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This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop'Lie Theory and Its Applications in Physics'held in Sofia, Bulgaria (on-line) in June 2021.Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field.The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras.This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

This book comprises state-of-the-art research results in the field of mechatronics and other closely related areas and that will be presented on occasion of the third “International Conference of Reliable Systems Engineering (ICoRSE 2023)” that will take place in Bucharest, Romania, between 07–08 September 2023.The first two ICoRSE editions brought together professors, Ph.D. students, and researchers in Europe, North America, and Asia, in countries such as: England, Albania, Austria, Bulgaria, Canada, Czech Republic, Germany, France, Italy, Portugal, Turkey, Ukraine, Uzbekistan, and Vietnam. In this year's edition of the conference, we have benefitted from the inclusion in the scientific committee of the conference of professors in all of these countries, and we cover a wide variety of topics, such as: theoretical and applied mechanics; cyber-physical systems, robotics, smart bio-medical and bio-mechatronic systems, new and intelligent materials and structures, modelling andsimulation in mechanics and mechatronics, smart mechatronic production and control system, optics, control systems, big data modelling, micro- and nanotechnology, automation, manufacturing optimization, and other.Since the book´s chapters represent contributions of scholars who work in both state-funded institutions and in the business environment, they reflect a clear picture of the novelties attained in the leading-edge sciences that are in the scope of the conference. It is our belief that the book is useful to both students and researchers in all areas of engineering, who will each find at least one topic worthy of their interest in this work.

This book gathers the latest advances, innovations, and applications in the field of sustainable energy systems, as presented by researchers and engineers at the International Conference Sustainable Energy Systems: Innovative Perspectives (SES), held in Saint-Petersburg, Russia, on October 29-30, 2020. It covers highly diverse topics, including applications of renewable energy sources, recycling of solid municipal and industrial waste, circular economy based on agricultural waste, energy-efficient and sustainable buildings, innovation management and technologies of sustainable cities, sustainable construction, creative construction technology and materials, construction simulation and virtual construction, BIM and rapid prototyping for construction, consumption practices in the digital era, sustainable operations management, and supply chain management in the digital era. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting ideas that will spur novel research directions and foster multidisciplinary collaborations.

The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits'theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel–Hopf, Poincaré–Birkhoff–Witt, and Cartier–Milnor–Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.

This book constitutes the refereed proceedings of the third Maple Conference, MC 2019, held in Waterloo, Ontario, Canada, in October 2019. The 21 revised full papers and 9 short papers were carefully reviewed and selected out of 37 submissions, one invited paper is also presented in the volume. The papers included in this book cover topics in education, algorithms, and applciations of the mathematical software Maple.

An important task of theoretical quantum physics is the building of idealized mathematical models to describe the properties of quantum matter. This book provides an introduction to the arguably most important method for obtaining exact results for strongly interacting models of quantum matter - the Bethe ansatz. It introduces and discusses the physical concepts and mathematical tools used to construct realistic models for a variety of different fields, including condensed matter physics and quantum optics. The various forms of the Bethe ansatz - algebraic, coordinate, multicomponent, and thermodynamic Bethe ansatz, and Bethe ansatz for finite systems - are then explained in depth and employed to find exact solutions for the physical properties of the integrable forms of strongly interacting quantum systems. The Bethe ansatz is one of the very few methodologies which can calculate physical properties non-perturbatively. Arguably, it is the only such method we have which is exact. This means, once the model has been set up, no further approximations or assumptions are necessary, and the relevant physical properties of the model can be computed exactly. Furthermore, an infinite set of conserved quantities can be obtained. The quantum mechanical model under consideration is fully integrable. This makes the search for quantum models which are amenable to an exact solution by the Bethe ansatz, and which are quantum integrable, so important and rewarding. The exact solution will provide benchmarks for other models, which do not admit an exact solution. Bethe ansatz techniques provide valuable insight into the physics of strongly correlated quantum matter.

