Orthogonal Polynomials Current Trends And Applications

Author by : Francisco Marcellán
Languange : en
Publisher by : Springer Nature
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Description : The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganés, Spain, from July 3 to July 6, 2018. These meetings were mainly focused to encourage research in the fields of approximation theory, special functions, orthogonal polynomials and their applications among graduate students as well as young researchers from Latin America, Spain and Portugal. The presentation of the state of the art as well as some recent trends constitute the aim of the lectures delivered in the EIBPOA by worldwide recognized researchers in the above fields. In this volume, several topics on the theory of polynomials orthogonal with respect to different inner products are analyzed, both from an introductory point of view for a wide spectrum of readers without an expertise in the area, as well as the emphasis on their applications in topics as integrable systems, random matrices, numerical methods in differential and partial differential equations, coding theory, and signal theory, among others.


Recent Trends In Orthogonal Polynomials And Approximation Theory

Author by : Guillermo Lopez Lagomasino
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday. This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.


Random Matrix Theory Interacting Particle Systems And Integrable Systems

Author by : Percy Deift
Languange : en
Publisher by : Cambridge University Press
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Description : This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.


Topics In Classical And Modern Analysis

Author by : Martha Abell
Languange : en
Publisher by : Springer Nature
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Description : Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.


Modern Trends In Constructive Function Theory

Author by : E. B. Saff
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the conference Constructive Functions 2014, held from May 26-30, 2014, at Vanderbilt University, Nashville, TN, in honor of Ed Saff's 70th birthday. The papers in this volume contain results on polynomial approximation, rational approximation, Log-optimal configurations on the sphere, random continued fractions, ratio asymptotics for multiple orthogonal polynomials, the bivariate trigonometric moment problem, minimal Riesz energy, random polynomials, Pade and Hermite-Pade approximation, orthogonal expansions, hyperbolic differential equations, Bergman polynomials, the Meijer $G$-function, polynomial ensembles, and integer lattice points.


Notions Of Positivity And The Geometry Of Polynomials

Author by : Petter Brändén
Languange : en
Publisher by : Springer Science & Business Media
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Description : The book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables. It is dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician, Professor at the University of Stockholm. With his extremely original contributions and broad vision, his impact on the topics of the planned volume cannot be underestimated. All contributors knew or have exchanged ideas with Dr. Borcea, and their articles reflect, at least partially, his heritage.


2011

Author by : Anonim
Languange : en
Publisher by : Walter de Gruyter
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Description : Particularly in the humanities and social sciences, festschrifts are a popular forum for discussion. The IJBF provides quick and easy general access to these important resources for scholars and students. The festschrifts are located in state and regional libraries and their bibliographic details are recorded. Since 1983, more than 639,000 articles from more than 29,500 festschrifts, published between 1977 and 2010, have been catalogued.


The Hermitian Two Matrix Model With An Even Quartic Potential

Author by : Maurice Duits
Languange : en
Publisher by : American Mathematical Soc.
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Description : The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.


Complex Methods In Approximation Theory

Author by : Francisco Marcellán
Languange : en
Publisher by : Universidad Almería
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Description : This book provides an up-to-date account of research in Approximation Theory and Complex Analysis, areas which are the subject of recent exciting developments.The level of presentation should be suitable for anyone with a good knowledge of analysis, including scientists with a mathematical background. The volume contains both research papers and surveys, presented by specialists in the field. The areas discussed are: Orthogonal Polynomials (with respect to classical and Sobolev inner products), Approximation in Several Complex Variables, Korovkin-type Theorems, Potential Theory, Ratinal Approximation and Linear Ordinary Differential Equations.


Function Spaces In Modern Analysis

Author by : Krzysztof Jarosz
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the Sixth Conference on Function Spaces, which was held from May 18-22, 2010, at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.


