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1000 tulosta hakusanalla Rafael Lopez
This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular. Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group. Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus.
Constant Mean Curvature Surfaces with Boundary
Rafael López
Springer-Verlag Berlin and Heidelberg GmbH Co. K
2013
sidottu
The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields.While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of “compact surfaces with boundaries,” narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs.The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.
Constant Mean Curvature Surfaces with Boundary
Rafael López
Springer-Verlag Berlin and Heidelberg GmbH Co. K
2016
nidottu
The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields.While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of “compact surfaces with boundaries,” narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs.The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.
Voice Made Visible: Multi-Octave Voice Training and Techniques for Performers
Rafael Lopez-Barrantes
TAYLOR FRANCIS LTD
2023
nidottu
Voice Made Visible is an exploration of voice training and performance practice based on the use and application of Multi-Octave Vocal Range techniques."Multi-Octave" is understood as the arsenal of sounds that exists uniquely within each human voice, beyond the comfortable average octave that we use in everyday life. In Voice Made Visible, Rafael Lopez-Barrantes builds on the voice work created by Alfred Wolfsohn and developed by Roy Hart and his company in France to assist students, artists, and those interested in the performing arts with their vocal practice. He draws from over three decades of multi-cultural performance and teaching, sharing the three fundamental pillars of his system: Fiction, News, and Body Source. This book will help readers unfold their understanding of the voice by strengthening it and inspire them to create new vocal paths for the stage, camera, and voice acting, as well as for their own personal expressive growth.Voice Made Visible is an invaluable resource for students of Acting and Voice courses, as well as working performing artists.For supplemental material, including pedagogical audio-visual clips, please visit www.barrantesvoicesystem.com.
Voice Made Visible: Multi-Octave Voice Training and Techniques for Performers
Rafael Lopez-Barrantes
TAYLOR FRANCIS LTD
2023
sidottu
Voice Made Visible is an exploration of voice training and performance practice based on the use and application of Multi-Octave Vocal Range techniques."Multi-Octave" is understood as the arsenal of sounds that exists uniquely within each human voice, beyond the comfortable average octave that we use in everyday life. In Voice Made Visible, Rafael Lopez-Barrantes builds on the voice work created by Alfred Wolfsohn and developed by Roy Hart and his company in France to assist students, artists, and those interested in the performing arts with their vocal practice. He draws from over three decades of multi-cultural performance and teaching, sharing the three fundamental pillars of his system: Fiction, News, and Body Source. This book will help readers unfold their understanding of the voice by strengthening it and inspire them to create new vocal paths for the stage, camera, and voice acting, as well as for their own personal expressive growth.Voice Made Visible is an invaluable resource for students of Acting and Voice courses, as well as working performing artists.For supplemental material, including pedagogical audio-visual clips, please visit www.barrantesvoicesystem.com.
Arte, estética freak y medios de comunicación
Rafael López Borrego
Independently Published
2019
nidottu
El aura es uno de los conceptos m s interesantes de los que hablaba el fil sofo Walter Benjamin. Se refer a a una serie de obras de arte, sobre todo fotogr ficas, que hab an sido realizadas no con una finalidad de reproducci n en medios de comunicaci n, sino con una voluntad diferente. Este concepto se perdi no solo en fotograf a sino en muchas de las obras de arte desde los a os 30 del siglo pasado hasta nuestros d as. C mo podr amos definir el aura en la actualidad? Seguimos teniendo obras con aura? La idea del aura se ha desplazado a otros campos que tienen que ver con el mercado y el postureo?Por otra parte vivimos rodeados de informaci n. Los medios de comunicaci n y las redes sociales han invadido por completo nuestra vida diaria. Tanto es as , que a veces es complicado distinguir la realidad de la ficci n, lo real de la mentira. Tenemos la responsabilidad de crear nuestra propia opini n. Los sentimientos jugar n un papel esencial a la hora de reciclar la informaci n recibida. Al mismo tiempo los medios son puro entretenimiento, uno de los escenarios donde se desarrolla una est tica de lo freak. Personas que venden informaci n sobre su vida o noticias que solo hablan de un mundo en completa destrucci n. Las redes sociales se han a adido a este juego informativo permitiendo ofrecer una imagen de nosotros mismos que se aleja de la vida real, acrecentando la vanidad y sirviendo de alimento para su desarrollo y existencia. Se trata de un mundo que se aleja de la vida real para ofrecer una imagen maquillada del mismo.
Durante milenios, la espiritualidad del ser humano se ha cimentado en tradiciones y en percepciones de la realidad, fabricadas a partir de creencias no comprobadas, apoyadas en ritos cargados de simbolismo que se valen de pensamientos, de recitaciones, de gestos y de movimientos, cuya funci n no es otra que ser la representaci n de algo, tal como en una obra de teatro, situaciones de la vida de este mundo son representadas. Es la hora en la que el teatro cae. La humanidad en masa est llamada a saltar de la rbita de la creencia a la rbita de la Experiencia. Estamos ante el ocaso de una humanidad af n a una era y el amanecer de otra nueva. He aqu un Secreto que de manera sigilosa ha ido pasando de custodio en custodio a lo largo de los siglos. Y este es el tiempo en que ha de ser compartido p blicamente.
El concepto de obra de arte ha cambiado totalmente a lo largo del siglo XX y el siglo XXI. Lo que antes se asociaba a la belleza ha sido sustituido por una serie de ideas que, en muchos casos, se acercan a lo conceptual y requieren la participaci n del espectador como sujeto activo frente a la obra. El cambio de soporte o la eliminaci n de los soportes tradicionales, las caracter sticas de una obra de arte contempor neo, la presencia del neobarroco en la est tica de muchos trabajos, la posibilidad de realizar obras figurativas o abstractas, la importancia de las ideas del situacionismo para el artista, las acciones art sticas m s pol micas o la presencia de artista fuera del sistema del arte, son algunos de los temas que se desarrollan en este ensayo. Si cada persona puede con ello conocer un poco mejor y extraer sus propias conclusiones acerca de c mo definir el arte en la actualidad, habremos cumplido nuestro objetivo.
Reimpresi n del original, primera publicaci n en 1878.
Reimpresi n del original, primera publicaci n en 1878.
Reimpresi n del original, primera publicaci n en 1878.
Reimpresi n del original, primera publicaci n en 1878.
Reimpresi n del original, primera publicaci n en 1878.
Reimpresi n del original, primera publicaci n en 1878.
Reimpresi n del original, primera publicaci n en 1878.
Reimpresi n del original, primera publicaci n en 1878.