Information and communication technologies play a crucial role in a number of modern industries. Among these, education has perhaps seen the greatest increases in efficiency and availability through Internet-based technologies. E-Learning as a Socio-Cultural System: A Multidimensional Analysis provides readers with a critical examination of the theories, models, and best practices in online education from a social perspective, evaluating blended, distance, and mobile learning systems with a focus on the interactions of their practitioners. Within the pages of this volume, teachers, students, administrators, policy makers, and IT professionals will all find valuable advice and enriching personal experiences in the field of online education.

This book, now in its second edition, introduces readers to quantum rings as a special class of modern high-tech material structures at the nanoscale. It deals, in particular, with their formation by means of molecular beam epitaxy and droplet epitaxy of semiconductors, and their topology-driven electronic, optical and magnetic properties. A highly complex theoretical model is developed to adequately represent the specific features of quantum rings. The results presented here are intended to facilitate the development of low-cost high-performance electronic, spintronic, optoelectronic and information processing devices based on quantum rings. This second edition includes both new and significantly revised chapters. It provides extensive information on recent advances in the physics of quantum rings related to the spin-orbit interaction and spin dynamics (spin interference in Rashba rings, tunable exciton topology on type II InAs/GaAsSb quantum nanostructures), the electron-phonon interaction in ring-like structures, quantum interference manifestations in novel materials (graphene nanoribbons, MoS2), and the effects of electrical field and THz radiation on the optical properties of quantum rings. The new edition also shares insights into the properties of various novel architectures, including coupled quantum ring-quantum dot chains and concentric quantum rings, topologic states of light in self-assembled ring-like cavities, and optical and plasmon m.odes in Moebius-shaped resonators.

This book is devoted to an investigation of some important problems of mod ern filtering theory concerned with systems of 'any nature being able to per ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to 27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent activity in this area is observed, researchers are trying consistently to generalize famous results, extend them to more broad classes of processes, realize and justify more simple procedures for processing measurement data in order to obtain more efficient filtering algorithms. As to nonlinear filter ing, it remains much as fragmentary. Here much progress has been made by R. L. Stratonovich and his successors in the area of filtering of Markov processes. In this volume an effort is made to advance in certain of these issues. The monograph has evolved over many years, coming of age by stages. First it was an impressive job of gathering together the bulk of the impor tant contributions to estimation theory, an understanding and moderniza tion of some of its results and methods, with the intention of applying them to recursive filtering problems."

This volume contains the proceedings of the NATO Advanced Study Institute "Symmetric Functions 2001: Surveys of Developments and Per- spectives", held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, during the two weeks 25 June - 6 July 2001. The objective of the ASI was to survey recent developments and outline research perspectives in various fields, for which the fundamental questions can be stated in the language of symmetric functions (along the way emphasizing interdisciplinary connections). The instructional goals of the event determined its format: the ASI consisted of about a dozen mini-courses. Seven of them served as a basis for the papers comprising the current volume. The ASI lecturers were: Persi Diaconis, William Fulton, Mark Haiman, Phil Hanlon, Alexander Klyachko, Bernard Leclerc, Ian G. Macdonald, Masatoshi Noumi, Andrei Okounkov, Grigori Olshanski, Eric Opdam, Ana- toly Vershik, and Andrei Zelevinsky. The organizing committee consisted of Phil Hanlon, Ian Macdonald, Andrei 0 kounkov, G rigori 0 lshanski (co-director), and myself ( co-director). The original ASI co-director Sergei Kerov, who was instrumental in determining the format and scope of the event, selection of speakers, and drafting the initial grant proposal, died in July 2000. Kerov's mathemat- ical ideas strongly influenced the field, and were presented at length in a number of ASI lectures. A special afternoon session on Monday, July 2, was dedicated to his memory.

Speckle photography is an advanced experimental technique used for quantitatve determination of density, velocity and temperature fields in gas, liquid, and plasma flows. This book presents the most important equations for the diffraction theory of speckle formation and the statistical properties of speckle fields. It also describes experimental set-ups and the equipment needed to implement these methods. Speckle photography methods for automatic data acquisition and processing are considered and examples for their use are given.

The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g., the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good") yields that the practical significance of optimal preplanned controls proves to be not great: such controls are usually sensitive to unregistered disturbances (includ ing the round-off errors which are inevitable when computer devices are used for forming controls), as there is the effect of disturbance accumulation in the control process which makes controls to be of little use on large time inter vals. This gap is mainly provoked by oversimplified settings of optimization problems. The outstanding result of control theory established in the end of the first half of our century is that controls in feedback form ensure the weak sensitivity of closed loop systems with respect to "small" unregistered internal and external disturbances acting in them (here we do not need to discuss performance indexes, since the considered phenomenon is of general nature). But by far not all optimal preplanned controls can be represented in a feedback form."

