How To Create A Jordan Algebra,
2013
Utah State University
How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile
How to... in 10 minutes or less
We show how to create a Jordan algebra in Maple using the commands AlgebraLibraryData and AlgebraData.
How To Create The Quaternion & Octonion Algebras,
2013
Utah State University
How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile
How to... in 10 minutes or less
We show how to create the quaternion and octonion algebras with the DifferentialGeometry software. For each algebra, there is a split-form also available.
On Contemplation In Mathematics,
2013
University of Western Ontario
On Contemplation In Mathematics, Frank Lucas Wolcott
Journal of Humanistic Mathematics
In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.
The Complexity Of Linear Algebra,
2013
California State University, San Bernardino
The Complexity Of Linear Algebra, Leann Kay Christensen
Theses Digitization Project
This study examines the complexity of linear algebra. Complexity means how much work, or the number of calculations or time it takes to perform a task. As linear algebra is used more and more in different fields, it becomes useful to study ways of reducing the amount of work required to complete basic procedures.
A Study Of Finite Symmetrical Groups,
2013
California State University, San Bernardino
A Study Of Finite Symmetrical Groups, Patrick Kevin Martinez
Theses Digitization Project
This study discovered several important groups that involve the classical and sporadic groups. These groups appeared as finite homomorphic images of the progenitors 3*8 : PGL₂(7), 2*¹⁴ : L₃ (2), 5*³ : S₃ and 7*2 : m S₃.
Polynomial Knot And Link Invariants From The Virtual Biquandle,
2013
Loyola Marymount University
Polynomial Knot And Link Invariants From The Virtual Biquandle, Alissa S. Crans, Allison Henrich, Sam Nelson
Mathematics, Statistics and Data Science Faculty Works
The Alexander biquandle of a virtual knot or link is a module over a 2-variable Laurent polynomial ring which is an invariant of virtual knots and links. The elementary ideals of this module are then invariants of virtual isotopy which determine both the generalized Alexander polynomial (also known as the Sawollek polynomial) for virtual knots and the classical Alexander polynomial for classical knots. For a fixed monomial ordering <, the Gr\"obner bases for these ideals are computable, comparable invariants which fully determine the elementary ideals and which generalize and unify the classical and generalized Alexander polynomials. We provide examples to illustrate the usefulness of these invariants and propose questions for future work.
Oddification Of The Cohomology Of Type A Springer Varieties,
2013
University of Richmond
Oddification Of The Cohomology Of Type A Springer Varieties, Heather M. Russell, Aaron D. Lauda
Department of Math & Statistics Faculty Publications
We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are ‘odd’ analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identifiedwith the …
An Extremal Problem For Characteristic Functions,
2013
University of Richmond
An Extremal Problem For Characteristic Functions, William T. Ross, Isabelle Chalendar, Stephan Ramon Garcia, Dan Timotin
Department of Math & Statistics Faculty Publications
Suppose E is a subset of the unit circle T and H∞C L∞ is the Hardy subalgebra. We examine the problem of Finding the distance from the characteristic function of E to zn H∞. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings.
Model Spaces: A Survey,
2013
University of Richmond
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
An Explicit Bijection Between Semistandard Tableaux And Non-Elliptic Sl3 Webs,
2013
University of Richmond
An Explicit Bijection Between Semistandard Tableaux And Non-Elliptic Sl3 Webs, Heather M. Russell
Department of Math & Statistics Faculty Publications
The sl3 spider is a diagrammatic category used to study the representation theory of the quantum group Uq(sl3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm. Recently, Tymoczko gave a simple version of this bijection in the case that the tableaux are standard and used it to study rotation and joins of webs. We build on Tymoczko’s bijection to give a simple and explicit algorithm for constructing all …
Endomorphisms Of Abelian Groups With Small Algebraic Entropy,
2013
Department of Mathematics and Computer Science, University of Udine,Viadelle Scienze,206,Loc.Rizzi,33100 Udine, Italy
Endomorphisms Of Abelian Groups With Small Algebraic Entropy, D. Dikranjan, Ketao Gong, P. Zanardo
Articles
We study the endomorphisms ϕ of abelian groups G having a “small” algebraic entropy h (where “small” usually means ). Using essentially elementary tools from linear algebra, we show that this study can be carried out in the group , where an automorphism ϕ with must have all eigenvalues in the open circle of radius 2, centered at 0 and ϕ must leave invariant a lattice in , i.e., be essentially an automorphism of . In particular, all eigenvalues of an automorphism ϕ with must be roots of unity. This is a particular case of a more general fact known …
Epistemic Updates On Algebras,
2013
Chapman University
Epistemic Updates On Algebras, Alexander Kurz, Alessandra Palmigiano
Engineering Faculty Articles and Research
We develop the mathematical theory of epistemic updates with the tools of duality theory. We focus on the Logic of Epistemic Actions and Knowledge (EAK), introduced by Baltag-Moss-Solecki, without the common knowledge operator. We dually characterize the product update construction of EAK as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. This dual characterization naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras (HAOs). As an application of this dual characterization, we …
Nominal Regular Expressions For Languages Over Infinite Alphabets,
2013
Chapman University
Nominal Regular Expressions For Languages Over Infinite Alphabets, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto
Engineering Faculty Articles and Research
We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques – as those popular in process calculi – we extend classical regular expressions with names (to model computational resources) and suitable operators (for allocation, deallocation, scoping of, and freshness conditions on resources). We discuss classes of such nominal regular expressions, show how such expressions have natural interpretations in terms of languages over infinite alphabets, and give Kleene theorems to characterise their formal languages in terms of nominal automata.
