Isomorphism Theory Research Articles

Towards mirror symmetry as duality for two dimensional abelian gauge theories

Superconformal sigma models with Calabi--Yau target spaces described as complete intersection subvarieties in toric varieties can be obtained as the low-energy limit of certain abelian gauge theories in two dimensions. We formulate mirror symmetry for this class of Calabi--Yau spaces as a duality in the abelian gauge theory, giving the explicit mapping relating the two Lagrangians. The duality relates inequivalent theories which lead to isomorphic theories in the low-energy limit. This formulation suggests that mirror symmetry could be derived using abelian duality. The application of duality in this context is complicated by the presence of nontrivial dynamics and the absence of a global symmetry. We propose a way to overcome these obstacles, leading to a more symmetric Lagrangian. The argument, however, fails to produce a derivation of the conjecture.

Infinite steinberg groups

The Steinberg group over a ring along an arbitrary set is defined. Its properties, structure, and isomorphism theory are studied.

Extensions of chain functors

Let K be a category of topological spaces and P ⊂ K a subcategory of good spaces; let moreover C K (resp. C p ) be the associated category of chain functors (cf. 1.3.) on K (resp. on P ) and the restriction functor. The main theorem (theorem 1.4.2.) asserts the existence of a kind of right adjoint with the following properties: 1) s C * is c-continuous (cf. 1.2.); 2) if determine isomorphic homology theories (on P ) , then so do (now on the larger category K ); 3) determine isomorphic homology theories on P. The main application of this result consists in an existence proof of a strong homology theory sh* on K agreeing with a prescribed sh* on P Suppose that C ϵ C p determines h * (on P ) then s h * will be the derived homology of s C * Due to properties 1) - 3) of s( ), this s h * is well-defined (in fact uniquely determined by h * and the axioms of a strong homology theory)c-continuous (constituting one of these axioms, which replaces Milnor’s clusteraxiom) and agrees, up to an isomorphism, with h * on ...

Privatization, System Membership, and Access to Home Health Care for the Elderly

Home health agency (HHA) access based on organizational and market factors is considered, employing a theoretical model of isomorphism for organizational factors and ecological and economic theories for market factors. Data derive from 1986 and 1987 telephone surveys that randomly sampled 185 HHAs from nine metropolitan areas in five states. Results show that competition limits restrictions on access; for-profit status and system membership increase the likelihood that clients will be refused for financial reasons. Findings support the isomorphism theory that fewer access and other behavioral differences appear within systems: nonprofits and for-profits tend to behave alike within systems, whereas freestanding nonprofits are less likely than their for-profit counterparts to refuse access. Findings for system members may account for some of the problems of legitimacy experienced by nonprofit health care organizations.

Coding Markov chains from the past

It is shown that a mixing Markov chain is a unilateral or one-sided factor of every ergodic process of equal or greater entropy. This extends the work of Sinai, who showed that the result holds for independent processes, and the work of Ornstein and Weiss, who showed that the result holds for mixing Markov chains in which all transition probabilities are positive. The proof exploits the Rothstein-Burton joinings-space formulation of Ornstein’s isomorphism theory, and uses a random coding argument.

The Geometry of Vision and the Mind Body Problem.

Contents: A refutation of naive realism, analyses of the topology and metric structure of visual space, including phenomenal visual depth perception, and extension of that analysis to the other senses, the mind body problem. How book differs - The variable curvature theory of visual space is novel and integrates other seemingly incompatible approaches. The theory of spatial isomorphism between phenomenal space and projection centers of the brain is also a novel contribution.

Duality in Calabi-Yau moduli space

We describe a duality in the moduli space of string vacua which pairs topologically distinct Calabi-Yau manifolds and shows that the yield isomorphic conformal theories. At the level of the geometrical description, this duality interchanges the roles of Kähler and complex structure moduli and thus pairs manifolds whose Euler numbers differ by χ → − χ. Amongst the interesting implications of this duality is the conclusion that by using both manifolds of a “mirror pair” the 27 3 and 27 3 couplings can be computed exactly by lowest-order geometrical calculations.

A TENSOR-THEORETIC ENHANCEMENT TO THE HILL CIPHER SYSTEM

The Hill matrix algorithm[3], published in 1929, is known for being the first purely algebraic cryptographic system and for starting the entire field of algebraic cryptology. In this paper, an operator derived from ring isomorphism theory is adapted for use in the Hill system which greatly increases the block size that a matrix can encrypt; specifically, a k×k invertible matrix over Z n represents an invertible matrix of order k 3, which produces ciphertext blocks k 2-times as long as the original matrix could. This enhancement increases the Hill system's security considerably.

Properties of binary and ternary mixtures in the vicinities of double critical points

The properties of binary mixtures with closed-loop diagrams are discussed. The topology of the phase diagram of a binary mixture with hydrogen-bonding is obtained in the mean-field approximation of the lattice mixture Hamiltonian. The algebraic formalism of fluctuation isomorphism theory is put forward. Changes of the phase diagram caused by small quantities of a third component and the boundaries of validity of Landau theory are considered.

