Download or read book Markov Fields over Countable Partially Ordered Sets Extrema and Splitting written by I. V. Evstigneev and published by American Mathematical Soc.. This book was released on 1994 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various notions of the Markov property relative to a partial ordering have been proposed by both physicists and mathematicians. This work develops techniques for stying Markov fields on partially ordered sets. We introduce random transformations of the index set which preserves the Markov property of the field. These transformations yield new classes of Markov fields starting from relatively simple ones. Examples include a model for crack formation and a model for the distribution of fibres in a composite material.

Download or read book Orders of a Quartic Field written by Jin Nakagawa and published by American Mathematical Soc.. This book was released on 1996 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author studies the Dirichlet series whose coefficients are the number of orders of a quartic field with given indices. Nakagawa gives an explicit expression of the Dirichlet series. Using this expression, its analytic properties are deduced. He also presents an asymptotic formula for the number of orders in a quartic field with index less than a given positive number.

Download or read book Global Aspects of Homoclinic Bifurcations of Vector Fields written by Ale Jan Homburg and published by American Mathematical Soc.. This book was released on 1996 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author investigates a class of smooth one parameter families of vector fields on some $n$-dimensional manifold, exhibiting a homoclinic bifurcation. That is, he considers generic families $x_\mu$, where $x_0$ has a distinguished hyperbolic singularity $p$ and a homoclinic orbit; an orbit converging to $p$ both for positive and negative time. It is assumed that this homoclinic orbit is of saddle-saddle type, characterized by the existence of well-defined directions along which it converges to the singularity $p$. The study is not confined to a small neighborhood of the homoclinic orbit. Instead, the position of the stable and unstable set of the homoclinic orbit is incorporated and it is shown that homoclinic bifurcations can lead to complicated bifurcations and dynamics, including phenomena like intermittency and annihilation of suspended horseshoes.

Download or read book The Economy As An Evolving Complex System II written by W. Brian Arthur and published by CRC Press. This book was released on 2018-05-04 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new view of the economy as an evolving, complex system has been pioneered at the Santa Fe Institute over the last ten years, This volume is a collection of articles that shape and define this view?a view of the economy as emerging from the interactions of individual agents whose behavior constantly evolves, whose strategies and actions are always adapting.The traditional framework in economics portrays activity within an equilibrium steady state. The interacting agents in the economy are typically homogenous, solve well-defined problems using perfect rationality, and act within given legal and social structures. The complexity approach, by contrast, sees economic activity as continually changing?continually in process. The interacting agents are typically heterogeneous, they must cognitively interpret the problems they face, and together they create the structures?markets, legal and social institutions, price patters, expectations?to which they individually react. Such structures may never settle down. Agents may forever adapt and explore and evolve their behaviors within structures that continually emerge and change and disappear?structures these behaviors co-create. This complexity approach does not replace the equilibrium one?it complements it.The papers here collected originated at a recent conference at the Santa Fe Institute, which was called to follow up the well-known 1987 SFI conference organized by Philip Anderson, Kenneth Arrow, and David Pines. They survey the new study of complexity and the economy. They apply this approach to real economic problems and they show the extent to which the initial vision of the 1987 conference has come to fruition.

Download or read book Second Order Sturm Liouville Difference Equations and Orthogonal Polynomials written by Alouf Jirari and published by American Mathematical Soc.. This book was released on 1995 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir presents machinery for analyzing many discrete physical situations, and should be of interest to physicists, engineers, and mathematicians. We develop a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. We discuss the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate [italic capital]L2 setting, and give necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions.

Download or read book Automorphisms of the Lattice of Recursively Enumerable Sets written by Peter Cholak and published by American Mathematical Soc.. This book was released on 1995 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: A version of Harrington's [capital Greek]Delta3-automorphism technique for the lattice of recursively enumerable sets is introduced and developed by reproving Soare's Extension Theorem. Then this automorphism technique is used to show two technical theorems: the High Extension Theorem I and the High Extension Theorem II. This is a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice.

Download or read book Hilbert Modules over Operator Algebras written by Paul S. Muhly and published by American Mathematical Soc.. This book was released on 1995 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses the three-dimensional generalization of category, offering a full definition of tricategory; a proof of the coherence theorem for tricategories; and a modern source of material on Gray's tensor product of 2-categories. Of interest to research mathematicians; theoretical physicists, algebraic topologists; 3-D computer scientists; and theoretical computer scientists. Society members, $19.00. No index. Annotation copyright by Book News, Inc., Portland, OR

Download or read book Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd Dimensional Manifold with Boundary written by Paul Kirk and published by American Mathematical Soc.. This book was released on 1996 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analytic perturbation theory for eigenvalues of Dirac operators on odd dimensional manifolds with boundary is described in terms of [italic]extended L2 eigenvectors [end italics] on manifolds with cylindrical ends. These are generalizations of the Atiyah-Patodi-Singer extended [italic capital]L2 kernel of a Dirac operator. We prove that they form a discrete set near zero and deform analytically, in contrast to [italic capital]L2 eigenvectors, which can be absorbed into the continuous spectrum under deformations when the tangential operator is not invertible. We show that the analytic deformation theory for extended [italic capital]L2 eigenvectors and Atiyah-Patodi-Singer eigenvectors coincides.

