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Articles 1 - 12 of 12
Full-Text Articles in Other Mathematics
The Topology, Geometry And Conformal Structure Of Properly Embedded Minimal Surfaces, Pascal Collin, Robert Kusner, William H. Meeks, Harold Rosenberg
The Topology, Geometry And Conformal Structure Of Properly Embedded Minimal Surfaces, Pascal Collin, Robert Kusner, William H. Meeks, Harold Rosenberg
Robert Kusner
This paper develops new tools for understanding surfaces with more than one end and infinite topology which are properly minimally embedded in Euclidean three-space. On such a surface, the set of ends forms a totally disconnected compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our main results is that the middle ends of the surface have quadratic area growth, and are thus not limit ends. This implies that the surface can have at most two limit ends, which occur at the top and bottom of the ordering, and thus only a countable …
Teaching Fractions, Natalie Miles
Teaching Fractions, Natalie Miles
Mahurin Honors College Capstone Experience/Thesis Projects
Because fractions are a vital part of mathematics instruction in schools and can be found in real life, it is important that all students understand and be able to utilize them. Teachers should choose strategies that will work best for their individual students, taking into account the various ways their students learn and the fraction knowledge students already possess. To effectively teach fractions, teachers must find ways to prompt student interest. Teachers can accomplish this through the use of technology. games. and manipulatives. Effective teachers must take into account the cultural diversity of their students. Teachers must be able to …
Preface, Thomas Hildebrandt, Alexander Kurz
Preface, Thomas Hildebrandt, Alexander Kurz
Engineering Faculty Articles and Research
No abstract provided.
Miniaturen. Studien Zu Kalkül Und Kreativität 1998-2002, Rudolf Kaehr
Miniaturen. Studien Zu Kalkül Und Kreativität 1998-2002, Rudolf Kaehr
Rudolf Kaehr
Informatik, künstlerische Praktik und Kunsttheorie der digitalen Bildtechnologien NULL&NICHTS; weder leer, noch nicht – oder Kraut und Rüben Gedanken zu einer autonomen Medienwissenschaft Das Menschenbild aus der Sicht einer polykontexturalen Systemtheorie Thesen zum trans-klassischen Menschenbild Gebaute Phantasien, unkontrollierbare Schwankungen Kreativität und Kalkül Ver_Endungen in/der Programmierbarkeit Diagrammatik: Denken a la Carte Zur Verstörung des (H)ortes der Zerstörung Zur Kenogrammatik der Medientheorie
Dynamic Semantic Web, Rudolf Kaehr
Dynamic Semantic Web, Rudolf Kaehr
Rudolf Kaehr
Dynamic Semantic Web (DSW) is based at first on the techniques, methods and paradigms of the emerging Semantic Web movement and its applications. DSW is advancing one fundamental step further from a static to a dynamic concept of the Semantic Web with extended flexibility in the navigation between ontologies and more profound transparency of the informational system. Web Services are now redefinded by Semantic Web. To proof the advantages of DSW, it is the main aim of this project to develop the tools and methods necessary to develop a DSW based Web Service (DSW business application). The existing framework of …
Pokémon® Cards And The Shortest Common Superstring, Mark Stamp, Austin Stamp
Pokémon® Cards And The Shortest Common Superstring, Mark Stamp, Austin Stamp
Faculty Publications, Computer Science
Evidence is presented that certain sequences of Pokémon cards are determined by selecting consecutive elements from a longer sequence. We then consider the problem of recovering the shortest common superstring (SCS), i.e., the shortest string that contains each of the Pokémon card sequences as a consecutive substring. The SCS problem arises in many applications, most notably in DNA sequencing.
Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall
Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall
Department of Math & Statistics Faculty Publications
It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.
Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro
Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro
Department of Math & Statistics Faculty Publications
For functions belonging to invariant subspaces of the backward shift operator Bf = (f − f(0))/z on spaces of analytic functions on the unit disk D, we explore, in a systematic way, the continuation properties of these functions.
Mathematical Magic, Arthur T. Benjamin
Mathematical Magic, Arthur T. Benjamin
All HMC Faculty Publications and Research
In this paper, we present simple strategies for performing mathematical calculations that appear magical to most audiences. Specifically, we explain how to square large numbers, memorize pi to 100 places and determine the day of the week of any given date.
Algebraic Semantics For Coalgebraic Logics, Clemens Kupke, Alexander Kurz, Dirk Pattinson
Algebraic Semantics For Coalgebraic Logics, Clemens Kupke, Alexander Kurz, Dirk Pattinson
Engineering Faculty Articles and Research
With coalgebras usually being defined in terms of an endofunctor T on sets, this paper shows that modal logics for T-coalgebras can be naturally described as functors L on boolean algebras. Building on this idea, we study soundness, completeness and expressiveness of coalgebraic logics from the perspective of duality theory. That is, given a logic L for coalgebras of an endofunctor T, we construct an endofunctor L such that L-algebras provide a sound and complete (algebraic) semantics of the logic. We show that if L is dual to T, then soundness and completeness of the algebraic semantics immediately yield the …
Coalgebras And Modal Expansions Of Logics, Alexander Kurz, Alessandra Palmigiano
Coalgebras And Modal Expansions Of Logics, Alexander Kurz, Alessandra Palmigiano
Engineering Faculty Articles and Research
In this paper we construct a setting in which the question of when a logic supports a classical modal expansion can be made precise. Given a fully selfextensional logic S, we find sufficient conditions under which the Vietoris endofunctor V on S-referential algebras can be defined and we propose to define the modal expansions of S as the logic that arises from the V-coalgebras. As an example, we also show how the Vietoris endofunctor on referential algebras extends the Vietoris endofunctor on Stone spaces. From another point of view, we examine when a category of ‘spaces’ (X,A), ie sets X …
Basic Neutrosophic Algebraic Structures And Their Application To Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy
Basic Neutrosophic Algebraic Structures And Their Application To Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Study of neutrosophic algebraic structures is very recent. The introduction of neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised data make use of the directed graphs or bipartite graphs. Thus the use of graphs has become inevitable in fuzzy models. The neutrosophic models are fuzzy models that permit …