The work shows the fascination of topology- and geometry-governed properties of self-rolled micro- and nanoarchitectures. The author provides an in-depth representation of the advanced theoretical and numerical models for analyzing key effects, which underlie engineering of transport, superconducting and optical properties of micro- and nanoarchitectures.

One service mathematics has rendered the 'Bt mm, ... si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point alIe.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

In this volume the investigations of filtering problems, a start on which has been made in 55], are being continued and are devoted to theoretical problems of processing stochastic fields. The derivation of the theory of processing stochastic fields is similar to that of the theory extensively developed for stochastic processes ('stochastic fields with a one-dimensional domain'). Nevertheless there exist essential distinctions between these cases making a construction of the theory for the multi-dimensional case in such a way difficult. Among these are the absence of the notion of the 'past-future' in the case of fields, which plays a fundamental role in constructing stochastic processes theory. So attempts to introduce naturally the notion of the causality (non-anticipativity) when synthesising stable filters designed for processing fields have not met with success. Mathematically, principal distinctions between multi-dimensional and one-dimensional cases imply that the set of roots of a multi-variable polyno mial does not necessary consist of a finite number of isolated points. From the main theorem of algebra it follows that in the one-dimensional case every poly nomial of degree n has just n roots (considering their multiplicity) in the com plex plane. As a consequence, in particular, an arbitrary rational function cents(."

I. Measures and quasimeasures. Integration.- 1. Realvalued measures on algebras of sets.- 1.1. Premeasures.- 1.2. Same tests for ?-additivity of premeasures.- 1.3. Measurable and topological Radon spaces.- 1.4. Cylindrical measures.- 2. Cylinder sets and cylindrical functions.- 2.1. General definition of cylinder set.- 2.2. Cylinder sets in a linear space X.- 2.3. Measurable linear space.- 2.4. Cylindrical functions.- 3. Quasimeasures. Integration.- 3.1. Quasimeasures.- 3.2. Integral with respect to a quasimeasure.- 3.3. Quasimeasures in a measurable linear space.- 3.4. Positive quasimeasures.- 3.5. Integration of noncylindrical functions.- 4. Supplement: Some notions related to the topology of linear spaces.- 4.1. Prenorms.- 4.2. Locally convex spaces.- 4.3. Duality of linear spaces.- 4.4. Rigged Hilbert spaces.- 4.5. Polars.- 4.6. Nuclear topology.- 4.7. Compactness.- 5. Chapter I: Supplementary remarks and historical comments.- II. Gaussian measures in Hilbert space.- 1. Gaussian measures in finite-dimensional spaces.- 1.1. Characteristic functional and density.- 1.2. Computation of certain integrals.- 1.3. Integration by parts.- 1.4. Solution of the Cauchy problem.- 2. Gaussian measures in Hilbert space.- 2.1. ?-additivity for a Gaussian cylindrical measure.- 2.2. Some transformations of Gaussian measures in X.- 2.3. Computation of integrals.- 2.4. Gaussian cylindrical measures with arbitrary correlation operator.- 3. Measurable linear functionals and operators.- 3.1. Measurable linear functionals.- 3.2. Measurable linear operators.- 3.3. Integration by parts.- 3.4. Expansion into orthogonal polynomials.- 4. Absolute continuity of Gaussian measures.- 4.1. Equivalence of measures in a product space.- 4.2. Equivalence of Gaussian measures which differ by their means.- 4.3. Equivalence of Gaussian measures with distinct correlation operators.- 4.4. Absolute continuity of measures obtained from Gaussian measures by certain transformations of space.- 5. Fourier-Wiener transformation.- 5.1. Fourier transformation with respect to a Gaussian measure.- 5.2. Fourier-Wiener transformation of entire nmctions.- 5.3. Connection between the Fourier-Wiener transformation and orthogonal polynomials.- 6. Complexvalued Gaussian quasimeasures.- 6.1. Feynman integrals.- 6.2. Integration of analytic functionals.- 6.3. Computation of certain Feynman integrals.- 7. Chapter II: Supplementary re marks and historical comments.- III. Measures in linear topological spaces.- 1. ?-additivity conditions for nonnegative cylindrical measures in the space X' dual to a locally convex space X.- 1.1. Sufficient conditions for ?-additivity. Strong regularity.- 1.2. Necessary conditions for ?-additivityM.- 1.3. The Hilbert space case.- 1.4. Integral representations of the group of unitary operators.- 1.5. Continuous cylindrical measures.- 2. Sequences of Radon measures.- 2.1. Weak compaetness in a spaee of measures.- 2.2. Weak completeness of spaees of measures.- 2.3. Properties of R-spaces.- 2.4. Examples of R-spaces.- 2.5. Weak compaetness of a family of measures in a space X'.- 3. Chapter III: Supplementary remarks and historical comments.- IV. Differentiable measures and distributions.- 1. Differentiable functions, differentiable expressions.- 1.1. Derivatives of a vector function.- 1.2. Higher order derivatives.- 1.3. Linear differential expressions.- 1.4. Symmetrie and dissipative differential operators.- 2. Differentiable measures.- 2.1. Derivative of a measure.- 2.2. The logarithmie derivative.- 2.3. The derivative of a measure as an element of the dual space.- 2.4. Higher order derivatives.- 3. Distributions and generalized functions.- 3.1. Test functions and measures.- 3.2. Distributions. Operations on distributions.- 3.3. Generalized funetions and kernels.- 3.4. Fourier transformation of distributions.- 3.5. Differential expressions for distributions.- 4. Positive definiteness. Quasi-invariant distributions and bidistributions.- 4.1. Positive distri