The International Chess Federation or FIDE (from the French Federation Internationale des Echecs) was founded in Paris in 1924 but only from 1950 began to award international titles. This book lists more than 18,000 players who received titles from 1950 through 2016. Entries include (where available) the player's full name, federation, date of birth, place of birth, date of death, place of death, title and year of award and peak rating (month and year), with references provided.

The NATO Advanced Research Workshop on Coherent Optical Processes in Semiconductors was held in Cambridge, England on August 11-14,1993. The idea of holding this Workshop grew from the recent upsurge in activity on coherent transient effects in semiconductors. The development of this field reflects advances in both light sources and the quality of semiconductor structures, such that tunable optical pulses are now routinely available whose duration is shorter than the dephasing time for excitonic states in quantum wells. It was therefore no surprise to the organisers that as the programme developed, there emerged a heavy emphasis on time-resolved four-wave mixing, particularly in quantum wells. Nevertheless, other issues concerned with coherent effects ensured that several papers on related problems contributed some variety. The topics discussed at the workshop centred on what is a rather new field of study, and benefited enormously by having participants representing many of the principal groups working in this area. Several themes emerged through the invited contributions at the Workshop. One important development has been the careful examination of the two-level model of excitonic effects; a model which has been remarkably successful despite the expected complexities arising from the semiconductor band structure. Indeed, modest extensions to the two level model have been able to offer a useful account for some of the complicated polarisation dependence of four-wave mixing signals from GaAs quantum wells. This work clearly is leading to an improved understanding of excitons in confined systems.

Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com­ plex nonlinear systems that cannot be broken down into the behavior of their con­ stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.

This volume contains the Proceedings of the NATO Advanced Research Workshop (ARW) and Emil-Warburg-Symposium (EWS)'Nonlinear Coherent Structures in Phy­ sics and Biology'held at the University of Bayreuth from June 1 -4, 1993. Director of the ARW was K. H. Spatschek, while F.G. Mertens acted as the co-director, host, and organizer of the EWS. The other members of the scientific organizing committee were A.R. Bishop (Los Alamos), J.C. Eilbeck (Edinburgh), and M. Remoissenet (Dijon). This was the eighth meeting in a series of interdisciplinary workshops founded by our French colleagues who had organized all the previous workshops, e.g. 1989 in Montpel­ lier and 1991 in Dijon. We were asked to organize the meeting this time in Germany. Of course, we wanted to keep the character defined by the previous meetings, which were always characterized by an open and friendly atmosphere, being not too large in quantity, but high in quality. This time altogether 103 participants attended the workshop. During the past years most of the participants met several times and discussed problems connected with the generation of nonlinear coherent structures in physics and biology.

This volume contains invited papers and contributions delivered at the International Conference on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland during the summer of 1993. The conference was supported by the NATO Scientific and Environmental Affairs Division as an Advanced Research Workshop. In fact, it was the first scientific conference in all Eastern Europe supported by NATO. The meeting was expected to establish contacts between East and West experts as well as to study the current state of the art in the area of Hamiltonian Mechanics and its applications. I am sure that the informal atmosphere of the city of Torun, the birthplace of Nicolaus Copernicus, stimulated many valuable scientific exchanges. The first idea for this cnference was carried out by Prof Andrzej J. Maciejewski and myself, more than two years ago, during his visit in Greece. It was planned for about forty well-known scientists from East and West. At that time participation of a scientist from Eastern Europe in an Organising Committee of a NATO Conference was not allowed. But always there is the first time. Our plans for such a'small'conference, as a first attempt in the new European situation -the Europe without borders -quickly passed away. The names of our invited speakers, authorities in their field, were a magnet for many colleagues from all over the world.

