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Articles 1231 - 1260 of 1405

Full-Text Articles in Algebra

Big Cwatsets And Hamming Code, Matthew Davis, Thomas M. Langley, Norah Mazel Oct 2005

Big Cwatsets And Hamming Code, Matthew Davis, Thomas M. Langley, Norah Mazel

Mathematical Sciences Technical Reports (MSTR)

In contrast to Lagrange's Theorem in Finite Group Theory, we show that the ratio of the largest proper cwatset of degree d to the size of binary d-space approaches 1 as d approaches infinity. We show how to explicitly construct large cwatsets as cosets of Hamming Codes, and discuss many open questions that arise.

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Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel May 2005

Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

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Graph Theory For The Secondary School Classroom., Dayna Brown Smithers May 2005

Graph Theory For The Secondary School Classroom., Dayna Brown Smithers

Electronic Theses and Dissertations

After recognizing the beauty and the utility of Graph Theory in solving a variety of problems, the author decided that it would be a good idea to make the subject available for students earlier in their educational experience. In this thesis, the author developed four units in Graph Theory, namely Vertex Coloring, Minimum Spanning Tree, Domination, and Hamiltonian Paths and Cycles, which are appropriate for high school level.

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A *-Closed Subalgebra Of The Smirnov Class, Stephan Ramon Garcia Jan 2005

A *-Closed Subalgebra Of The Smirnov Class, Stephan Ramon Garcia

Pomona Faculty Publications and Research

We study real Smirnov functions and investigate a certain *-closed subalgebra of the Smirnov class N^+ containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space H^p ∩ H^p [overscore over the second H^p]. This leads to a natural analog of the Riesz projection on a certain quotient space of L^p for p ϵ (0, 1). We also study a Herglotz-like integral transform for singular measures on the unit circle ∂D.

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The Solvability Of Polynomials By Radicals: A Search For Unsolvable And Solvable Quintic Examples, Robert Lewis Beyronneau Jan 2005

The Solvability Of Polynomials By Radicals: A Search For Unsolvable And Solvable Quintic Examples, Robert Lewis Beyronneau

Theses Digitization Project

This project centers around finding specific examples of quintic polynomials that were and were not solvable. This helped to devise a method for finding examples of solvable and unsolvable quintics.

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Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth Jan 2005

Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth

Mathematics Faculty Publications

In this note, we prove that in a Hausdorff topological abelian group, the closed subgroup generated by all compact elements is equal to teh closed subgroup generated by all compact elements which are topologically p-torsion for some prime p. In particular, this yields a new, short solution to a question raised by Armacost [A]. Using Pontrjagin duality, we obtain new descriptions of the identity component of a locally compact abelian group.

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Introduction To Bimatrices, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2005

Introduction To Bimatrices, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component of each other. The study of bialgebraic structures led to the invention of new notions like birings, Smarandache birings, bivector spaces, linear bialgebra, bigroupoids, bisemigroups, etc. But most of these are abstract algebraic concepts except, the bisemigroup being used in …

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Fuzzy And Neutrosophic Analysis Of Women With Hiv/Aids, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2005

Fuzzy And Neutrosophic Analysis Of Women With Hiv/Aids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Fuzzy theory is one of the best tools to analyze data, when the data under study is an unsupervised one, involving uncertainty coupled with imprecision. However, fuzzy theory cannot cater to analyzing the data involved with indeterminacy. The only tool that can involve itself with indeterminacy is the neutrosophic model. Neutrosophic models are used in the analysis of the socio-economic problems of HIV/AIDS infected women patients living in rural Tamil Nadu. Most of these women are uneducated and live in utter poverty. Till they became seriously ill they worked as daily wagers. When these women got admitted in the hospital …

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N-Algebraic Structures And S-N-Algebraic Structures, Florentin Smarandache, Vasantha Kandasamy Jan 2005

N-Algebraic Structures And S-N-Algebraic Structures, Florentin Smarandache, Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, for the first time we introduce the notions of Ngroups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. We expect the reader to be well versed in group theory and have at least basic knowledge about Smarandache groupoids, Smarandache loops, Smarandache semigroups and bialgebraic structures and Smarandache bialgebraic structures. The book is organized into six chapters. The first chapter gives the basic notions of S-semigroups, S-groupoids and S-loops thereby making the book self-contained. Chapter two introduces N-groups and their Smarandache analogues. In chapter three, Nloops and Smarandache N-loops are introduced and analyzed. Chapter four …

