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Articles 1 - 10 of 10
Full-Text Articles in Mathematics
Partial Automorphism Semigroups, Jennifer Chubb, Valentina Harizanov, Andrei Morozov, Sarah Pingrey, Eric Ufferman
Partial Automorphism Semigroups, Jennifer Chubb, Valentina Harizanov, Andrei Morozov, Sarah Pingrey, Eric Ufferman
Mathematics
We study the relationship between algebraic structures and their inverse semigroups of partial automorphisms. We consider a variety of classes of natural structures including equivalence structures, orderings, Boolean algebras, and relatively complemented distributive lattices. For certain subsemigroups of these inverse semigroups, isomorphism (elementary equivalence) of the subsemigroups yields isomorphism (elementary equivalence) of the underlying structures. We also prove that for some classes of computable structures, we can reconstruct a computable structure, up to computable isomorphism, from the isomorphism type of its inverse semigroup of computable partial automorphisms.
Full Algebra Of Generalized Functions And Non-Standard Asymptotic Analysis, Todor D. Todorov, Hans Vernaeve
Full Algebra Of Generalized Functions And Non-Standard Asymptotic Analysis, Todor D. Todorov, Hans Vernaeve
Mathematics
We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions. We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution. We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a connection between our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article …
Multiscale Deformable Registration Of Noisy Medical Images, Dana C. Paquin, Doron Levy, Lei Xing
Multiscale Deformable Registration Of Noisy Medical Images, Dana C. Paquin, Doron Levy, Lei Xing
Mathematics
Multiscale image registration techniques are presented for the registration of medical images using deformable registration models. The techniques are particularly effective for registration problems in which one or both of the images to be registered contains significant levels of noise. A brief overview of existing deformable registration techniques is presented, and experiments using B-spline free-form deformation registration models demonstrate that ordinary deformable registration techniques fail to produce accurate results in the presence of significant levels of noise. The hierarchical multiscale image decomposition described in E. Tadmor, S. Nezzar, and L. Vese’s, ”A multiscale image representation using hierarchical (BV, L2 …
Local Geometry Of Zero Sets Of Holomorphic Functions Nears The Torus, Jim Agler, John E. Mccarthy, Mark Stankus
Local Geometry Of Zero Sets Of Holomorphic Functions Nears The Torus, Jim Agler, John E. Mccarthy, Mark Stankus
Mathematics
We call a holomorphic function f on a domain in Cn locally toral at the point P in the n-torus if the intersection of the zero set of f with the n-torus has dimension n−1 at P. We study the interplay between the structure of locally toral functions and the geometry of their zero sets.
Sheaf Theoretic Formulation Of Entanglement, Goro C. Kato
Sheaf Theoretic Formulation Of Entanglement, Goro C. Kato
Mathematics
A formulation in terms of sheaf theoretic (or categorical) notions for quantum entanglement is given with direct experimental consequences. The notions from sheaf theory and category theory give structural theory, i.e., qualitative theory, as a candidate for quantum gravity. Its advantage is the following: it provides not only space-time background independent, but also scale independent.This theory is called the theory of temporal topos (or simply t-topos theory).
Microcosm To Macrocosm Via The Notion Of A Sheaf (Observers In Terms Of T-Topos), Goro Kato
Microcosm To Macrocosm Via The Notion Of A Sheaf (Observers In Terms Of T-Topos), Goro Kato
Mathematics
The fundamental approach toward matter, space and time is that particles (either objects of macrocosm or microcosm), space and time are all presheafified. Namely, the concept of a presheaf is most fundamental for matter, space and time. An observation of a particle is represented by a morphism from the observed particle (its associated presheaf) to the observer (its associated presheaf) over a specified object (called a generalized time period) of a t-site (i.e. a category with a Grothendieck topology). This formulation provides a scale independent and background space-time free theory (since, for the t-topos theoretic formulation, space and time are …
A Positive Mass Theorem On Asymptotically Hyperbolic Manifolds With Corners Along A Hypersurface, Vincent Bonini, Jie Qing
A Positive Mass Theorem On Asymptotically Hyperbolic Manifolds With Corners Along A Hypersurface, Vincent Bonini, Jie Qing
Mathematics
In this paper we take an approach similar to that in [13] to establish a positive mass theorem for spin asymptotically hyperbolic manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a solution to a perturbed eigenfunction equation to obtain an asymptotic expansion of the solution in the right order. This allows us to understand the change of the mass aspect of a conformal change of asymptotically hyperbolic metrics.
A Lost Theorem: Definite Integrals In An Asymptotic Setting, Ray Cavalcante, Todor D. Todorov
A Lost Theorem: Definite Integrals In An Asymptotic Setting, Ray Cavalcante, Todor D. Todorov
Mathematics
No abstract provided.
A Manifold Structure For The Group Of Orbifold Diffeomorphisms Of A Smooth Orbifold, Joseph E. Borzellino, Victor Brunsden
A Manifold Structure For The Group Of Orbifold Diffeomorphisms Of A Smooth Orbifold, Joseph E. Borzellino, Victor Brunsden
Mathematics
For a compact, smooth Cr orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for 1 ≤ r < ∞ and a Fréchet manifold if r = ∞. In each case, the local model is the separable Banach (Fréchet) space of Cr (C ∞, resp.) orbisections of the tangent orbibundle.
On Powers Associated With Sierpiński Numbers, Riesel Numbers And Polignac's Conjecture, Mark Kozek, Michael Filaseta, Carrie Finch
On Powers Associated With Sierpiński Numbers, Riesel Numbers And Polignac's Conjecture, Mark Kozek, Michael Filaseta, Carrie Finch
Mathematics
We address conjectures of P. Erdős and conjectures of Y.-G. Chen concerning the numbers in the title. We obtain a variety of related results, including a new smallest positive integer that is simultaneously a Sierpiński number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k,k2, k3,...,kr are simultaneously Sierpiński numbers.