الصفحة 1
الصفحة 1
Notes on Coxeter Transformations and the McKay Correspondence
One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram. The Coxeter transformation is the main tool in the proof of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincaré series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers.
Natural Skincare Cosmetics
Aging skin is suffering of decrease pigment-containing cells and overproduction of melanin in the skin, also changes in the connective tissue reduce the skin's strength and elasticity. Over the last 20 years, clinical and laboratory studies have identified the benefits of an array of natural ingredients for skin care. A variety of skin care products exist in today’s marketplace. They fulfill a variety of functions by either acting directly on the skin (e.g., moisturizers) or being a cosmetically elegant vehicle for the delivery of specific active ingredients (e.g., sunscreens or antipruritic or antiacne medicaments). Certain ingredients used in cosmeceuticals may be claimed to be therapeutic for common skin diseases. These ingredients are regulated as over the counter (OTC) drug monographs for acne, dermatitis/psoriasis, skin protectant, topical analgesia and sunscreens, by the Food and Drug Administration (FDA)
Natural anti-aging skin care
Ageing is a natural phenomenon which is a fold, ridge and crease in the skin that occurs due to loss of body mass, poor hydration, disintegration of dermis and epidermis junction. The Skin ageing process involves many changes that occur due to the combination of both endogenous factors and exogenous factors. The ageing of the skin occurs due to various mechanisms like glycation, free radical, cell cycle, and cellular and molecular mechanism of skin ageing. In this review article, we have discussed the treatment, worldwide newer therapies and marketed formulation that are currently available for the reduction of skin ageing.
Methods of Celestial Mechanics ; Vol. II : Application to Planetary System, Geodynamics and Satellite Geodesy
G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. Volume II is devoted to the applications and to the presentation of the program system CelestialMechanics. Three major areas of applications are covered: (1) Orbital and rotational motion of extended celestial bodies. The properties of the Earth-Moon system are developed from the simplest case (rigid bodies) to more general cases, including the rotation of an elastic Earth, the rotation of an Earth partly covered by oceans and surrounded by an atmosphere, and the rotation of an Earth composed of a liquid core and a rigid shell (Poincaré model). (2) Artificial Earth Satellites. The oblateness perturbation acting on a satellite and the exploitation of its properties in practice is discussed using simulation methods (CelestialMechanics) and (simplified) first order perturbation methods. The perturbations due to the higher-order terms of the Earth's gravitational potential and resonant perturbations are considered thereafter. Special attention is paid to satellites of the Global Navigation Satellite Systems and to geostationary satellites. The characteristics of and models for the two most important non-gravitational forces, atmospheric drag and radiation pressure, are presented as well as the most relevant forces acting on high- and low-orbiting satellites. (3) Evolution of the Planetary System. The outer planetary system consisting of the planets Jupiter to Pluto is studied over long time intervals using simulation methods and spectral analysis (CelestialMechanics). The properties of the inner systems, in particular of the Earth's orbit, are made visible by integrating the entire system over long time intervals relevant for climate change. The distribution of minor planets and their orbital properties, regular orbits, and chaotic orbits are easily generated and analyzed using CelestialMechanics. The volume concludes with the discussion of important mathematical tools of the program system and of the principles of spectral analysis.
Means, Ends and Medical Care
In this remarkable book, Gary Wright brings his thirty years of experience as a physician in pediatric and family medicine together with his Ph.D. in philosophy to address the important problem of the nature of good medical reasoning. Wright gives a brilliant analysis of the complex internal structure of our concepts of health and disease, showing that our present models are wholly incapable of dealing with the realities of actual human disease. He then shows the error of assuming that we always know in advance what the medical and moral ends are for any medical situation. This leads to a radical questioning of so-called "rational actor" or "economic" models of rationality that are popular in medicine today.
Investigating the Body in the Victorian Asylum : Doctors, Patients, and Practices
This book explores how the body was investigated in the late nineteenth-century asylum in Britain. As more and more Victorian asylum doctors looked to the bodily fabric to reveal the ‘truth’ of mental disease, a whole host of techniques and technologies were brought to bear upon the patient's body. These practices encompassed the clinical and the pathological, from testing the patient's reflexes to dissecting the brain.
Intuition and the Axiomatic Method
All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method,
Introduction to Stochastic Calculus for Finance : A New Didactic Approach
The justifcation is mainly pedagogical. These lecture notes start with an elementary approach to stochastic calculus due to Föllmer, who showed that one can develop Ito's calculus "pathwise" as an exercise in real analysis. The text opens to students interested in finance a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model.
Hyperbolic Geometry
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications.
