This research monograph sets out to study the notion of a local moduli suite of algebraic objects like e.g. schemes, singularities or Lie algebras and provides a framework for this. The basic idea is to work with the action of the kernel of the Kodaira-Spencer map, on the base space of a versal family. The main results are the existence, in a general context, of a local moduli suite in the category of algebraic spaces, and the proof that, generically, this moduli suite is the quotient of a canonical filtration of the base space of the versal family by the action of the Kodaira-Spencer kernel. Applied to the special case of quasihomogenous hypersurfaces, these ideas provide the framework for the proof of the existence of a coarse moduli scheme for plane curve singularities with fixed semigroup and minimal Tjurina number . An example shows that for arbitrary the corresponding moduli space is not, in general, a scheme. The book addresses mathematicians working on problems of moduli, in algebraic or in complex analytic geometry. It assumes a working knowledge of deformation theory.
Auf der Grundlage einer Einführung in die kommutative Algebra, algebraische Geometrie und komplexe Analysis werden zunächst Kurvensingularitäten untersucht. Daran schließen Ergebnisse an, die zum ersten Mal in einem Lehrbuch aufgenommen wurden, das Verhalten von Invarianten in Familien, Standardbasen für konvergente Potenzreihenringe, Approximationssätze, Grauerts Satz über die Existenz der versellen Deformation. Das Buch richtet sich an Studenten höherer Semester, Doktoranden und Dozenten. Es ist auf der Grundlage mehrerer Vorlesungen und Seminaren an den Universitäten in Kaiserslautern und Saarbrücken entstanden.
This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.
This publication is based on the plant processes and reaction sites for which reliable knowledge on both their physiology and biochem-istry and the mode of herbicidal action is available. Targets of the agrochemical research, such as enzymes of biosynthetic pathways or herbicide-binding peptides in the photosynthetic membrane, are highlighted. Detailed knowledge about the target sites will allow bio-chemical model systems to evaluate the biological activity of newly synthesized compounds before their conventional screening in the greenhouse. Quantitative structure/activity relationships should be performed more reliably with simple biological species or enzymol-ogy assays, to aid in the rational design of pesticides. This text is highly valuable for plant physiologists, pathologists, and chemists in the agrochemical industry and universities.
I Introductory Articles.- 1 Classification Problems in the Representation Theory of Finite-Dimensional Algebras.- 2 Noncommutative Gröbner Bases, and Projective Resolutions.- 3 Construction of Finite Matrix Groups.- II Keynote Articles.- 4 Derived Tubularity: a Computational Approach.- 5 Problems in the Calculation of Group Cohomology.- 6 On a Tensor Category for the Exceptional Lie Groups.- 7 Non-Commutative Gröbner Bases and Anick's Resolution.- 8 A new Existence Proof of Janko's Simple Group J4.- 9 The Normalization: a new Algorithm, Implementation and Comparisons.- 10 A Computer Algebra Approach to sheaves over Weighted Projective Lines.- 11 Open Problems in the Theory of Kazhdan-Lusztig polynomials.- 12 Relative Trace Ideals and Cohen Macaulay Quotients.- 13 On Sims' Presentation for Lyons' Simple Group.- 14 A Presentation for the Lyons Simple Group.- 15 Reduction of Weakly Definite Unit Forms.- 16 Decision Problems in Finitely Presented Groups.- 17 Some Algorithms in Invariant Theory of Finite Groups.- 18 Coxeter Transformations associated with Finite Dimensional Algebras.- 19 The 2-Modular Decomposition Numbers of Co2.- 20 Bimodule and Matrix Problems.
Eighty-two percent of German boys and girls between the ages of ten and eighteen belonged to Hitlerjugend_Hitler Youth_or one of its affiliates by the time membership became fully compulsory in 1939. These adolescents were recognized by the SS, an exclusive cadre of Nazi zealots, as a source of future recruits to its own elite ranks, which were made up largely of men under the age of thirty. In this book, Gerhard Rempel examines the special relationship that developed between these two most youthful and dynamic branches of the National Socialist movement and concludes that the coalition gave nazism much of its passionate energy and contributed greatly to its initial political and military success. Rempel center his analysis of the HJ-SS relationship on two branches of the Hitler Youth. The first of these, the Patrol Service, was established as a juvenile police force to pursue ideological and social deviants, political opponents, and non-conformists within the HJ and among German youth at large. Under SS influence, however, membership in the organization became a preliminary apprenticeship for boys who would go on to be agents and soldiers in such SS-controlled units as the Gestapo and Death's Head Formations. The second, the Land Service, was created by HJ to encourage a return to farm living. But this battle to reverse "the flight from the land" took on military significance as the SS sought to use the Land Service to create "defense-peasants" who would provide a reliable food supply while defending the Fatherland. The transformation of the Patrol and Land services, like that of the HJ generally, served SS ends at the same time that it secured for the Nazi regime the practical and ideological support of Germany's youth. By fostering in the Hitler Youth as "national community" of the young, the SS believed it could convert the popular movement of nazism into a protomilitary program to produce ideologically pure and committed soldiers and leaders who would keep the movement young and vital.
