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Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space
The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.
$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics
The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.
An Introductory Study on China's Cultural Transformation in Recent Times
This book examines in detail the basic trajectory of the cultural transformation and brings to light the extrinsic conditions and intrinsic mechanisms involved. It focuses on the period from after the Opium Wars to the New Culture Movement, as the New Culture Movement can be considered a pivotal phase in the cultural transformation of modern-day China. The New Culture Movement was a revolutionary eruption triggered by the accumulation of all the new qualitative cultural factors since the Opium Wars. Superficially, the movement’s goal seemed to be to overthrow the traditional culture. But in essence its true objective was to conduct an overall “screening” of that culture. The book elabo...
Qaidu and the Rise of the Independent Mongol State In Central Asia
Qaidu (1236-1301), one of the great rebels in the history of the Mongol Empire, was the grandson of Ogedei, the son Genghis Khan had chosen to be his heir. This boof recounts the dynastic convolutions and power struggle leading up to his rebellion and subsequent events.
Chevalley Supergroups
In the framework of algebraic supergeometry, the authors give a construction of the scheme-theoretic supergeometric analogue of split reductive algebraic group-schemes, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In particular, all Lie superalgebras of both basic and strange types are considered. This provides a unified approach to most of the algebraic supergroups considered so far in the literature, and an effective method to construct new ones. The authors' method follows the pattern of a suitable scheme-theoretic revisitation of Chevalley's construction of semisimple algebraic groups, adapted to the reductive case. As an intermediate step, they prove an existence theorem for Chevalley bases of simple classical Lie superalgebras and a PBW-like theorem for their associated Kostant superalgebras.
Tungsten Carbide
Tungsten Carbide - Processing and Applications, provides fundamental and practical information of tungsten carbide from powder processing to machining technologies for industry to explore more potential applications. Tungsten carbide has attracted great interest to both engineers and academics for the sake of its excellent properties such as hard and wear-resistance, high melting point and chemically inert. It has been applied in numerous important industries including aerospace, oil and gas, automotive, semiconductor and marine as mining and cutting tools, mould and die, wear parts, etc., which also has a promising future particularly due to enabling to resist high temperature and are extremely hard.
Iwasawa Theory, Projective Modules, and Modular Representations
This paper shows that properties of projective modules over a group ring $\mathbf{Z}_p[\Delta]$, where $\Delta$ is a finite Galois group, can be used to study the behavior of certain invariants which occur naturally in Iwasawa theory for an elliptic curve $E$. Modular representation theory for the group $\Delta$ plays a crucial role in this study. It is necessary to make a certain assumption about the vanishing of a $\mu$-invariant. The author then studies $\lambda$-invariants $\lambda_E(\sigma)$, where $\sigma$ varies over the absolutely irreducible representations of $\Delta$. He shows that there are non-trivial relationships between these invariants under certain hypotheses.
Definable Additive Categories: Purity and Model Theory
Most of the model theory of modules works, with only minor modifications, in much more general additive contexts (such as functor categories, categories of comodules, categories of sheaves). Furthermore, even within a given category of modules, many subcategories form a ``self-sufficient'' context in which the model theory may be developed without reference to the larger category of modules. The notion of a definable additive category covers all these contexts. The (imaginaries) language which one uses for model theory in a definable additive category can be obtained from the category (of structures and homomorphisms) itself, namely, as the category of those functors to the category of abelian groups which commute with products and direct limits. Dually, the objects of the definable category--the modules (or functors, or comodules, or sheaves)--to which that model theory applies may be recovered as the exact functors from the, small abelian, category (the category of pp-imaginaries) which underlies that language.
Biographical Dictionary of Chinese Women, Volume II
This volume of the Biographical Dictionary of Chinese Women completes the four-volume project and contains more than 400 biographies of women active in the Tang through Ming dynasties (618-1644). Many of the entries are the result of original research and provide the only substantial information on women available in English. Of note is the inclusion of a large number of women who reached positions of authority during this period as well as women artists and writers, especially poets, during this period of increased female literacy and more liberal social attitudes to women's cultural roles. Wherever possible, entries incorporate translations of poems and sometimes prose works so as to let the women speak for themselves. The book also includes a multitude of entertainers and actresses. The volume includes a Guide to Chinese Words Used, a Chronology of Dynasties and Major Rulers, a Finding List by Background or Fields of Endeavor, and a Glossary of Chinese Names. It will prove to be a useful tool for research and teaching.
Rearranging Dyson-Schwinger Equations
Dyson-Schwinger equations are integral equations in quantum field theory that describe the Green functions of a theory and mirror the recursive decomposition of Feynman diagrams into subdiagrams. Taken as recursive equations, the Dyson-Schwinger equations describe perturbative quantum field theory. However, they also contain non-perturbative information. Using the Hopf algebra of Feynman graphs the author follows a sequence of reductions to convert the Dyson-Schwinger equations to a new system of differential equations.
