"Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. In this accessible book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including a valuable selection of exercises.

viii 2. As a natural continuation of the section on the Platonic solids, a detailed and complete classi?cation of ?nite Mobius ] groupsal a Klein has been given with the necessary background material, such as Cayley s theorem and the Riemann Hurwitz relation. 3. Oneofthemostspectaculardevelopmentsinalgebraandge- etry during the late nineteenth century was Felix Klein s theory of the icosahedron and his solution of the irreducible quintic in termsofhypergeometricfunctions.Aquick, direct, andmodern approach of Klein s main result, the so-called Normalformsatz, has been given in a single large section. This treatment is in- pendent of the material in the rest of the book, and is suitable for enrichment and undergraduate/graduate research projects. All known approaches to the solution of the irreducible qu- tic are technical; I have chosen a geometric approach based on the construction of canonical quintic resolvents of the equation of the icosahedron, since it meshes well with the treatment of the Platonic solids given in the earlier part of the text. An - gebraic approach based on the reduction of the equation of the icosahedron to the Brioschi quintic by Tschirnhaus transfor- tions is well documented in other textbooks. Another section on polynomial invariants of ?nite Mobius ] groups, and two new appendices, containing preparatory material on the hyper- ometric differential equation and Galois theory, facilitate the understanding of this advanced material."

During the last few years, routine applications of NMR techniques have been further developed. Spectrometers of the latest generation offer new types of experiments, such as spinlock and inverse-detected methods. In this third, revised and expanded edition, new methodology is introduced and incorporated into new exercises. In addition, a new chapter has been introduced which demonstrates the fully detailed interpretation of two typical examples.

This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed. Beginning with a thorough treatment of the natural numbers via Peano's axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff's axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections between topics. Elements of Mathematics is ideal for students seeking a deep and engaging mathematical challenge based on elementary tools. Whether enhancing the early undergraduate curriculum for high achievers, or constructing a reflective senior capstone, instructors will find ample material for enquiring mathematics majors. No formal prerequisites are assumed beyond high school algebra, making the book ideal for mathematics circles and competition preparation. Readers who are more advanced in their mathematical studies will appreciate the interleaving of ideas and illuminating historical details.

This textbook treats two important and related matters in convex geometry: the quantification of symmetry of a convex set-measures of symmetry-and the degree to which convex sets that nearly minimize such measures of symmetry are themselves nearly symmetric-the phenomenon of stability. By gathering the subject's core ideas and highlights around Grunbaum's general notion of measure of symmetry, it paints a coherent picture of the subject, and guides the reader from the basics to the state-of-the-art. The exposition takes various paths to results in order to develop the reader's grasp of the unity of ideas, while interspersed remarks enrich the material with a behind-the-scenes view of corollaries and logical connections, alternative proofs, and allied results from the literature. Numerous illustrations elucidate definitions and key constructions, and over 70 exercises-with hints and references for the more difficult ones-test and sharpen the reader's comprehension. The presentation includes: a basic course covering foundational notions in convex geometry, the three pillars of the combinatorial theory (the theorems of Caratheodory, Radon, and Helly), critical sets and Minkowski measure, the Minkowski-Radon inequality, and, to illustrate the general theory, a study of convex bodies of constant width; two proofs of F. John's ellipsoid theorem; a treatment of the stability of Minkowski measure, the Banach-Mazur metric, and Groemer's stability estimate for the Brunn-Minkowski inequality; important specializations of Grunbaum's abstract measure of symmetry, such as Winternitz measure, the Rogers-Shepard volume ratio, and Guo's Lp -Minkowski measure; a construction by the author of a new sequence of measures of symmetry, the kth mean Minkowski measure; and lastly, an intriguing application to the moduli space of certain distinguished maps from a Riemannian homogeneous space to spheres-illustrating the broad mathematical relevance of the book's subject.

In this book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years. In trying to make this monograph accessible not just to research mathematicians but mathematics graduate students as well, the author included sizeable pieces of material from upper level undergraduate courses, additional graduate level topics such as Felix Klein¿s classic treatise of the icosahedron, and a valuable selection of exercises at the end of each chapter.

This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed. Beginning with a thorough treatment of the natural numbers via Peano's axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff's axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections between topics. Elements of Mathematics is ideal for students seeking a deep and engaging mathematical challenge based on elementary tools. Whether enhancing the early undergraduate curriculum for high achievers, or constructing a reflective senior capstone, instructors will find ample material for enquiring mathematics majors. No formal prerequisites are assumed beyond high school algebra, making the book ideal for mathematics circles and competition preparation. Readers who are more advanced in their mathematical studies will appreciate the interleaving of ideas and illuminating historical details.

