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Articles 1 - 30 of 33
Full-Text Articles in Algebra
A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge
A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating …
The Digraph Of The Square Mapping On Elliptic Curves, Katrina Glaeser
The Digraph Of The Square Mapping On Elliptic Curves, Katrina Glaeser
Mathematical Sciences Technical Reports (MSTR)
Consider a subgroup of an elliptic curve generated by a point P of order n. It is possible to match any point Q to an integer k (mod n) such that Q = kP using a brute force method. By observing patterns in the digraph of the squaring map on the integers modulo n it is possible to perform this matching. These techniques can be applied to solving the Elliptic Curve Discrete Log Problem given a complete graph of the square mapping k P -> k^2 P for the elliptic curve points.
Continuous Trace C*-Algebras, Gauge Groups And Rationalization, John R. Klein, Claude Schochet, Samuel B. Smith
Continuous Trace C*-Algebras, Gauge Groups And Rationalization, John R. Klein, Claude Schochet, Samuel B. Smith
Mathematics Faculty Research Publications
Let ζ be an n-dimensional complex matrix bundle over a compact metric space X and let Aζ denote the C*-algebra of sections of this bundle. We determine the rational homotopy type as an H-space of UAζ, the group of unitaries of Aζ. The answer turns out to be independent of the bundle ζ and depends only upon n and the rational cohomology of X. We prove analogous results for the gauge group and the projective gauge group of a principal bundle over a compact metric space X.
Application Of Dual-Tree Complex Wavelet Transforms To Burst Detection And Rf Fingerprint Classification, Randall W. Klein
Application Of Dual-Tree Complex Wavelet Transforms To Burst Detection And Rf Fingerprint Classification, Randall W. Klein
Theses and Dissertations
This work addresses various Open Systems Interconnection (OSI) Physical (PHY) layer mechanisms to extract and exploit RF waveform features (”fingerprints”) that are inherently unique to specific devices and that may be used to provide hardware specific identification (manufacturer, model, and/or serial number). This is addressed by applying a Dual-Tree Complex Wavelet Transform (DT-CWT) to improve burst detection and RF fingerprint classification. A ”Denoised VT” technique is introduced to improve performance at lower SNRs, with denoising implemented using a DT-CWT decomposition prior to Traditional VT processing. A newly developed Wavelet Domain (WD) fingerprinting technique is presented using statistical WD fingerprints with …
Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang
Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang
Department of Mathematics: Dissertations, Theses, and Student Research
Toric varieties are varieties equipped with a torus action and constructed from cones and fans. In the joint work with Suanne Au and Mark E. Walker, we prove that the equivariant K-theory of an affine toric variety constructed from a cone can be identified with a group ring determined by the cone. When a toric variety X(Δ) is smooth, we interpret equivariant K-groups as presheaves on the associated fan space Δ. Relating the sheaf cohomology groups to equivariant K-groups via a spectral sequence, we provide another proof of a theorem of Vezzosi and Vistoli: equivariant K …
Discrete Logarithm Over Composite Moduli, Marcus L. Mace
Discrete Logarithm Over Composite Moduli, Marcus L. Mace
Mathematical Sciences Technical Reports (MSTR)
In an age of digital information, security is of utmost importance. Many encryption schemes, such as the Diffie-Hellman Key Agreement and RSA Cryptosystem, use a function which maps x to y by a modular power map with generator g. The inverse of this function - trying to find x from y - is called the discrete logarithm problem. In most cases, n is a prime number. In some cases, however, n may be a composite number. In particular, we will look at when n = p^b for a prime p. We will show different techniques of obtaining graphs of this …
Structural Properties Of Power Digraphs Modulo N, Joseph Kramer-Miller
Structural Properties Of Power Digraphs Modulo N, Joseph Kramer-Miller
Mathematical Sciences Technical Reports (MSTR)
We define G(n, k) to be a directed graph whose set of vertices is {0, 1, ..., n−1} and whose set of edges is defined by a modular relation. We say that G(n, k) is symmetric of order m if we can partition G(n, k) into subgraphs, each containing m components, such that all the components in a subgraph are isomorphic. We develop necessary and sufficient conditions for G(n, k) to contain symmetry when n is odd and square-free. Additionally, we use group theory to describe the structural properties of the subgraph of G(n, k) containing only those vertices relatively …
Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au
Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au
Department of Mathematics: Dissertations, Theses, and Student Research
Mu-Wan Huang, Mark Walker and I established an explicit formula for the equivariant K-groups of affine toric varieties. We also recovered a result due to Vezzosi and Vistoli, which expresses the equivariant K-groups of a smooth toric variety in terms of the K-groups of its maximal open affine toric subvarieties. This dissertation investigates the situation when the toric variety X is neither affine nor smooth. In many cases, we compute the Čech cohomology groups of the presheaf KqT on X endowed with a topology. Using these calculations and Walker's Localization Theorem for equivariant K-theory, we give explicit formulas …
Solids Of Revolution About The Line Y=Mx, Harvey Marquis Iii
Solids Of Revolution About The Line Y=Mx, Harvey Marquis Iii
Undergraduate Research Conference
No abstract provided.