Interpolation Processes

Author by : Giuseppe Mastroianni
Languange : en
Publisher by : Springer Science & Business Media
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Description : Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that - peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vértesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., - sultsondivergentinterpolationprocesses,usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent - terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in this eld (orthogonal polynomials, moduli of smoothness,K-functionals, etc.), as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.


Advances In Non Archimedean Analysis

Author by : Jesus Araujo-Gomez
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains papers based on lectures given at the Eleventh International Conference on $p$-adic Functional Analysis, which was held from July 5-9, 2010, in Clermont-Ferrand, France. The articles collected here feature recent developments in various areas of non-Archimedean analysis: Hilbert and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach function spaces, and measure and integration. Other topics discussed in this volume include $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic functions, the spectrum of some algebras of analytic functions, and maximal ideals of the ultrametric corona algebra.


In The Tradition Of Ahlfors Bers V

Author by : Mario Bonk
Languange : en
Publisher by : American Mathematical Soc.
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Description : The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic geometry, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields of mathematics, such as algebraic geometry, dynamical systems, topology, geometric group theory, mathematical physics, and number theory. Recent years have seen a flowering of this legacy with an increased interest in their work. This current volume contains articles on a wide variety of subjects that are central to this legacy. These include papers in Kleinian groups, classical Riemann surface theory, translation surfaces, algebraic geometry and dynamics. The majority of the papers present new research, but there are survey articles as well.


Arithmetic Geometry Cryptography And Coding Theory 2009

Author by : David R. Kohel
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 12th conference on Arithmetic, Geometry, cryptography and coding Theory, held in Marseille, France from March 30 to April 3, 2009, as well as the first Geocrypt conference, held in pointe-a-pitre, guadeloupe, from April 27 to may 1, 2009, and the European science Foundation exploratory workshop on curves, coding Theory, and Cryptography, held in Marseille, France from March 25 to 29, 2009. The articles Contained in this volume come from three related symposia organized by the group Arithmetique et Theorie de I' Information in Marseille. The topics cover arithmetic properties of curves and higher dimensional varieties with applications to codes and cryptography.


Orthogonal Polynomials Current Trends And Applications

Author by : Francisco Marcellán
Languange : en
Publisher by : Unknown
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Description : The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganés, Spain, from July 3 to July 6, 2018. These meetings were mainly focused to encourage research in the fields of approximation theory, special functions, orthogonal polynomials and their applications among graduate students as well as young researchers from Latin America, Spain and Portugal. The presentation of the state of the art as well as some recent trends constitute the aim of the lectures delivered in the EIBPOA by worldwide recognized researchers in the above fields. In this volume, several topics on the theory of polynomials orthogonal with respect to different inner products are analyzed, both from an introductory point of view for a wide spectrum of readers without an expertise in the area, as well as the emphasis on their applications in topics as integrable systems, random matrices, numerical methods in differential and partial differential equations, coding theory, and signal theory, among others.


Homotopy Theory Of Function Spaces And Related Topics

Author by : Yves Félix
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote crossfertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.


Topology Of Algebraic Varieties And Singularities

Author by : Anatoly Libgober
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain. The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.


Symplectic Topology And Measure Preserving Dynamical Systems

Author by : Albert Fathi
Languange : en
Publisher by : American Mathematical Soc.
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Description : The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Symplectic Topology and Measure Preserving Dynamical Systems held in Snowbird, Utah in July 2007. The aim of the conference was to bring together specialists of symplectic topology and of measure preserving dynamics to try to connect these two subjects. One of the motivating conjectures at the interface of these two fields is the question of whether the group of area preserving homeomorphisms of the 2-disc is or is not simple. For diffeomorphisms it was known that the kernel of the Calabi invariant is a normal proper subgroup, so the group of area preserving diffeomorphisms is not simple. Most articles are related to understanding these and related questions in the framework of modern symplectic topology.


Nonlinear Elliptic Partial Differential Equations

Author by : J. P. Gossez
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.


Groups Algebras And Applications

Author by : César Polcino Milies
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3-8, 2009, in Sao Paulo, Brazil. It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding Theory.