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Introduction To Linear Bialgebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2005

Introduction To Linear Bialgebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very powerful algebraic tool that can yield itself to applications. With the recent introduction of bimatrices (2005) we have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear bialgebra and also give the applications of these algebraic …

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Applications Of Bimatrices To Some Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2005

Applications Of Bimatrices To Some Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduced by us help in the analysis of such real world problems and they happen to be mathematical tools which can give the hidden pattern of the problem under investigation. This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and describe some of its properties. …

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From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber Jan 2005

From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber

Mathematics, Statistics and Data Science Faculty Works

We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism called the "Jacobiator". Similarly, a Lie 2-group is a categorified version of a Lie group. If G is a simply-connected compact simple Lie group, there is a 1-parameter family of Lie 2-algebras g_k each having Lie(G) as its Lie algebra of objects, but with a Jacobiator built from the canonical 3-form on G. There appears to be no Lie 2-group …

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Rational Hyperholomorphic Functions In R4, Daniel Alpay, Michael Shapiro, Dan Volok Jan 2005

Rational Hyperholomorphic Functions In R4, Daniel Alpay, Michael Shapiro, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of Cauchy-Kovalevskaya quotients of polynomials, the second in terms of realizations and the third in terms of backward-shift invariance. Also introduced and studied are the counterparts of the Arveson space and Blaschke factors.

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Point Evaluation And Hardy Space On A Homogeneous Tree, Daniel Alpay, Dan Volok Jan 2005

Point Evaluation And Hardy Space On A Homogeneous Tree, Daniel Alpay, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We consider stationary multiscale systems as defined by Basseville, Benveniste, Nikoukhah and Willsky. We show that there are deep analogies with the discrete time non stationary setting as developed by the first author, Dewilde and Dym. Following these analogies we define a point evaluation with values in a C*–algebra and the corresponding “Hardy space” in which Cauchy’s formula holds. This point evaluation is used to define in this context the counterpart of classical notions such as Blaschke factors.

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Weak Factorizations, Fractions And Homotopies, Alexander Kurz, Jiří Rosický Jan 2005

Weak Factorizations, Fractions And Homotopies, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

We show that the homotopy category can be assigned to any category equipped with a weak factorization system. A classical example of this construction is the stable category of modules. We discuss a connection with the open map approach to bisimulations proposed by Joyal, Nielsen and Winskel.

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Primitive Ideals Of Semigroup Graded Rings, Hema Gopalakrishnan Dec 2004

Primitive Ideals Of Semigroup Graded Rings, Hema Gopalakrishnan

Mathematics Faculty Publications

Prime ideals of strong semigroup graded rings have been characterized by Bell, Stalder and Teply for some important classes of semigroups. The prime ideals correspond to certain families of ideals of the component rings called prime families. In this paper, we define the notion of a primitive family and show that primitive ideals of such rings correspond to primitive families of ideals of the component rings.

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Mathematics Placement Test: Helping Students Succeed, Norma Rueda, Carole Sokolowski Oct 2004

Mathematics Placement Test: Helping Students Succeed, Norma Rueda, Carole Sokolowski

Mathematics Faculty Publications

A study was conducted at Merrimack College in Massachusetts to compare the grades of students who took the recommended course as determined by their mathematics placement exam score and those who did not follow this recommendation. The goal was to decide whether the mathematics placement exam used at Merrimack College was effective in placing students in the appropriate mathematics class. During five years, first-year students who took a mathematics course in the fall semester were categorized into four groups: those who took the recommended course, those who took an easier course than recommended, those who took a course more difficult …

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Vector Operations In Superscalar Architectures, Nathan Daniel Flinn Oct 2004

Vector Operations In Superscalar Architectures, Nathan Daniel Flinn

Electrical & Computer Engineering Theses & Dissertations

Vector calculations are very prevalent today. Though the vector-processing computer is quite an old concept, superscalar processors lack hardware support for vector operations. This thesis investigates whether an ordinary superscalar computer architecture can be designed to include hardware support for improved vector operations without drastically changing the existing superscalar design and behavior. A computer architecture design was created and implemented that included the vector multiply (dot product) operation. The design includes a Vector Operations Unit that captures incoming vector operations and generates the necessary set of machine instructions to complete the vector operation internally. It then delivers these instructions to …

