Universality of sequences of operators related to Taylor series

In this note, the universality of a sequence of operators associated to the partial sums of the Taylor series of a holomorphic function is investigated. The emphasis is put on the fact that the Taylor series are evaluated at a prescribed point and the variable is the center of the expansion. The dynamics of the sequence of operators linked to the partial sums of a power series that is not generated by an entire function is also studied.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitividad (MINECO). Españ

Spectral Theory in Banach Spaces and Harmonic Analysis

The workshop brought together 49 researchers from 11 different countries, representing two different research areas, spectral theory in Banach spaces and harmonic analysis, in order to promote the exchange of methods and recent results of these two areas. The 28 talks focused on the H ∞ -functional calculus for sectorial operators, related boundedness results on singular integrals, square function estimates and their application to the Kato square root problem, and regularity estimates for parabolic differential operators. They also raised many questions which lead to lively discussions, in particular during the afternoons, which were, for the most part, kept free of talks

(Tres problemas clásicos en Análisis Matemático)

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Análisis Matemático y Matemática Aplicada, leída el 17-05-2021The title of this dissertation alludes to the study of three classical problems of mathematical analysis. All the results that have been obtained as the fruit of four years of hard work are related, wholly or partially to at least one of the following three fields:• Banach spaces of polynomials: This is a vast field as the educated reader knows well. In particular we have studied continuity properties of polynomials on Banach spaces and topological relationships among polynomial spaces.• Algebraic genericity and lineability: This is the study of the algebraic structure within certain sets in a linear space. We give an answer to a question posed by Gurariy in the early 2000’s and, as a matter of fact, we prove a generalizationto the question formulated by Gurariy. We also link the notion of algebraic genericity to the study of sequences of operators related to Taylor series. • The classical Bohr radius problem: We provide an estimated on the n-dimensional Bohr radius for the polydisk Dn that improves other previous estimates...El título de esta tesis alude al estudio de tres problemas clásicos. Los resultados que se han obtenido, que son el fruto del arduo trabajo llevado a cabo durante los últimos cuatro años, están relacionados, total o parcialmente, con algunos de estos tres temas clásicos del Análisis Matemático: • Espacios de Banach de polinomios: Este es un tema muy extenso, como cualquier lector avezado entenderá enseguida. Siendo más concretos, estudiamos propiedades relacionadas con la continuidad de polinomios en espacios de Banach. También estudiamos la relación existente entre las topologías inducidas por diversas normas en un espacio de polinomios. • Genericidad Algebraica y lineabilidad: Este tema consiste en el estudio de las estructuras algebraicas contenidas en determinados conjuntos de un espacio vectorial o un álgebra. En este sentido, aportamos una solución completa a un problema planteado por V. Gurariy poco después del año 2000. De hecho, la solución proporcionada aquí es, en realidad, una generalización del problema original formulado por V. Gurariy. También investigamos problemas vinculados a la noción de genericidad algebraica en el contexto de sucesiones de operadores relacionados con series de Taylor. • El problema clásico del radio de Bohr: Como principal aportación a este problema, damos una acotación (inferior) del radio de Bohr n-dimensional para el polidisco Dn que mejora estimaciones previas...Fac. de Ciencias MatemáticasTRUEunpu

Dynamical Systems; Proceedings of an IIASA Workshop, Sopron, Hungary, September 9-13, 1985

The investigation of special topics in systems dynamics -- uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory -- has become a major issue at the System and Decision Sciences Research Program of IIASA. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under variations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of nonlinear dynamic systems theory to biomathematics and ecology. The proceedings of a workshop on the "Mathematics of Dynamic Processes", dealing with these topics is presented in this volume

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

Hypercyclic sequences of PDE-preserving operators

AbstractA sequence T=(Tn) of continuous linear operators Tn:X→X is said to be hypercyclic if there exists a vector x∈X, called hypercyclic for T, such that {Tnx:n⩾0} is dense. A continuous linear operator, acting on some suitable function space, is PDE-preserving for a given set of convolution operators, when it map every kernel set for these operators invariantly. We establish hypercyclic sequences of PDE-preserving operators on H(Cd), and study closed infinite-dimensional subspaces of, except for zero, hypercyclic vectors for these sequences

A complex systems approach to education in Switzerland

The insights gained from the study of complex systems in biological, social, and engineered systems enables us not only to observe and understand, but also to actively design systems which will be capable of successfully coping with complex and dynamically changing situations. The methods and mindset required for this approach have been applied to educational systems with their diverse levels of scale and complexity. Based on the general case made by Yaneer Bar-Yam, this paper applies the complex systems approach to the educational system in Switzerland. It confirms that the complex systems approach is valid. Indeed, many recommendations made for the general case have already been implemented in the Swiss education system. To address existing problems and difficulties, further steps are recommended. This paper contributes to the further establishment complex systems approach by shedding light on an area which concerns us all, which is a frequent topic of discussion and dispute among politicians and the public, where billions of dollars have been spent without achieving the desired results, and where it is difficult to directly derive consequences from actions taken. The analysis of the education system's different levels, their complexity and scale will clarify how such a dynamic system should be approached, and how it can be guided towards the desired performance