The Mathieu groups have many fascinating and unusual characteristics and have been studied at length since their discovery. This book provides a unique, geometric perspective on these groups. The amalgam method is explained and used to construct M24, enabling readers to learn the method through its application to a familiar example. The same method is then used to construct, among others, the octad graph, the Witt design and the Golay code. This book also provides a systematic account of 'small groups', and serves as a useful reference for the Mathieu groups. The material is presented in such a way that it guides the reader smoothly and intuitively through the process, leading to a deeper understanding of the topic.
This book focuses on the classic Steiner Problem and illustrates how results of the problem's development have generated the Theory of Minimal Networks, that is systems of "rubber" branching threads of minimal length. This theory demonstrates a brilliant interconnection among differential and computational geometry, topology, variational calculus, and graph theory. All necessary preliminary information is included, and the book's simplified format and nearly 150 illustrations and tables will help readers develop a concrete understanding of the material. All nontrivial statements are proved, and plenty of exercises are included.
This study deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) it investigates extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.
The book presents a new scientific approach to the problem of biomechanical systems description.This approach is based on development of a universal anthropomorphic model and employment of methodology of imitational dynamic modeling (IDM). The novelty of this approach is that there appears a possibility to operate with a whole class of models, derived from the universal model on the basis of motion separation principle. This is followed by utilization of iterational procedures realizing the method of successive approximations and resulting in description of the real motion with the pre-set accuracy level. By use of the IDM there has been for the first time ascertained certain laws governing human locomotions: presence of so-called controlling and stabilizing interlink moments, wavelike speeding of forces extremums along the kinematic chain, adaptation of control functions for astronauts motion coordination preservation. The book includes new theoretical conceptions explaining the deterioration of functional state of skeletal-muscular apparatus of astronauts due to zero-gravity influence.
Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().
The rapid evolution of technology and mathematical methods in this century has led to the recognition and accumulation of a large quantity of scientific facts. At the same time, however, in studying natural bodies, primary attention has not been paid to their total character; the body either ceased to be an individual, as in the case of mathematical methods, or has become a complex of separate, not always closely connected characteristics examined by laboratory analyses. The goniometric study of a crystal, for example, has developed into the determination of constants of the crystal lattice, but the examination of minerals from a specific deposit was concerned primarily with the chemical analysis of their admixtures. In geological sciences a thorough morphological investigation has preserved its original importance, particularly in geomorphology and paleontology. Even in petrography, the three-dimensional description of rocks was replaced by the study of thin sections, since the optical microscope does not permit examination of an uneven surface as a result of a restricted depth of observation field. The art of ancient naturalists of conceiving the object in its entirety, with all its particularities, has not developed with time, as would have been desirable.
This book takes you to the "classical academy of shamanism", Siberian tribal spirituality that gave birth to the expression "shamanism." For the first time, in this volume Znamenski has rendered in readable English more than one hundred books and articles that describe all aspects of Siberian shamanism: ideology, ritual, mythology, spiritual pantheon, and paraphernalia. It will prove valuable to anthropologists, historians of religion, psychologists and practitioners of shamanism.
Et moi ... - si j'avait su comment en revcnir. One service mathematics has rendered the je n'y scrais point aile.' human race. It has put common sense back where it belongs, on the topmost shclf next Jules Verne to the dusty canister labdlcd 'discarded non· The series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
The EZ Big Book of Alcoholics Anonymous is a page-by-page translation of the original Alcoholics Anonymous published by AA founder Bill Wilson in the 1930s. It is intended to carry the AA message to modern readers who find the original Big Book hard to digest for any reason. The language is gender-neutral, and references to spirituality are more inclusive. The book shows you how to: Quit drinking Find a personal Higher Power Livei n the now Face problems fearlessly Discover the real you Make great friends in AA Advance Reviews The anonymous author of this work has taken a bold step by updating the language of the original Big Book, which has barely changed since its introduction in 1939. John Elm, PhD, AA member Finally, a version of the Big Book has arrived that's as inclusive as the program itself. The language does not assume the reader is male or Christian. Jules Cardello, LMSW, Social Worker The simple, direct writing makes the message of the Big Book much easier to understand without any loss of meaning. Anonymous AA Member
The long-term operation of rails has been studied with focus on (1) the formation and behavior of structural-phase states and nanoscale structures, (2) the modelling of the processes occurring in the surface layers of rails under severe plastic deformation and (3) the methods and techniques for assessing the structural and phase states of rails, internal stresses, and their evolution during the life cycle. The book references 264 original resources and includes their direct web link for in-depth reading. Keywords: Long Rails, Long-term Operation, Transmission Electron Microscopy, Steel, Differentiated Hardening, Structural Phase States, Nanoscale Structures, Wear, Deformation Effects, Recrystallization, Segregation, Homogenization, Relaxation, Phase Transitions, Phase Decomposition, Amorphization, Sintering, Filling of Micro- and Nanopores, Nanocapillaries, Severe Plastic Deformation, Megaplastic Deformation.
Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.
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