Download or read book On the Martingale Problem for Interactive Measure Valued Branching Diffusions written by Edwin Arend Perkins and published by American Mathematical Soc.. This book was released on 1995 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops stochastic integration with respect to ``Brownian trees'' and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well-posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.

Download or read book Pseudofunctors on Modules with Zero Dimensional Support written by I-Chiau Huang and published by American Mathematical Soc.. This book was released on 1995 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms are local with finitely generated residue field extensions is constructed.

Download or read book Tilting in Abelian Categories and Quasitilted Algebras written by Dieter Happel and published by American Mathematical Soc.. This book was released on 1996 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: We generalize tilting with respect to a tilting module of projective dimension at most one for an Artin algebra to tilting with respect to a torsion pair in an Abelian category. Our construction is motivated by the connection between tilting and derived categories. We develop a general theory for such tilting, and are led to a generalization of tilting algebras which we call quasitilted algebras. This class also contains the canonical algebras, and we show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. We also give other characterizations of quasitilted algebras, and give methods for constructing such algebras.

Download or read book Factorizing the Classical Inequalities written by Grahame Bennett and published by American Mathematical Soc.. This book was released on 1996 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir describes a new way of looking at the classical inequalities. The most famous such results, (those of Hilbert, Hardy, and Copson) may be interpreted as inclusion relationships, l[superscript italic]p [subset equality symbol] [italic capital]Y, between certain (Banach) sequence spaces, the norm of the injection being the best constant of the particular inequality. The inequalities of Hilbert, Hardy, and Copson all share the same space [italic capital]Y. That space -- alias [italic]ces([italic]p) -- is central to many celebrated inequalities, and thus is studied here in considerable detail.

Download or read book Textile Systems for Endomorphisms and Automorphisms of the Shift written by Masakazu Nasu and published by American Mathematical Soc.. This book was released on 1995 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.

Download or read book The 2 Dimensional Attractor of x t mu x t f x t 1 written by Hans-Otto Walther and published by American Mathematical Soc.. This book was released on 1995 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: See attachment.

Download or read book Generalized Tate Cohomology written by John Patrick Campbell Greenlees and published by American Mathematical Soc.. This book was released on 1995 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [italic capital]G be a compact Lie group, [italic capitals]EG a contractible free [italic capital]G-space and let [italic capitals]E~G be the unreduced suspension of [italic capitals]EG with one of the cone points as basepoint. Let [italic]k*[over][subscript italic capital]G be a [italic capital]G-spectrum. Let [italic capital]X+ denote the disjoint union of [italic capital]X and a [italic capital]G-fixed basepoint. Define the [italic capital]G-spectra [italic]f([italic]k*[over][subscript italic capital]G) = [italic]k*[over][subscript italic capital]G [up arrowhead symbol] [italic capitals]EG+, [italic]c([italic]k*[over][subscript italic capital]G) = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G), and [italic]t([italic]k[subscript italic capital]G)* = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) [up arrowhead symbol] [italic capitals]E~G. The last of these is the [italic capital]G-spectrum representing the generalized Tate homology and cohomology theories associated to [italic]k[subscript italic capital]G. Here [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) is the function space spectrum. The authors develop the properties of these theories, illustrating the manner in which they generalize the classical Tate-Swan theories.

Download or read book The Method of Layer Potentials for the Heat Equation in Time Varying Domains written by John L. Lewis and published by American Mathematical Soc.. This book was released on 1995 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir consists of three papers in which we develop the method of layer potentials for the heat equation in time-varying domains. In Chapter I we show certain singular integral operators on [italic]L[superscript italic]p are bounded. in Chapter II, we develop a modification of the David buildup scheme to obtain [italic]L[superscript italic]p boundedness of the double layer heat potential on the boundary of our domains. In Chapter III, we use the results of the first two chapters to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure.

Download or read book An Arithmetic Riemann Roch Theorem for Singular Arithmetic Surfaces written by Wayne Aitken and published by American Mathematical Soc.. This book was released on 1996 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following gives a development of Arakelov theory general enough to handle not only regular arithmetic surfaces but also a large class of arithmetic surfaces whose generic fiber has singularities. This development culminates in an arithmetic Riemann-Roch theorem for such arithmetic surfaces. The first part of the memoir gives a treatment of Deligne's functorial intersection theory, and the second develops a class of intersection functions for singular curves which behaves analogously to the canonical Green's functions introduced by Arakelov for smooth curves.