Algebra Commons^™

On The Action Of Weight-Preserving Sets, Matthew Badger

Mathematical Sciences Technical Reports (MSTR)

We introduce weight-preserving sets of binary words. Any transformation that respects the row and column weights of a 0-1 matrix can be decomposed as a composition of two types of action on the matrix. We conjecture that weight-preserving sets perform only one type of action, permutations of rows and columns; i.e., weight-preserving sets are cwatsets.

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.

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.

Binomial Identities With Pascalgt, Tyler J. Evans

Tyler Evans

No abstract provided.

Balance In Generalized Tate Cohomology, Alina Iacob

Alina Iacob

No abstract provided.

Balance In Generalized Tate Cohomology, Alina Iacob

Alina Iacob

We consider two preenveloping classes of left R-modules ℐ, ℰ such that Inj ⊂ ℐ ⊂ ℰ, and a left R-module N. For any left R-module M and n ≥ 1 we define the relative extension modules (M, N) and prove the existence of an exact sequence connecting these modules and the modules (M, N) and (M, N). We show that there is a long exact sequence of (M, −) associated with a Hom(−, ℰ) exact sequence 0 → N′ → N → N′′ → 0 and a long exact sequence of (−, N) associated with a Hom(−, ℰ) exact …

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.

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.

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.

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.

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.

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.

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 …

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. …

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

Mathematics 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 …

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 …

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 …

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 …

An Explicit Fusion Algebra Isomorphism For Twisted Quantum Doubles Of Finite Groups, Christopher Goff

Christopher Goff