Bücher veröffentlicht von Birkhauser Verlag AG

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author's two-volume work on inequalities.

This volume explores recent advances in the use of pluripotent stem cells (PSCs) and adult stem cells (ASCs) in basic and clinical applications.

The Bialowieza Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Bialowieza natural forest in Poland, are among the most important meetings in the field.

Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur's proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula.

Fraenkel was a world-renowned mathematician in pre-Second World War Germany, whose work on set theory was fundamental to the development of modern mathematics.

New chapters in this edition discuss the profound effects oflifestyle change on sexual function, alternative and internet drugs that affectsexual function, endovascular approaches to ED, penile length considerations,the effect of radiation on erectile function, and optimizing ED research.

This book addresses the historiography of mathematics as it was practiced during the 19th and 20th centuries by paying special attention to the cultural contexts in which the history of mathematics was written. In the 19th century, the history of mathematics was recorded by a diverse range of people trained in various fields and driven by different motivations and aims. These backgrounds often shaped not only their writing on the history of mathematics, but, in some instances, were also influential in their subsequent reception. During the period from roughly 1880-1940, mathematics modernized in important ways, with regard to its content, its conditions for cultivation, and its identity; and the writing of the history of mathematics played into the last part in particular. Parallel to the modernization of mathematics, the history of mathematics gradually evolved into a field of research with its own journals, societies and academic positions. Reflecting both a new professional identity and changes in its primary audience, various shifts of perspective in the way the history of mathematics was and is written can still be observed to this day. Initially concentrating on major internal, universal developments in certain sub-disciplines of mathematics, the field gradually gravitated towards a focus on contexts of knowledge production involving individuals, local practices, problems, communities, and networks. The goal of this book is to link these disciplinary and methodological changes in the history of mathematics to the broader cultural contexts of its practitioners, namely the historians of mathematics during the period in question.

The work on Autonomic Road Transport Support (ARTS) presented here aims at meeting the challenge of engineering autonomic behavior in Intelligent Transportation Systems (ITS) by fusing research from the disciplines of traffic engineering and autonomic computing.

The main focus of this book is on the interconnection of two unorthodox scientific ideas, the varying-gravity hypothesis and the expanding-earth hypothesis.

George Gratzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998).

This book provides a road map for defining the care of acute heart failure (HF) patients in the short stay or observation unit setting.

Now in a revised second edition, this comprehensive text covers all aspects of male hypogonadism from the basic science to clinical management, comprehensively explaining and applying new insights to the treatment of hypogonadal men.

This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general.

The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers.Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in real-dimension four, while almost simultaneously James Cockle introduced a commutative four-dimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something thatfor a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable.While the algebra of bicomplex numbers is a four-dimensional real algebra, it is useful to think of it as a ¿complexification¿ of the field of complex numbers; from this perspective, the bicomplex algebra possesses the properties of a one-dimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike. The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one-or multidimensional complex analysis.

This visionary and engaging book provides a mathematical perspective on the fundamental ideas of numbers, space, life, evolution, the brain and the mind. The author suggests how a development of mathematical concepts in the spirit of category theory may lead to unravelling the mystery of the human mind and the design of universal learning algorithms.The book is divided into two parts, the first of which describes the ideas of great mathematicians and scientists, those who saw sparks of light in the dark sea of unknown. The second part, Memorandum Ergo, reflects on how mathematics can contribute to the understanding of the mystery of thought. It argues that the core of the human mind is a structurally elaborated object that needs a creation of a broad mathematical context for its understanding. Readers will discover the main properties of the expected mathematical objects within this context, called ERGO-SYSTEMS, and readers will see how these ¿systems¿ may serve as prototypes for design of universal learning computer programs. This is a work of great, poetical insight and is richly illustrated. It is a highly attractive read for all those who welcome a mathematical and scientific way of thinking about the world.

Current cancer therapies are focused on three general strategies: modifying intrinsic radiosensitivity via molecular targeting, manipulating microenvironmental factors to enhance tumor susceptibility to radiation, and improving delivery of radiation to critical tumor locations while sparing normal tissues.

Organized into seven distinct parts arranged by thematic topics, the papers included cover basic methods and applications of CFD, flows with moving boundaries and interfaces, phase-field modeling, computer science and high-performance computing (HPC) aspects of flow simulation, mathematical methods, biomedical applications, and FSI.

This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders.

In the post human-genome project era, cancer specific genomic maps are redesigning tumor taxonomy by evolving from histopathology to molecular pathology. The success of a cancer drug today is fundamentally based on the success in identifying target genes that control beneficial pathways. The overwhelming power of genomics and proteomics has enlightened researchers about the fact that the PI3K-mTOR pathway is the most commonly up-regulated signal transduction pathway in various cancers, either by virtue of its activation downstream of many cell surface growth factor receptors or by virtue of its collateral and compensatory circuitry with RAS-MAPK pathway. Oncogenic signaling in the majority of solid tumors is sustained via the PI3K-AKT-mTOR pathway. Because of its prominent role in many cancer types, the PI3K-mTOR pathway has become a major therapeutic target. The volume includes two complementary parts which address the problem of etiology and disease progression and is intended to portray the very basic mechanisms of the PI3K-AKT-mTOR signaling pathway¿s involvement in various facets of the cancer, including stem cell renewal, cell metabolism, angiogenesis, genetic instability, and drug resistance. Significant progress has been made in recent years elucidating the molecular mechanism of cancer cell proliferation, angiogenesis, and drug-resistance in relation to the PI3K-mTOR pathway and this volume provides an in-depth overview of recent developments made in this area.¿

This volume presents the lecture notes from two courses given by Davar Khoshnevisan and René Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis.René Schilling¿s notes are an expanded version of his course on Lévy and Lévy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Lévy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Lévy-Itô decomposition. On the other, it identifies the infinitesimal generator of the Lévy process as a pseudo-differential operator whose symbol is the characteristic exponent of the process, making it possible to study the properties of Feller processes as space inhomogeneous processes that locally behave like Lévy processes. The presentation is self-contained, and includes dedicated chapters that review Markov processes, operator semigroups, random measures, etc. Inturn, Davar Khoshnevisan¿s course investigates selected problems in the field of stochastic partial differential equations of parabolic type. More precisely, the main objective is to establish an Invariance Principle for those equations in a rather general setting, and to deduce, as an application, comparison-type results. The framework in which these problems are addressed goes beyond the classical setting, in the sense that the driving noise is assumed to be a multiplicative space-time white noise on a group, and the underlying elliptic operator corresponds to a generator of a Lévy process on that group. This implies that stochastic integration with respect to the above noise, as well as the existence and uniqueness of a solution for the corresponding equation, become relevant in their own right. These aspects are also developed and supplemented by a wealth of illustrative examples.

This is a comprehensive survey on the research on the parabolic Anderson model - the heat equation with random potential or the random walk in random potential - of the years 1990 - 2015.

It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces.

Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world's most famous designs.

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs.

This book offers a comprehensive overview of alpha-1 antitrypsin deficiency, an inherited condition that leads to lung disease in adults and liver disease in adults and children and is associated with chronic obstructive lung disease in adults.