Mobile systems / Security, Engineering / Security of critical infrastructure and Military science / Security.

Cyber Security: Analytics, Technology and Automation

Roland Glowinski

Michal Krizek

Sergey Korotov

The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well. Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems. The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.

Conjugate Gradient Algorithms and Finite Element Methods

Jacques Periaux

Pedro Diez

Tero Tuovinen

Olli Bräysy

This volume addresses challenges and solutions in transport and mobility of people and goods with respect to environment, safety, security and socio–economics issues, exploring advanced computational research work and the latest innovations in transport. This book brings together lectures presented at the ECCOMAS Thematic CM3 Conference on Transport held in Jyväskylä, Finland, 25-27 May 2015. It is divided into three parts, I: Reviews and Perspective, II: Computational Methods and Models and III: Translational Research. Each of these parts consists of contributions that present solutions to many transport challenges in this complex, rapidly changing subject. The work contains the latest achievements of European research and technological developments needed for the next decade through computational results of scientific and technical experts who have made essential contributions in transport efficiency in Europe. The material presented here is the state of the art in Transport Modeling, Simulation and Optimization in the fields of Aeronautics, Automotive, Logistics, Maritime and Rails. Furthermore, this volume also answers the question how to apply Computational Research in Transport in order to provide innovative solutions to Green Transportation challenges of identified in the ambitious Horizon 2020 program. This book is intended for students, researchers, engineers and practitioners that are computationally involved in the deployment of Intelligent Transport Systems (ITS) in the areas of optimal use of road, traffic and travel data, traffic and freight management ITS services, road safety and security, sea traffic management, etc.

New Challenges for the Greening of Transport Systems

Computational Methods and Models for Transport

Lev Baskin

Boris Plamenevskii

Oleg Sarafanov

This volume studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Devices based on the phenomenon of electron resonant tunneling are widely used in electronics. Efforts are directed towards refining properties of resonance structures. There are prospects for building new nano size electronics elements based on quantum dot systems. However, the role of resonance structure can also be given to a quantum wire of variable cross-section. Instead of an "electrode - quantum dot - electrode" system, one can use a quantum wire with two narrows. A waveguide narrow is an effective potential barrier for longitudinal electron motion along a waveguide. The part of the waveguide between two narrows becomes a "resonator" , where electron resonant tunneling can occur. This phenomenon consists in the fact that, for an electron with energy E, the probability T(E) to pass from one part of the waveguide to the other part through the resonator has a sharp peak at E = Eres, where Eres denotes a "resonant" energy. Such quantum resonators can find applications as elements of nano electronics devices and provide some advantages in regard to operation properties and production technology. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.

Quantum Waveguides of Variable Cross-Section, Asymptotics, Numerics, and Applications

Resonant Tunneling

This book focus on critical infrastructure protection. The chapters present detailed analysis of the issues and challenges in cyberspace and provide novel solutions in various aspects. The first part of the book focus on digital society, addressing critical infrastructure and different forms of the digitalization, strategic focus on cyber security, legal aspects on cyber security, citizen in digital society, and cyber security training. The second part focus on the critical infrastructure protection in different areas of the critical infrastructure. The chapters cover the cybersecurity situation awareness, aviation and air traffic control, cyber security in smart societies and cities, cyber security in smart buildings, maritime cyber security, cyber security in energy systems, and cyber security in healthcare. The third part presents the impact of new technologies upon cyber capability building as well as new challenges brought about by new technologies. These new technologies are among others are quantum technology, firmware and wireless technologies, malware analysis, virtualization.

Critical Infrastructure Protection

Cyber Security

This book studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Compared to its first edition, this book includes four new chapters, redistributes the content between chapters and modifies the estimates of the remainders in the asymptotics of resonant tunneling characteristics. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.

For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.

Modelling and Numerical Simulation

Partial Differential Equations

Jordi Pons-Prats

This book gathers the outcomes of the second ECCOMAS CM3 Conference series on transport, which addressed the main challenges and opportunities that computation and big data represent for transport and mobility in the automotive, logistics, aeronautics and marine-maritime fields. Through a series of plenary lectures and mini-forums with lectures followed by question-and-answer sessions, the conference explored potential solutions and innovations to improve transport and mobility in surface and air applications. The book seeks to answer the question of how computational research in transport can provide innovative solutions to Green Transportation challenges identified in the ambitious Horizon 2020 program. In particular, the respective papers present the state of the art in transport modeling, simulation and optimization in the fields of maritime, aeronautics, automotive and logistics research. In addition, the content includes two white papers on transport challenges and prospects. Given its scope, the book will be of interest to students, researchers, engineers and practitioners whose work involves the implementation of Intelligent Transport Systems (ITS) software for the optimal use of roads, including safety and security, traffic and travel data, surface and air traffic management, and freight logistics.

Digital Innovations in Surface and Air Transport Systems

Computation and Big Data for Transport

Marko M Mäkelä

This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered. Contents: Part I: Nonsmooth Analysis:IntroductionConvex AnalysisNonsmooth Differential TheoryNonsmooth GeometryNonsmooth Optimization TheoryPart II: Nonsmooth Optimization:IntroductionA Survey of Bundle MethodsProximal Bundle Method for Nonconvex Constrained OptimizationNumerical ExperimentsPart III: Nonsmooth Optimal Control:IntroductionPreliminariesDistributed Parameter Control Problems Optimal Shape Design Boundary Control for Stefan Type Problems Readership: Applied mathematicians, mathematicians, operations researchers, engineers, economists and mathematical physicists. keywords:Nonsmooth Optimization;Nondifferentiable Programming;Bundle Methods;Convex Analysis;Nonconvexity;Subgradients;Tangent and Normal Cones;Optimal Control;Optimal Shape Design;Continuous Casting

Pekka Neittaanmäki

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