Combinatorics And Physics

Author by : Kurusch Ebrahimi-Fard
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.


Approximation Theory

Author by : Luc Wuytack
Languange : en
Publisher by : North-Holland
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Description : /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! The field of numerical analysis has witnessed many significant developments in the 20th century and will continue to enjoy major new advances in the years ahead. Therefore, it seems appropriate to compile a "state-of-the-art" volume devoted to numerical analysis in the 20th century. This volume on "Approximation Theory" is the first of seven volumes that will be published in this Journal. It brings together the papers dealing with historical developments, survey papers and papers on recent trends in selected areas. In his paper, G.A. Watson gives an historical survey of methods for solving approximation problems in normed linear spaces. He considers approximation in Lp and Chebyshev norms of real functions and data. Y. Nievergelt describes the history of least-squares approximation. His paper surveys the development and applications of ordinary, constrained, weighted and total least-squares approximation. D. Leviatan discusses the degree of approximation of a function in the uniform of Lp norm. The development of numerical algorithms is strongly related to the type of approximating functions that are used, e.g. orthogonal polynomials, splines and wavelets, and several authors describe these different approaches. E. Godoy, A. Ronveaux, A. Zarzo, and I. Area treat the topic of classical orthogonal polynomials R. Piessens, in his paper, illustrates the use of Chebyshev polynomials in computing integral transforms and for solving integral equations. Some developments in the use of splines are described by G. Nürnberger, F. Zeilfelder (for the bivariate case), and by R.-H. Wang in the multivariate case. For the numercial treatment of functions of several variables, radial basis functions are useful tools. R. Schaback treats this topic in his paper. Certain aspects of the computation of Daubechie wavelets are explained and illustrated in the paper by C. Taswell, P. Guillaume and A. Huard explore the case of multivariate Padée approximation. Special functions have played a crucial role in approximating the solutions of certain scientific problems. N. Temme illustrates the usefulness of parabolic cylinder functions and J.M. Borwein, D.M. Bradley, R.E. Crandall provide a compendium of evaluation methods for the Riemann zeta function. S. Lewanowicz develops recursion formulae for basic hypergeometric functions. Aspects of the spectral theory for the classical Hermite differential equation appear in the paper by W.M. Everitt, L.L. Littlejohn and R. Wellman. Many applications of approximation theory are to be found in linear system theory and model reduction. The paper of B. De Schutter gives an overview of minimal state space realization in linear system theory and the paper by A. Bultheel and B. De Moor describes the use of rational approximation in linear systems and control. For problems whose solutions may have singularities or infinite domains, sinc approximation methods are of value. F. Stenger summarizes the results in this field in his contribution. G. Alefeld and G. Mayer provide a survey of the historical developoment of interval analysis, including several applications of interval mathematics to numerical computing. These papers illustrate the profound impact that ideas of approximation theory have had in the creation of numerical algorithms for solving real-world scientific problems. Furthermore, approximation-theortical concepts have proved to be basic tools in the analysis of the applicability of these algorithms. We thank the authors of the above papers for their willingness to contribute to this volume. Also, we very much appreciate the referees for their role in making this volume a valuable source of information for the next millennium.


Geometric Analysis Of Several Complex Variables And Related Topics

Author by : Y. Barkatou
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the Workshop on Geometric Analysis of Several Complex Variables and Related Topics, which was held from May 10-14, 2010, in Marrakesh, Morocco. The articles in this volume present current research and future trends in the theory of several complex variables and PDE. Of note are two survey articles: The first presents recent results on the solvability of complex vector fields with critical points while the second concerns the Lie group structure of the automorphism groups of CR manifolds. The other articles feature original research in major topics of analysis dealing with analytic and Gevrey regularity, existence of distributional traces, the $\bar\partial$-Neumann operator, automorphisms of hypersurfaces, holomorphic vector bundles, spaces of harmonic forms, and Gysin sequences.


