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1999

Algebra

Articles 1 - 7 of 7

Full-Text Articles in Mathematics

Splitting Tiled Surfaces With Abelian Conformal Tiling Group, Sean A. Broughton Sep 1999

Splitting Tiled Surfaces With Abelian Conformal Tiling Group, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

Let p be a reflection on a closed Riemann Surface S, i.e., an anti-conformal involutary isometry of S with a non-empty fixed point subset. Let Sp denote the fixed point subset of p, which is also called the mirror of p. If S −Sp has two components, then p is called separating and we say that S splits at the mirror Sp. Otherwise p is called non-separating. We assume that the system of mirrors, Sq, as q varies over all reflections in the isometry group Aut*(S) defines a tiling of the surface, consisting of triangles. In turn, the tiling determines …

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Divisible Tilings In The Hyperbolic Plane, Sean A. Broughton, Dawn M. Haney, Lori T. Mckeough, Brandy M. Smith Aug 1999

Divisible Tilings In The Hyperbolic Plane, Sean A. Broughton, Dawn M. Haney, Lori T. Mckeough, Brandy M. Smith

Mathematical Sciences Technical Reports (MSTR)

We consider triangle-quadrilateral pairs in the hyperbolic plane which "kaleidoscopically" tile the plane simultaneously. In this case the tiling by quadrilaterals is called a divisible tiling. All possible such divisible tilings are classified. There are a finite number of 1,2, and 3 parameter families as well as a finite number of exceptional cases.

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Tilings Which Split A Mirror, Jim Belk Jun 1999

Tilings Which Split A Mirror, Jim Belk

Mathematical Sciences Technical Reports (MSTR)

We consider the mirror of a reflection which consists of its subset of fixed points. We investigate a number of conditions on the tiling that guarantee that the surface splits at a mirror.

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Automorphic Subsets Of The N-Dimensional Cube Are Translations Of Cwatsets, Matthew Lepinski Apr 1999

Automorphic Subsets Of The N-Dimensional Cube Are Translations Of Cwatsets, Matthew Lepinski

Mathematical Sciences Technical Reports (MSTR)

It is known that automorphic subsets are generalizations of cwatsets. In this paper we show that an automorphic subset is the translation of some cwatset, and therefore that each automorphic subset is internally isomorphic to a cwatset.

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The Topological Snake Lemma And Corona Algebras, Claude Schochet Jan 1999

The Topological Snake Lemma And Corona Algebras, Claude Schochet

Mathematics Faculty Research Publications

We establish versions of the Snake Lemma from homological algebra in the context of topological groups, Banach spaces, and operator algebras. We apply this tool to demonstrate that if ƒ : B → B′ is a quasi-unital C*-map of separable C*-algebras, so that it induces a map of Corona algebras ƒ̄ : QB → QB′, and if ƒ is mono, then the induced map ƒ̄ is also mono.

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(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz Jan 1999

(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz

Engineering Faculty Articles and Research

We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications.

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Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache Jan 1999

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

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