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Coalgebras And Modal Expansions Of Logics, Alexander Kurz, Alessandra Palmigiano Jan 2004

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 …

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Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg Jan 2004

Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg

Department of Math & Statistics Faculty Publications

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

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The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson Jan 2004

The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson

Department of Math & Statistics Faculty Publications

This note examines the subspaces of the space of Cauchy transforms of measures on the unit circle that are invariant under the backward shift operator f --> z-1 (f—f (0)). We examine this question when the space of Cauchy transforms is endowed with both the norm and weak* topologies.

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Common Cyclic Vectors For Normal Operators, William T. Ross, Warren R. Wogen Jan 2004

Common Cyclic Vectors For Normal Operators, William T. Ross, Warren R. Wogen

Department of Math & Statistics Faculty Publications

If μis a finite compactly supported measure on C, then the set Sμ of multiplication operators Mᵩ : L2 (μ) --> L2 (μ), Mᵩ f = ᵩ f, where ᵩ ϵ L ∞ (μ) is injective on a set of full μ measure, is the complete set of cyclic multiplication operators on L2 (μ) In this paper, we explore the question as to whether or not Sμ has a common cyclic vector

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Basic Neutrosophic Algebraic Structures And Their Application To Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2004

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 …

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Higher Dimensional Algebra Vi: Lie 2-Algebra, John C. Baez, Alissa S. Crans Jan 2004

Higher Dimensional Algebra Vi: Lie 2-Algebra, John C. Baez, Alissa S. Crans

Mathematics, Statistics and Data Science Faculty Works

The theory of Lie algebras can be categorified starting from a new notion of `2-vector space', which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector spaces as objects, `linear functors' as morphisms and `linear natural transformations' as 2-morphisms. We define a `semistrict Lie 2-algebra' to be a 2-vector space L equipped with a skew-symmetric bilinear functor [ . , . ] : L x L -> L satisfying the Jacobi identity up to a completely antisymmetric trilinear natural transformation called the `Jacobiator', which in turn must satisfy a certain law of its …

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Algebraic Semantics For Coalgebraic Logics, Clemens Kupke, Alexander Kurz, Dirk Pattinson Jan 2004

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 …

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Preface, Thomas Hildebrandt, Alexander Kurz Jan 2004

Preface, Thomas Hildebrandt, Alexander Kurz

Engineering Faculty Articles and Research

No abstract provided.

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Mathematical Card Tricks, Sarah Zimmermann May 2003

Mathematical Card Tricks, Sarah Zimmermann

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

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Evaluating The Performance Of Multiple Classifier Systems: A Matrix Algebra Representation Of Boolean Fusion Rules, Justin M. Hill Mar 2003

Evaluating The Performance Of Multiple Classifier Systems: A Matrix Algebra Representation Of Boolean Fusion Rules, Justin M. Hill

Theses and Dissertations

Given a finite collection of classifiers one might wish to combine, or fuse, the classifiers in hopes that the multiple classifier system (MCS) will perform better than the individuals. One method of fusing classifiers is to combine their final decision using Boolean rules (e.g., a logical OR, AND, or a majority vote of the classifiers in the system). An established method for evaluating a classifier is measuring some aspect of its Receiver Operating Characteristic (ROC) curve, which graphs the trade-off between the conditional probabilities of detection and false alarm. This work presents a unique method of estimating the performance of …

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The Structure Of Residuated Lattices, Kevin K. Blount, Constantine Tsinakis Jan 2003

The Structure Of Residuated Lattices, Kevin K. Blount, Constantine Tsinakis

Mathematics Faculty Publications

A residuated lattice is an ordered algebraic structure [formula] such that is a lattice, is a monoid, and \ and / are binary operations for which the equivalences [formula] hold for all a,b,c ∈ L. It is helpful to think of the last two operations as left and right division and thus the equivalences can be seen as "dividing" on the right by b and "dividing" on the left by a. The class of all residuated lattices is denoted by ℛℒ The study of such objects originated in the context of the theory of ring ideals in the 1930s. The …

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A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu Jan 2003

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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