A Generalized White Noise Space Approach To Stochastic Integration For A Class Of Gaussian Stationary Increment Processes,
2013
Chapman University
A Generalized White Noise Space Approach To Stochastic Integration For A Class Of Gaussian Stationary Increment Processes, Daniel Alpay, Alon Kipnis
Mathematics, Physics, and Computer Science Faculty Articles and Research
Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in this space. We then use this transform to define the stochastic integral and prove an associated Itô formula.
On Discrete Analytic Functions: Products, Rational Functions, And Reproducing Kernels,
2013
Chapman University
On Discrete Analytic Functions: Products, Rational Functions, And Reproducing Kernels, Daniel Alpay, Palle Jorgensen, Ron Seager, Dan Volok
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis.
Recent Progress On Truncated Toeplitz Operators,
2013
University of Richmond
Recent Progress On Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason’s seminal paper [88] from 2007.
Special Type Of Subset Topological Spaces,
2013
University of New Mexico
Special Type Of Subset Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book we construct special subset topological spaces using subsets from semigroups or groups or rings or semirings. Such study is carried out for the first time and it is both interesting and innovative. Suppose P is a semigroup and S is the collection of all subsets of P together with the empty set, then S can be given three types of topologies and all the three related topological spaces are distinct and results in more types of topological spaces. When the semigroup is finite, S gives more types of finite topological spaces. The same is true in case …
Subset Groupoids,
2013
University of New Mexico
Subset Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors introduce the new notion of constructing non associative algebraic structures using subsets of a groupoid. Thus subset groupoids are constructed using groupoids or loops. Even if we use subsets of loops still the algebraic structure we get with it is only a groupoid. However we can get a proper subset of it to be a subset loop which will be isomorphic with the loop which was used in the construction of the subset groupoid. To the best of the authors’ knowledge this is the first time non associative algebraic structures are constructed using subsets. We get …
Singular Value Inequalities: New Approaches To Conjectures,
2013
University of North Florida
Singular Value Inequalities: New Approaches To Conjectures, Peter Chilstrom
UNF Graduate Theses and Dissertations
Singular values have been found to be useful in the theory of unitarily invariant norms, as well as many modern computational algorithms. In examining singular value inequalities, it can be seen how these can be related to eigenvalues and how several algebraic inequalities can be preserved and written in an analogous singular value form. We examine the fundamental building blocks to the modern theory of singular value inequalities, such as positive matrices, matrix norms, block matrices, and singular value decomposition, then use these to examine new techniques being used to prove singular value inequalities, and also look at existing conjectures.
Residuated Frames With Applications To Decidability,
2013
University of Denver
Residuated Frames With Applications To Decidability, Nikolaos Galatos, Peter Jipsen
Mathematics, Physics, and Computer Science Faculty Articles and Research
Residuated frames provide relational semantics for substructural logics and are a natural generalization of Kripke frames in intuitionistic and modal logic, and of phase spaces in linear logic. We explore the connection between Gentzen systems and residuated frames and illustrate how frames provide a uniform treatment for semantic proofs of cut-elimination, the finite model property and the finite embeddability property, which imply the decidability of the equational/universal theories of the associated residuated lattice-ordered groupoids. In particular these techniques allow us to prove that the variety of involutive FL-algebras and several related varieties have the finite model property.