Proceedings of the NATO Advanced Study Institute, held in Cambridge, UK, from 25th June to 6th July, 2001

The last decade has been witness to many exciting and rapid developments in the fields of Nuclear Physics and Intermediate Energy Physics, the interface between Nuclear and Elementary Particle Physics. These developments involved to a large extent the sub nucleonic degrees of freedom in nuclei. In deep inelastic lepton scattering from nuclei, for example, it was observed that the quark structure of the nucleon is influenced by the nuclear medium. Also, the spin-dependent structure function of the nucleon was found to differ from sum rules based on SU(3) symmetry, a discrepancy referred to as the'spin crisis'. In pion electroproduction at threshold and in the production of pions and other mesons in heavy ion collisions at intermediate energies interesting experimental results have been obtained, which triggered lively theoretical discussions. Furthermore, the search for the quark-gluon plasma phase of hadronic matter, a phase that is supposed to have existed in the first few seconds of the Big Bang, has been intensified. Not only were these developments accompanied by technical developments, such as the building of new experimental facilities, but also extensive theoretical efforts have been directed towards understanding these phenomena. These concerted efforts will hopefully lead to an understanding of the transition from the non-perturbative QCD regime to the perturbative one, in which the quark structure of nucleons is better understood. All of the aforementioned developments occur at a high pace, making it difficult to incorporate them into the courses offered to advanced students.

This volume contains the lectures and contributions presented at the NATO Advanced Study Institute (ASI) on'Frontier Topics in Nuclear Physics', held at Predeal in Romania from 24 August to 4 September 1993. The ASI stands in a row of 23 Predeal Summer Schools organized by the Institute of Atomic Physics (Bucharest) in Predeal or Poiana-Brasov during the last 25 years. The main topics of the ASI were cluster radioactivity, fission and fusion. the production of very heavy elements, nuclear structure described with microscopic and collective models, weak: interaction and double beta decay, nuclear astrophysics, and heavy ion reactions from low to ultrarelativistic energies. The content of this book is ordered according to these topics. The ASI started with a lecture by Professor Greiner on the'Present and future of nuclear physics', showing the most important new directions of research and the interdisciplinary relations of nuclear physics with other fields of physics. This lecture is printed in the first chapter of the book.

The Cargese Workshop'Quantum Field Theory and String Theory'was held from May 10 to May 21, 1993. The broad spectrum of the work presented at the Workshop was the reflec­ tion of a time of intensive search for new ways of solving some of the most fun­ damental problems in string theory, quantum gravity and non-perturbative field theory. A number of talks indicated the emergence of new promising domains of investigation. It is this very diversity of topics which, in our opinion, represents one of the most attractive features of the present volume which we hope will provide a good orientation in the abundant flow of ideas and publications in modern quantum field theory. Many contributions to the present proceedings are concerned with two di­ mensional quantum field theory. The continuous advances in the domain of two dimensional integrable theories on the lattice as well as in the continuum, including conformal field theories, Liouville field theory and matrix models of two dimensional quantum gravity are very well represented. Other papers address physically realistic (and therefore very complicated) problems like de­ veloped turbulence, the Hofstadter problem, higher dimensional gravity and phenomenological strings. A new elegant class of topological field theories is presented. New ideas in the string representation of multicolor quantum chromo dynamics were widely discussed at the Workshop, more particularly the example of the exactly solvable two dimensional case.

Ladies and Gentlemen, dear colleagues, Welcome in Bodrum to the NASion Hot and Dense Nuclear Matter! Welcome also to Mrs. Governor Dr. Lale AYTAMAN. We are very honored, that you, Governor of the Mugla-State, came here to greet us. We are particularly grateful to you that you offered help and assured us to do everything that we can enjoy two safe weeks in Bodrum, in this wonderful area of your country. I have chosen Bodrum as the place for our NASI because I like this historic region where many cultures meet (e. g., Oriental and European (Greek, Roman) culture) and where you find numerous places which played a role in ancient science and in early Christianity- I mention Milet (Thales) and Ephesus (Apostle Paulus), both of which are close by. Our NASI will exhibit the most recent developments in high energy heavy ion physics. The meeting is both a school and a conference: A school, because there are very many advanced students, who frequently are themselves already top researchers, attending the lectures of distinguished scientists and leading researchers. It is also a conference because new material, new results of this exciting and wonderful field - our field - high energy heavy ion physics will be presented. It is the topic of hot and dense nuclear matter, which we are focusing on.