Target Assays for Modern Herbicides and Related Phytotoxic Compounds is a laboratory guide that features 38 comprehensive contributions to determine and quantitate the inhibition activity of modern herbicides and related phytotoxic compounds at their targets. Using algal or higher-plant model species as well as cell-free enzymatic systems, assays are described for use with modern equipment typically found in a biochemical laboratory. Many details of the tests described in this volume are being published for the first time. Assays discussed include carotenoid and chlorophyll biosynthesis and degradation, photosynthetic electron transport, amino acid biosynthesis, fatty acid formation, and cell division. Some model systems and related topics are also described. Each chapter represents an easy-to-read recipe with minimal theory including some key references for further reading. Original data from the experiments are provided, and most of the notable laboratories around the world are represented. Target Assays for Modern Herbicides and Related Phytotoxic Compounds features updated methodology and procedures that will be a tremendous asset to plant biochemists; agriculture, plant protection, and weed control experts; agrochemical herbicide specialists in industry and government; and students in agricultural biochemistry and physiology.
Derived from the highly acclaimed series Materials Science and Technology, this book covers the properties as well as the present and emerging applications of intermetallics. Mechanical characteristics, microstructure as well as the environmental influence on intermetallics are treated in depth. In addition, the prospects and risks inherent in materials development as well as typical applications of intermetallics are critically assessed. It is the author's aim to provide the basis for understanding the physical mechanisms, which influence the properties of the materials and ultimately their areas of application. Materials covered include: Titanium Aluminides and Related Phases * Nickel Aluminides and Related Phases * Iron Aluminides and Related Phases * Cu-Base Phases * A15 Phases * Laves Phases * Rare-Earth Compound * Beryllides * Silicides Intermetallics is a valuable source of information for researchers and graduate students working in materials science, metallurgy, condensed-matter physics, and engineering.
This book discusses in detail the experience of German warfare in the first World War, focusing specifically on the battle of the Somme. The Somme, together with other regions of northern France, had also lain under German domination. Its inhabitants had been rigorously suppressed and their possessions carted off as booty. Finally, during their 1917 withdrawal, the Germans had subjected the whole region to Operation Alberich, a retreat involving unparalleled brutality which left the population in occupation of a wilderness wrought by war (the "scorched earth policy"). A well-known, and well-researched account, the authors have combined their research skills to produce a book which includes private testimonies. Amongst these are many unknown or previously unpublished letters and diaries as well as numerous photographs.
The English translation of the three-volume Exegetisches Wrterbuch zum Neuen Testament, this monumental work by an ecumenical group of scholars is first of all a complete English dictionary of New Testament Greek. Going beyond that, however EDNT also serves as a guide to the usage of every New Testament word in its various contexts, and it makes a significant contribution to New Testament exegesis and theology. EDNT's thorough, lengthy discussions of more significant words and its grouping of words related by root and meaning (with alphabetical cross-references) distinguish it from simpler Greek-English lexicons. Advancing the discussion of the Theological Dictionary of the Old Testament, EDNT summarizes more recent treatments of numerous questions in New Testament study and takes into consideration newer viewpoints of linguistics.
Risk-taking, school, sex, church, entertainment, language, and class are among the factors that Gerhard (sociology, State U. College, Buffalo, New York) and psychotherapist Ursula consider as they explore how American youth culture has changed and stayed the same since the 16th-century Puritan colonies. They discuss the life of children and adolesc
This open access book provides a comprehensive overview of the state of the art in research and applications of Foundation Models and is intended for readers familiar with basic Natural Language Processing (NLP) concepts. Over the recent years, a revolutionary new paradigm has been developed for training models for NLP. These models are first pre-trained on large collections of text documents to acquire general syntactic knowledge and semantic information. Then, they are fine-tuned for specific tasks, which they can often solve with superhuman accuracy. When the models are large enough, they can be instructed by prompts to solve new tasks without any fine-tuning. Moreover, they can be applied to a wide range of different media and problem domains, ranging from image and video processing to robot control learning. Because they provide a blueprint for solving many tasks in artificial intelligence, they have been called Foundation Models. After a brief introduction to basic NLP models the main pre-trained language models BERT, GPT and sequence-to-sequence transformer are described, as well as the concepts of self-attention and context-sensitive embedding. Then, different approaches to improving these models are discussed, such as expanding the pre-training criteria, increasing the length of input texts, or including extra knowledge. An overview of the best-performing models for about twenty application areas is then presented, e.g., question answering, translation, story generation, dialog systems, generating images from text, etc. For each application area, the strengths and weaknesses of current models are discussed, and an outlook on further developments is given. In addition, links are provided to freely available program code. A concluding chapter summarizes the economic opportunities, mitigation of risks, and potential developments of AI.
This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.
The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.
The book deals with the relationship between Friedrich Meinecke, who is often considered to be the leading German historian of the first half of the twentieth century, and several of his students who, after the Nazi seizure of power, were forced to emigrate because of their Jewish descent or their political views. The letters published here to Meinecke from Hans Rothfels, Dietrich Gerhard, Hajo Holborn, Felix Gilbert, Hans Rosenberg, and others show these scholars' deep respect for their old teacher, but also their growing distance from his historical interests and methods. In a period of struggle between democracy and Nazi dictatorship, the letters address the problems of emigration and remigration, German-Jewish and German-American identity, and historiography in both Germany and the United States.
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