This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.

This monograph discusses cosmological inflation and provides exact and slow roll solutions. It also reviews new and advanced approaches of exact solutions construction with canonical scalar fields, including application of generating functions methods, the superpotential and many others. This book presents the reduction of the Friedmann equation to the Abel equation, which is a very useful tool in cosmology. It offers new solutions and discusses its properties.Additionally, it touches upon the role of phantom scalar field cosmology and analyzes phantonical models. It describes brane cosmology with scalar fields, providing exact solutions construction using the superpotential method as well as Darboux transformations.This book provides detailed calculations throughout.

This book, now in its second edition, introduces readers to quantum rings as a special class of modern high-tech material structures at the nanoscale. It deals, in particular, with their formation by means of molecular beam epitaxy and droplet epitaxy of semiconductors, and their topology-driven electronic, optical and magnetic properties. A highly complex theoretical model is developed to adequately represent the specific features of quantum rings. The results presented here are intended to facilitate the development of low-cost high-performance electronic, spintronic, optoelectronic and information processing devices based on quantum rings. This second edition includes both new and significantly revised chapters. It provides extensive information on recent advances in the physics of quantum rings related to the spin-orbit interaction and spin dynamics (spin interference in Rashba rings, tunable exciton topology on type II InAs/GaAsSb quantum nanostructures), the electron-phonon interaction in ring-like structures, quantum interference manifestations in novel materials (graphene nanoribbons, MoS2), and the effects of electrical field and THz radiation on the optical properties of quantum rings. The new edition also shares insights into the properties of various novel architectures, including coupled quantum ring-quantum dot chains and concentric quantum rings, topologic states of light in self-assembled ring-like cavities, and optical and plasmon m.odes in Moebius-shaped resonators.

This book constitutes the proceedings of the 13th International Computer Science Symposium in Russia, CSR 2018, held in Moscow, Russia, in May 2018. The 24 full papers presented together with 7 invited lectures were carefully reviewed and selected from 42 submissions. The papers cover a wide range of topics such as algorithms and data structures; combinatorial optimization; constraint solving; computational complexity; cryptography; combinatorics in computer science; formal languages and automata; algorithms for concurrent and distributed systems; networks; and proof theory and applications of logic to computer science.

This textbook presents the basic concepts and methods of fluid mechanics, including Lagrangian and Eulerian descriptions, tensors of stresses and strains, continuity, momentum, energy, thermodynamics laws, and similarity theory. The models and their solutions are presented within a context of the mechanics of multiphase media. The treatment fully utilizes the computer algebra and software system Mathematica (R) to both develop concepts and help the reader to master modern methods of solving problems in fluid mechanics. Topics and features: Glossary of over thirty Mathematica (R) computer programs Extensive, self-contained appendix of Mathematica (R) functions and their use Chapter coverage of mechanics of multiphase heterogeneous media Detailed coverage of theory of shock waves in gas dynamics Thorough discussion of aerohydrodynamics of ideal and viscous fluids an d gases Complete worked examples with detailed solutions Problem-solving approach Foundations of Fluid Mechanics with Applications is a complete and accessible text or reference for graduates and professionals in mechanics, applied mathematics, physical sciences, materials science, and engineering. It is an essential resource for the study and use of modern solution methods for problems in fluid mechanics and the underlying mathematical models. The present, softcover reprint is designed to make this classic textbook available to a wider audience.

This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.

