Heinz Bauer (1928-2002) was one of the prominent figures in Convex Analysis and Potential Theory in the second half of the 20th century. The Bauer minimum principle and Bauer's work on Silov's boundary and the Dirichlet problem are milestones in convex analysis. Axiomatic potential theory owes him what is known by now as Bauer harmonic spaces. These Selecta collect more than twenty of Bauer's research papers including his seminal papers in Convex Analysis and Potential Theory. Above his research contributions Bauer is best known for his art of writing survey articles. Five of his surveys on different topics are reprinted in this volume. Among them is the well-known article Approximation and Abstract Boundary, for which he was awarded with the Chauvenet Price by the American Mathematical Association in 1980.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem. The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory. The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.
Automatic computing has undergone drastic changes since the pioneering days of the early Fifties, one of the most obvious being that today the majority of computer programs are no longer written in machine code but in some programming language like FORTRAN or ALGOL. However, as desirable as the time-saving achieved in this way may be, still a high proportion of the preparatory work must be attributed to activities such as error estimates, stability investigations and the like, and for these no programming aid whatsoever can be of help. In this respect, ALGOL, as an internationally standardized notation which avoids computer-oriented concepts, provides another advantage, not often mentioned, but one which was already the guiding principle at the very beginning of the programming language venture: indeed, a correct ALGOL program is the abstractum of a computing process for which the necessary analyses have already been performed. It is the very purpose of this Handbook to establish such abstract formulations of certain computing processes. Therefore, numerical methods given in this Hand book in the form of ALGOL procedures may be put to immediate use wherever ALGOL is known and understood; in fact, application of such a method reduces to little more than calling the corresponding procedure.
This book aims at restructuring some fundamentals in measure and integration theory. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents and elementary integrals. It develops the new approach started around 1970 by Topsoe and others into a systematic theory. The theory is much more powerful than the traditional means and has striking implications all over measure theory and beyond.
This first volume in the series on "Comparative Brain Research in Mammals" deals with the brains of Insectivora. The importance of Insectivora lies above all in the fact that, (1) insectivore-like ancestors are regarded as the initial group for the evolution of higher mammals, and (2) the insectivore brains retained many conservative traits, though the animals have adapted to different living environments. Therefore, the study of Insectivora brains enables an insight into the size and composition of the brain structure of earlier ancestors of the higher mammals including primates and humans; in addition, it illumi nates the various evolutionary trends which made the successful adaptation to different biotopes possible. The alterations which the brain has experienced in the course of the phylo geny and the related adaptive radiation will be examined in the succeeding volumes on the brains of other Eutheria, e.g., bats (Volume 2) and primates (Volume 4). In Volume 3 the brains of marsupials will be compared with those of conservative and evolved Eutheria.
The human body is uniformly, both by specialists and patients, regarded as a machine too weak to fight cancer. But this is a misconception. First, without our immune system we would be overstretched by cancer cells within short term. Second, even in cases of late stage disease so-called spontaneous regressions and cures can happen. Spontaneous regressions are listed, but not explained in the scientific literature to this day. A careful look on case studies reveals that a majority of cases happened after a hefty feverish infection. Third, several epidemiologic studies show that a personal history with feverish infections reduces the likely-hood to develop cancer later. Meanwhile we know that a certain class of immune stimulating danger signals plays a role. PRRL, which are made by pathogens but not tumours, can induce an immune reaction against cancer cells. This essay investigates whether and how bacterial and viral PRRL substances could be used to treat and prevent cancer.
River Morphology deals with the interaction between flowing waters in rivers and their environment. Based on the representation of basic flow parameters, the geometry, classification and historic development of rivers are treated. Any change in the environment, occurring naturally or caused by man, leads to very sensitive reactions in river flow and transport. Thus this synopsis of geoscientific studies and hydraulic engineering experience is presented to help develop the unterstanding of how to handle nature with care.
A chronicle written only by someone for whom the present important. Goethe, Maximen und Reflexionen The second volume of our company's history differs from the first in several ways. With a great appreciation of history, Heinz Sarkowski has impressively reconstructed the company cor- spondence, which is fortunately almost completely preserved, and made it speak. * There is an inexhaustible amount of c- respondence pertaining to the period I have taken it upon myself to cover, and working through it properly not only would have required many years, but also would have detracted from the immediacy of the account. Thus, I decided to proceed from personal experience, to describe what has happened and to provide details gleaned from the correspondence. I have - counted here by no means only my own, but rather the personal experiences of the many company members and employees who are mentioned below. With the founding of the New York firm, developments branch out, becoming parallel but separate, and the change from one scene to another repeatedly interrupts the continuing course of events and the chronological flow of the report. In this connection, the occasional repetition of certain facts was - avoidable. In some places, however, it seemed more appropriate not to interrupt particular lines of development, but to describe them in continuity without regard to specific periods of time.
Acute Phase Proteins covers all major aspects of acute phase proteins (APP) starting with molecular mechanisms regulating their synthesis and ending with their functional significance. The book features 36 chapters addressing such topics as acute phase response and the APP; major APP and their structure and functions; regulation of APP synthesis, the cytokines and hormones implicated in these processes, and molecular mechanisms involved; signal transduction of cytokines in hepatocytes and posttranscriptional processes; and quantitative and qualitative evaluation of APP in clinical practice. The book will be an important reference for immunologists, molecular biologists, cellular biologists, biochemists, and clinical chemists.
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