Herbals as nutraceuticals : Their role in healthcare
Herbal nutraceuticals demonstrate a variety of therapeutic benefits and have been found to prevent, treat, and even cure a range of diseases. This new book provides insight into nutraceuticals and their function in human health, highlighting their antimicrobial and immune-inflammatory properties. It describes the nutraceutical properties of various medicinal herbs and details the role of nutraceuticals in treating diseases such as Alzheimer's, Parkinson's, obesity, diabetes, cancer, cardiovascular diseases, skincare issues, and more.
Gravitation and Experiment : Poincaré Seminar 2006
This book is the sixth in a series of lectures of the S´ eminaire Poincar´ e,whichis directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background.
From Hyperbolic Systems to Kinetic Theory : A Personalized Quest
Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity!
Foundations of Hyperbolic Manifolds
The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow’s rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare«s fundamental polyhedron theorem.
Finite element analysis for building assessment : Advanced use and practical recommendations
Existing structures represent a heterogeneous category in the global built environment as often characterized by the presence of archaic materials, damage and disconnections, uncommon construction techniques and subsequent interventions throughout the building history. In this scenario, the common linear elastic analysis approach adopted for new buildings is incapable of an accurate estimation of structural capacity, leading to overconservative results, invasive structural strengthening, added intervention costs, excessive interference to building users and possible losses in terms of aesthetics or heritage values. For a rational and sustainable use of the resources, this book deals with advanced numerical simulations, adopting a practical approach to introduce the fundamentals of Finite Element Method, nonlinear solution procedures and constitutive material models.
Establishing medical reality : Essays in the metaphysics and epistemology of biomedical science
This volume approaches the philosophy of medicine from the broad naturalist perspective that holds that philosophy must be continuous with, constrained by, and relevant to empirical results of the natural and social sciences and that believes that the history, sociology, politics, and ethics of science provide relevant information for philosophical analysis. One traditional topic covered by several of the contributions is the nature of disease, but the approach is largely from the philosophy of science rather than traditional linguistic analysis. The complex interplay of epistemological and sociological factors in producing evidence in medicine is discussed by chapters on collective medical discussion making, experimental medicine, " genetic" diseases, mental illness, and race and gender categories. The upshot is a volume that ties medicine to contemporary issues in philosophy of science and metaphysics like no other.
Entropy Methods for the Boltzmann Equation : Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Engineering Geology for Underground Rocks
This book clearly and systematically explains underground engineering geology principles, methods, theories and case studies, depicts engineering problems in underground rock engineering and how to study and solve them. It specially emphasizes mechanical and hydraulic couplings in rock engineering for wellbore stability, mining near aquifers and other underground structures where inflow is a problem. Using the methods and models given in this book, the reader is able to analyse underground geological engineering problems and also for the design of underground structures.
Einstein, 1905-2005 : Poincaré Seminar 2005
This volume is devoted to Einstein's 1905 papers and their legacy. After a presentation of Einstein's epistemological approach to physics, and the genesis of special relativity, a centenary perspective is offered. The geometry of relativistic spacetime is explained in detail. Single photon experiments are presented, as a spectacular realization of Einstein's light quanta hypothesis. A previously unpublished lecture by Einstein, which presents an illuminating point of view on statistical physics in 1910, at the dawn of quantum mechanics, is reproduced. The volume ends with an essay on the historical, physical and mathematical aspects of Brownian motion.
Education, Arts, and Morality : Creative Journeys
Inspired by Howard Gruber’s Evolving Systems Approach, these studies explore creativity in several domains. The idea that the creative person embodies a system of loosely coupled sub-systems – knowledge, purpose, and affect that work together, is viewed here in different chapters that explore this concept. These include autobiographies of incarcerated youth, curricula for moral and civic responsibility, changing attitudes of readers to text (romance novels), as well as case studies of highly creative individuals, such as George Bernard Shaw. Gruber’s approach provides concepts as well as methodological tools which the authors apply to diverse creative processes.
Data center networking : Network topologies and traffic management in large-scale data centers
Provides a comprehensive reference in large data center networking. It first summarizes the developing trend of DCNs, and reports four novel DCNs, including a switch-centric DCN, a modular DCN, a wireless DCN, and a hybrid DCN. Furthermore another important factor in DCN targets at managing and optimizing the network activity at the level of transfers to aggregate correlated data flows and thus directly to lower down the network traffic resulting from such data transfers. In particular, the book reports the in-network aggregation of incast transfer, shuffle transfer, uncertain incast transfer, and the cooperative scheduling of uncertain multicast transfer.
