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The papers presented in this open access book address diverse challenges in decarbonizing energy systems, ranging from operational to investment planning problems, from market economics to technical and environmental considerations, from distribution grids to transmission grids, and from theoretical considerations to data provision concerns and applied case studies. While most papers have a clear methodological focus, they address policy-relevant questions at the same time. The target audience therefore includes academics and experts in industry as well as policy makers, who are interested in state-of-the-art quantitative modelling of policy relevant problems in energy systems. The 2nd International Symposium on Energy System Optimization (ISESO 2018) was held at the Karlsruhe Institute of Technology (KIT) under the symposium theme ΓÇ£Bridging the Gap Between Mathematical Modelling and Policy SupportΓÇ¥ on October 10th and 11th 2018. ISESO 2018 was organized by the KIT, the Heidelberg Institute for Theoretical Studies (HITS), the Heidelberg University, the German Aerospace Center and the University of Stuttgart.

Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics.The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.

With contributions by numerous experts

This book is a collection of short papers from the 11th International ISAAC Congress 2017 in Vaxjoe, Sweden. The papers, written by the best international experts, are devoted to recent results in mathematics with a focus on analysis.

Local smoothing of Fourier integral operators and Hermite functions.- On () -classes on the Engel group.- Gelfand triples for the Kohn-Nirenberg quantization on homogeneous Lie groups.- A multiplicity result for a non-homogeneous subelliptic problem with Sobolev exponent.- The Dixmier trace and the noncommutative residue for multipliers on compact manifolds.- On the focusing energy-critical 3D quintic inhomogeneous NLS.- Lifespan of solutions to nonlinear Schr├╢dinger equations with general homogeneous nonlinearity of the critical order.- Spectral theory for magnetic Schr├╢dinger operators in exterior domains with exploding and oscillating long-range potentials.- Simple proof of the estimate of solutions to Schr├╢dinger equations with linear and sub-linear potentials in modulation spaces.- Remark on asymptotic order for the energy critical nonlinear damped wave equation to the linear heat equation via the Strichartz estimates.- On uniqueness for the generalized Choquard equation.- Characterization of the ground state to the intercritical NLS with a linear potential by the virial functional.- Well-posedness for a generalized Klein-Gordon-Schr├╢dinger equations.

This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering.

The book consists of articles based on the XXXVII Bialowieza Workshop on Geometric Methods in Physics, 2018.

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones.

The book consists of articles based on the XXXVIII Biäowie¿a Workshop on Geometric Methods in Physics, 2019. The series of Biäowie¿a workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics.For the past eight years, the Biäowie¿a Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Biäowie¿a forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities.The chapter ¿Toeplitz Extensions in Noncommutative Topology and Mathematical Physics¿ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24¿28, 2019.The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems.The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling.

This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory.

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays.

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov- ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil- ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal- ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen- tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter- action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol- ume treats various aspects of CR geometry and the Bergman kernel/ pro- jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.

This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.

This volume is the Proceedings of the Third Korea-China-Japan Inter­ national Symposium on Ring Theory held jointly with the Second Korea­ Japan Joint Ring Theory Seminar which took place at the historical resort area of Korea, Kyongju, June 28-July 3, 1999. It also includes articles by some invited mathematicians who were unable to attend the conference. Over 90 mathematicians from 12 countries attended this conference. The conference is held every 4 years on a rotating basis. The first con­ ference was held in 1991 at Guilin, China. In 1995 the second conference took place in Okayama, Japan. At the second conference it was decided to include Korea, who hosted this conference of 1999. During the past century Ring Theory has diversified into many subar­ eas. This is reflected in these articles from over 25 well-known mathemati­ cians covering a broad range of topics, including: Classical Ring Theory, Module Theory, Representation Theory, and the theory of Hopf Algebras. Among these peer reviewed papers are invited survey articles as well as research articles. The survey articles provide an overview of various areas for researchers looking for a new or related field to investigate, while the research articles give the flavor of current research. We feel that the variety of related topics will stimulate interaction between researchers. Moreover the Open Problems section provides guidance for future research. This book should prove attractive to a wide audience of algebraists. Gary F. Birkenmeier, Lafayette, U. S. A.