This volume entitled 'The Role of Chemistry in the Evolution of Molecular Medicine' contains a collection of papers that form the proceedings of the Symposium held at the University of Szeged (27-29 June 2003).
As well as covering developments in the field over the last 60 years, the proceedings of this Symposium has laid the foundations for the future of the field of molecular medicine. Contributors span a wide range of molecular science disciplines including mathematics, physics, computer science, chemistry, biochemistry, biology and medicine, and cover the whole territory in agreement with the legacy of Professor Albert Szent-Gyorgyi.
This volume was particularly inspired by the booklet published in 1960 by Albert Szent-Gyorgyi under the title 'Introduction to submolecular biology', and the contents of this booklet have been included here in its entirety as an Appendix.
General topics include:
- Advanced computations
- Molecular computations
- Drug discovery"

In an ever-increasing domain of activity, Amino Acids, Peptides and Proteins provides an annual compilation of the world's research effort into this important area of biological chemistry. Comprising a comprehensive review of significant developments at this biology/chemistry interface, each volume opens with an overview of amino acids and their applications. Work on peptides is reviewed over several chapters, ranging from current trends in their synthesis and conformational and structural analysis, to peptidomimetics and the discovery of peptide-related molecules in nature. The application of advanced techniques in structural elucidation is incorporated into all chapters, whilst periodic chapters on metal complexes of amino acids, peptides and beta-lactams extend the scope of coverage. Efficient searching of specialist topics is facilitated by the sub-division of chapters into discrete subject areas, allowing annual trends to be monitored. All researchers in the pharmaceutical and allied industries, and at the biology/chemistry interface in academia will find this an indispensable reference source. Volume 36 covers literature published during 2003.

Amino Acids, Peptides and Proteins comprises a comprehensive review of significant developments at this biology/chemistry interface. Each volume of this Specialist Periodical Report opens with an overview of amino acids and their applications. Work on peptides is reviewed over several chapters, ranging from current trends in their synthesis and conformational and structural analysis, to peptidomimetics and the discovery of peptide-related molecules in nature. The application of advanced techniques in structural elucidation is incorporated into all chapters, whilst periodic chapters on metal complexes of amino acids, peptides and beta-lactams extend the scope of coverage. Efficient searching of specialist topics is facilitated by the sub-division of chapters into discrete subject areas, allowing annual trends to be monitored. Researchers in the pharmaceutical and allied industries, and at the biology/chemistry interface in academia will find this an indispensable reference source. Specialist Periodical Reports provide systematic and detailed review coverage in major areas of chemical research. Compiled by teams of leading experts in their specialist fields, this series is designed to help the chemistry community keep current with the latest developments in their field. Each volume in the series is published either annually or biennially and is a superb reference point for researchers. www.rsc.org/spr

Diplomarbeit aus dem Jahr 2002 im Fachbereich BWL - Investition und Finanzierung, Note: 1,3, Johann Wolfgang Goethe-Universitat Frankfurt am Main (Wirtschaftswissenschaften), Sprache: Deutsch, Abstract: Inhaltsangabe: Einleitung: Venture Capital wurde in den letzten Jahren zunehmend als Kapitalanlage entdeckt, hat sich zu einer eigenstandigen Anlagekategorie entwickelt und stellt aufgrund des damit verbundenen Ertragspotentials und der Diversifikationsmoglichkeiten eine interessante Alternative zu den klassischen Anlageinstrumenten dar. Ein Engagement in Venture Capital wird jedoch immer noch als spekulativ und intransparent angesehen. Der vorliegende quantitative Ansatz versucht empirische Abhangigkeiten der Performance von anderen Faktoren aufzuzeigen und dadurch zu einer hoheren Markttransparenz beizutragen. Als Basis fur die empirische Untersuchung konnte eine in Umfang und Qualitat bisher einzigartige Stichprobe erhoben werden. Der Datensatz enthalt detaillierte Angaben uber die erwirtschaftete Beteiligungsrenditen von 27 Fonds von 9 in den USA und Europa ansassigen Venture Capital Gesellschaften und umfasst 680 realisierte Investments im Zeitraum von 1971 bis 2001. Problemstellung: Der Markt fur Venture Capital (VC) ist in den 90er Jahren weltweit extrem dynamisch gewachsen. Trotz des Wachstumseinbruchs, der sich im Jahre 2000 abzeichnete hat sich die Branche zu einem bedeutenden Industriezweig entwickelt. Es ist seit langerem allgemein bekannt, dass man mit Engagements in VC gutes Geld verdienen kann. Dass dieser Sektor sich jedoch auch nach anderen Kriterien von anderen Anlageinstrumenten abhebt, ist eine nicht so weit verbreitete Erkenntnis. Empirische Marktuntersuchungen konnten helfen diese Wissenslucke teilweise zu schliessen, sind allerdings aufgrund der begrenzten Verfugbarkeit von Daten und Intransparenz, bisher eher die Ausnahme. Dies ist insbesondere mit dem privaten Charakter des VC-Marktes und der Zuruckhaltung der VC-Gesellschaften mit der Herau

In an ever-increasing domain of activity, Amino Acids, Peptides and Proteins provides an annual compilation of the world's research effort into this important area of biological chemistry. Volume 34 provides a review of literature published during 2001. Comprising a comprehensive review of significant developments at this biology/chemistry interface, each volume opens with an overview of amino acids and their applications. Work on peptides is reviewed over several chapters, ranging from current trends in their synthesis and conformational and structural analysis, to peptidomimetics and the discovery of peptide-related molecules in nature. The application of advanced techniques in structural elucidation is incorporated into all chapters, whilst periodic chapters on metal complexes of amino acids, peptides and beta-lactams extend the scope of coverage. Efficient searching of specialist topics is facilitated by the sub-division of chapters into discrete subject areas, allowing annual trends to be monitored. All researchers in the pharmaceutical and allied industries, and at the biology/chemistry interface in academia will find this an indispensable reference source. Specialist Periodical Reports provide systematic and detailed review coverage in major areas of chemical research. Compiled by teams of leading authorities in the relevant subject areas, the series creates a unique service for the active research chemist, with regular, in-depth accounts of progress in particular fields of chemistry. Subject coverage within different volumes of a given title is similar and publication is on an annual or biennial basis.