Error Correcting Codes Finite Geometries And Cryptography

Author by : Aiden A. Bruen
Languange : en
Publisher by : American Mathematical Soc.
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Description : This interdisciplinary volume contains papers from both a conference and special session on Error-Control Codes, Information Theory and Applied Cryptography. The conference was held at the Fields Institute in Toronto, On, Canada from December 5-6, 2007, and the special session was held at the Canadian Mathematical Society's winter meeting in London, ON, Canada from December 8-10, 2007. The volume features cutting-edge theoretical results on the Reed-Muller and Reed-Solomon codes, classical linear codes, codes from nets and block designs, LDPC codes, perfect quantum and orthogonal codes, iterative decoding, magnetic storage and digital memory devices, and MIMO channels. There are new contributions on privacy reconciliation, resilient functions, cryptographic hash functions, and new work on quantum coins. Related original work in finite geometries concerns two-weight codes coming from partial spreads, (0, 1) matrices with forbidden configurations, Andre embeddings, and representations of projective spaces in affine planes. Great care has been taken to ensure that high expository standards are met by the papers in this volume. Accordingly, the papers are written in a user-friendly format. The hope is that this volume will be of interst and of benefit both to the experienced and to newcomers alike.


Recent Advances In Harmonic Analysis And Applications

Author by : Dmitriy Bilyk
Languange : en
Publisher by : Springer Science & Business Media
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Description : Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.


Entropy And The Quantum

Author by : Robert Sims
Languange : en
Publisher by : American Mathematical Soc.
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Description : These lecture notes provide a pedagogical introduction to quantum mechanics and to some of the mathematics that has been motivated by this field. They are a product of the school ``Entropy and the Quantum'', which took place in Tucson, Arizona, in 2009. They have been written primarily for young mathematicians, but they will also prove useful to more experienced analysts and mathematical physicists. In the first contribution, William Faris introduces the mathematics of quantum mechanics. Robert Seiringer and Eric Carlen review certain recent developments in stability of matter and analytic inequalities, respectively. Bruno Nachtergaele and Robert Sims review locality results for quantum systems, and Christopher King deals with additivity conjectures and quantum information theory. The final article, by Christian Hainzl, describes applications of analysis to the Shandrasekhar limit of stellar masses.


Nonlinear Partial Differential Equations And Hyperbolic Wave Phenomena

Author by : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.


Mathematical And Statistical Methods For Imaging

Author by : Habib Ammari
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the NIMS Thematic Workshop on Mathematical and Statistical Methods for Imaging, which was held from August 10-13, 2010, at Inha University, Incheon, Korea. The goal of this volume is to give the reader a deep and unified understanding of the field of imaging and of the analytical and statistical tools used in imaging. It offers a good overview of the current status of the field and of directions for further research. Challenging problems are addressed from analytical, numerical, and statistical perspectives. The articles are devoted to four main areas: analytical investigation of robustness; hypothesis testing and resolution analysis, particularly for anomaly detection; new efficient imaging techniques; and the effects of anisotropy, dissipation, or attenuation in imaging.


Ultrafilters Across Mathematics

Author by : Vitaly Bergelson
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume originated from the International Congress ``ULTRAMATH: Applications of Ultrafilters and Ultraproducts in Mathematics'', which was held in Pisa, Italy, from June 1-7, 2008. The volume aims to present the state-of-the-art of applications in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts. It contains two general surveys on ultrafilters in set theory and on the ultraproduct construction, as well as papers that cover additive and combinatorial number theory, nonstandard methods and stochastic differential equations, measure theory, dynamics, Ramsey theory, algebra in the space of ultrafilters, and large cardinals. The papers are intended to be accessible and interesting for mathematicians who are not experts on ultrafilters and ultraproducts. Greater prominence has been given to results that can be formulated and presented in non-special terms and be, in principle, understandable by any mathematician, and to those results that connect different areas of mathematics, revealing new facets of known important topics.