The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g., the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good") yields that the practical significance of optimal preplanned controls proves to be not great: such controls are usually sensitive to unregistered disturbances (includ ing the round-off errors which are inevitable when computer devices are used for forming controls), as there is the effect of disturbance accumulation in the control process which makes controls to be of little use on large time inter vals. This gap is mainly provoked by oversimplified settings of optimization problems. The outstanding result of control theory established in the end of the first half of our century is that controls in feedback form ensure the weak sensitivity of closed loop systems with respect to "small" unregistered internal and external disturbances acting in them (here we do not need to discuss performance indexes, since the considered phenomenon is of general nature). But by far not all optimal preplanned controls can be represented in a feedback form."

This two-volume set of LNCS 7965 and LNCS 7966 constitutes the refereed proceedings of the 40th International Colloquium on Automata, Languages and Programming, ICALP 2013, held in Riga, Latvia, in July 2013. The total of 124 revised full papers presented were carefully reviewed and selected from 422 submissions. They are organized in three tracks focussing on algorithms, complexity and games; logic, semantics, automata and theory of programming; and foundations of networked computation.

lEt moi, .... si j'avait Sll comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile: ' where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded 0- sense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1re of this series."

In this volume the investigations of filtering problems, a start on which has been made in 55], are being continued and are devoted to theoretical problems of processing stochastic fields. The derivation of the theory of processing stochastic fields is similar to that of the theory extensively developed for stochastic processes ('stochastic fields with a one-dimensional domain'). Nevertheless there exist essential distinctions between these cases making a construction of the theory for the multi-dimensional case in such a way difficult. Among these are the absence of the notion of the 'past-future' in the case of fields, which plays a fundamental role in constructing stochastic processes theory. So attempts to introduce naturally the notion of the causality (non-anticipativity) when synthesising stable filters designed for processing fields have not met with success. Mathematically, principal distinctions between multi-dimensional and one-dimensional cases imply that the set of roots of a multi-variable polyno mial does not necessary consist of a finite number of isolated points. From the main theorem of algebra it follows that in the one-dimensional case every poly nomial of degree n has just n roots (considering their multiplicity) in the com plex plane. As a consequence, in particular, an arbitrary rational function cents(."

This book is devoted to an investigation of some important problems of mod ern filtering theory concerned with systems of 'any nature being able to per ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to 27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent activity in this area is observed, researchers are trying consistently to generalize famous results, extend them to more broad classes of processes, realize and justify more simple procedures for processing measurement data in order to obtain more efficient filtering algorithms. As to nonlinear filter ing, it remains much as fragmentary. Here much progress has been made by R. L. Stratonovich and his successors in the area of filtering of Markov processes. In this volume an effort is made to advance in certain of these issues. The monograph has evolved over many years, coming of age by stages. First it was an impressive job of gathering together the bulk of the impor tant contributions to estimation theory, an understanding and moderniza tion of some of its results and methods, with the intention of applying them to recursive filtering problems."

Fluid mechanics (FM) is a branch of science dealing with the investi gation of flows of continua under the action of external forces. The fundamentals of FM were laid in the works of the famous scientists, such as L. Euler, M. V. Lomonosov, D. Bernoulli, J. L. Lagrange, A. Cauchy, L. Navier, S. D. Poisson, and other classics of science. Fluid mechanics underwent a rapid development during the past two centuries, and it now includes, along with the above branches, aerodynamics, hydrodynamics, rarefied gas dynamics, mechanics of multi phase and reactive media, etc. The FM application domains were expanded, and new investigation methods were developed. Certain concepts introduced by the classics of science, however, are still of primary importance and will apparently be of importance in the future. The Lagrangian and Eulerian descriptions of a continuum, tensors of strains and stresses, conservation laws for mass, momentum, moment of momentum, and energy are the examples of such concepts and results. This list should be augmented by the first and second laws of thermodynamics, which determine the character and direction of processes at a given point of a continuum. The availability of the conservation laws is conditioned by the homogeneity and isotrop icity properties of the Euclidean space, and the form of these laws is related to the Newton's laws. The laws of thermodynamics have their foundation in the statistical physics."

One service mathematics has rendered the 'Bt mm, ... si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point alIe.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

Parameterized complexity is currently a thriving field in complexity theory and algorithm design. A significant part of the success of the field can be attributed to Michael R. Fellows.
This Festschrift has been published in honor of Mike Fellows on the occasion of his 60th birthday. It contains 20 papers that showcase the important scientific contributions of this remarkable man, describes the history of the field of parameterized complexity, and also reflects on other parts of Mike Fellows's unique and broad range of interests, including his work on the popularization of discrete mathematics for young children.
The volume contains several surveys that introduce the reader to the field of parameterized complexity and discuss important notions, results, and developments in this field.