Strong tree-cographs are birkhoff graphs

In this paper a class of undirected graphs is considered which can be derived from trees by a finite sequence of operations involving disjoint union and complementation. The graphs obtained in this way are called tree-cographs. The isomorphism problem for tree-cographs is obviously polynomial, due to their similarity to cographs.The notion of a Birkhoff graph is introduced. We represent graphs by their adjacency matrices. Any automorphism of a graph A is then representable by a permutation matrix P which commutes with A. But there may exist also doubly stochastic matrices X which commute with A, i.e. satisfy XA=AX, and which are not permutation matrices. A graph A is called a Birkhoff graph iff every doubly stochastic matrix X which commutes with A is a convex sum of automorphisms of A.If in the derivation of tree-cographs disjoint union is restricted to pairwise non-isomorphic components, then a class of “strong” tree-cographs is obtained. It is shown that strong tree-cographs are Birkhoff graphs. Furthermore, two strong tree-cographs A and B are isomorphic iff there exists a doubly stochastic matrix X satisfying XA=BX. Every such X is a convex sum of isomorphisms of A and B.The results of this paper may be considered as first steps towards a polyhedral theory of graph isomorphism.

Weak sequential denseness in Banach spaces

H. P. Rosenthal (Some recent discoveries in the isomorphic theory of Banach spaces, Bull. Amer. Math. Soc. 84 (1978), 803-831) has shown that for separable Banach spaces, X contains no subspace isomorphic to l iff every bounded subset of X is weakly sequentially dense in its weak closure (bwsd property). We show this is true for Banach spaces in general and compare the bwsd property to weak sequential denseness on arbitrary sets (weak N- sequential) and on relatively weakly compact sets (weak angelic).

Weak Sequential Denseness in Banach Spaces

H. P. Rosenthal [Some recent discoveries in the isomorphic theory of Banach spaces, Bull. Amer. Math. Soc. 84 (1978), 803-831] has shown that for separable Banach spaces, $X$ contains no subspace isomorphic to ${l_1}$ iff every bounded subset of $X$ is weakly sequentially dense in its weak closure (bwsd property). We show this is true for Banach spaces in general and compare the bwsd property to weak sequential denseness on arbitrary sets (weak $N$-sequential) and on relatively weakly compact sets (weak angelic).

Representations of crossed products by coactions and principal bundles

The main purpose of this paper is to establish a covariant representation theory for coactions of locally compact groups on C ∗ {C^{\ast }} -algebras (including a notion of exterior equivalence), to show how these results extend the usual notions for actions of groups on C ∗ {C^{\ast }} -algebras, and to apply these ideas to classes of coactions termed pointwise unitary and locally unitary to obtain a complete realization of the isomorphism theory of locally trivial principal G G -bundles in this context. We are also able to obtain all (Cartan) principal G G -bundles in this context, but their isomorphism theory remains elusive.

The Evolution of Hospice in America Toward Organizational Homogeneity

This article describes and explores the evolution of hospice in America. Using a theory of organizational isomorphism developed by DiMaggio and Powell (1983), the authors assess the development of hospice under conditions of uncertainty, co-optation by external forces, and professionalization by existing health care practitioners. The authors find that hospice programs have become isomorphic over time. That is, they have become more similar to each other as well as to other health care organizations.

An isomorphism theory for Bernoulli free Z-skew-compact group actions

An isomorphism theory for Bernoulli free Z-skew-compact group actions

Infinite Dimensional Linear Realization Theory

The problem of constructing linear time invariant state space models that are compatible with a given input-output map is examined. The class of models considered includes many systems of an infinite dimensional nature where the control action and sensing are restricted to subsets of the region over which the system is distributed. Concepts of controllability and observability are defined and it is shown how, under certain assumptions, the uncontrollable and unobservable parts of a system may be factored out. The main realization theorem is set in a time domain framework and a detailed analysis of state space isomorphism theory (“uniqueness of realizations”), is presented.

On a condition for minimality of Markovian splitting subspaces

Given a stationary Gaussian vector process, consider a Markovian splitting subspace X contained in the frame space which is either observable or constructible. Such an X will be called reduced . In this paper we show that a Markovian splitting subspace is minimal if and only if it is reduced. This was claimed in some earlier papers but there are nontrivial gaps in the proofs presented there. The proof is based on a lemma staling that all reduced X have quasi-equivalent structural functions. This property is also important in isomorphism theory for minimal splitting subspaces.

The isomorphism theory of projective pseudo-orthogonal groups

The isomorphism theory of projective pseudo-orthogonal groups

Finite coding factors of Markov generators

Using Thouvenot’s relativized isomorphism theory, the author develops a conditionalized version of the Friedman—Ornstein result on Markov processes. This relativized statement is used to study the way in which a factor generated by a finite length stationary coding sits in a Markov process. All such factors split off if they are maximal in entropy. Moreover, one can show that if a finite coding factor fails to split off, it is relatively finite in a larger factor which either generates or itself splits off.

Relatively Finitely Determined Implies Relatively Very Weak Bernoulli

In the isomorphism theory of Bernoulli shifts, the or Hamming distance plays an important role. Two finite state stationary processes are close in the metric if, on the average, strings from one process can be matched with strings from the other process so that their outputs agree with high frequency. Since such agreement must hold in the arbitrarily distant future, it might at first seem difficult to control the pairing.