The Effects Of The Use Of Technology In Mathematics Instruction On Student Achievement, Ron Y. Myers
The Effects Of The Use Of Technology In Mathematics Instruction On Student Achievement, Ron Y. Myers
FIU Electronic Theses and Dissertations
The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics …
Fixing Numbers Of Graphs And Groups, Courtney Gibbons, Joshua D. Laison
Fixing Numbers Of Graphs And Groups, Courtney Gibbons, Joshua D. Laison
Articles
The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the trivial automorphism of G fixes every vertex in S. The fixing set of a group Γ is the set of all fixing numbers of finite graphs with automorphism group Γ. Several authors have studied the distinguishing number of a graph, the smallest number of labels needed to label G so that the automorphism group of the labeled graph is trivial. The fixing number can be thought of as a variation of the distinguishing number in which every label …
The Dixmier-Douady Invariant For Dummies, Claude Schochet
The Dixmier-Douady Invariant For Dummies, Claude Schochet
Mathematics Faculty Research Publications
The Dixmier-Douady invariant is the primary tool in the classification of continuous trace C*-algebras. These algebras have come to the fore in recent years because of their relationship to twisted K-theory and via twisted K-theory to branes, gerbes, and string theory.
This note sets forth the basic properties of the Dixmier-Douady invariant using only classical homotopy and bundle theory. Algebraic topology enters the scene at once since the algebras in question are algebras of sections of certain fibre bundles.
Banach Algebras And Rational Homotopy Theory, Gregory Lupton, N. Christopher Phillips, Claude Schochet, Samuel B. Smith
Banach Algebras And Rational Homotopy Theory, Gregory Lupton, N. Christopher Phillips, Claude Schochet, Samuel B. Smith
Mathematics Faculty Research Publications
Let A be a unital commutative Banach algebra with maximal ideal space Max(A). We determine the rational H-type of GLn(A), the group of invertible n x n matrices with coefficients in A, in terms of the rational cohomology of Max(A). We also address an old problem of J. L. Taylor. Let Lcn(A) denote the space of "last columns" of GLn(A). We construct a natural isomorphism
Ȟs(Max(A);ℚ) ≅ π2n-1-s(Lcn(A)) ⊗ ℚ …
Review: A Class Of Solutions To The Quantum Colored Yang-Baxter Equation, Gizem Karaali
Review: A Class Of Solutions To The Quantum Colored Yang-Baxter Equation, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Permutation Patterns, Reduced Decompositions With Few Repetitions And The Bruhat Order, Daniel Alan Daly
Permutation Patterns, Reduced Decompositions With Few Repetitions And The Bruhat Order, Daniel Alan Daly
Electronic Theses and Dissertations
This thesis is concerned with problems involving permutations. The main focus is on connections between permutation patterns and reduced decompositions with few repetitions. Connections between permutation patterns and reduced decompositions were first studied various mathematicians including Stanley, Billey and Tenner. In particular, they studied pattern avoidance conditions on reduced decompositions with no repeated elements. This thesis classifies the pattern avoidance and containment conditions on reduced decompositions with one and two elements repeated. This classification is then used to obtain new enumeration results for pattern classes related to the reduced decompositions and introduces the technique of counting pattern classes via reduced …
Search Bounds For Zeros Of Polynomials Over The Algebraic Closure Of Q, Lenny Fukshansky
Search Bounds For Zeros Of Polynomials Over The Algebraic Closure Of Q, Lenny Fukshansky
CMC Faculty Publications and Research
We discuss existence of explicit search bounds for zeros of polynomials with coefficients in a number field. Our main result is a theorem about the existence of polynomial zeros of small height over the field of algebraic numbers outside of unions of subspaces. All bounds on the height are explicit.
The Generalized Burnside And Representation Rings, Eric B. Kahn
The Generalized Burnside And Representation Rings, Eric B. Kahn
University of Kentucky Doctoral Dissertations
Making use of linear and homological algebra techniques we study the linearization map between the generalized Burnside and rational representation rings of a group G. For groups G and H, the generalized Burnside ring is the Grothendieck construction of the semiring of G × H-sets with a free H-action. The generalized representation ring is the Grothendieck construction of the semiring of rational G×H-modules that are free as rational H-modules. The canonical map between these two rings mapping the isomorphism class of a G-set X to the class of its permutation module …
Review: On Quantum Yang-Baxter Coherent Algebra Sheaves, Gizem Karaali
Review: On Quantum Yang-Baxter Coherent Algebra Sheaves, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Graded Structure And Hopf Structures In Parabosonic Algebra. An Alternative Approach To Bosonisation, Gizem Karaali
Review: Graded Structure And Hopf Structures In Parabosonic Algebra. An Alternative Approach To Bosonisation, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Dynamical Yang-Baxter Maps With An Invariance Condition, Gizem Karaali
Review: Dynamical Yang-Baxter Maps With An Invariance Condition, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Solutions For The Constant Quantum Yang-Baxter Equation From Lie (Super)Algebras, Gizem Karaali
Review: Solutions For The Constant Quantum Yang-Baxter Equation From Lie (Super)Algebras, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Set-Theoretic Solutions Of The Yang-Baxter Equation, Graphs And Computations, Gizem Karaali
Review: Set-Theoretic Solutions Of The Yang-Baxter Equation, Graphs And Computations, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Local-To-Global Spectral Sequences For The Cohomology Of Diagrams, David Blanc, Mark W. Johnson, James M. Turner
Local-To-Global Spectral Sequences For The Cohomology Of Diagrams, David Blanc, Mark W. Johnson, James M. Turner
University Faculty Publications and Creative Works
We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings. © 2008 Elsevier B.V. All rights reserved.
Superbimatrices And Their Generalizations, Florentin Smarandache, W.B Vasantha Kandasamy
Superbimatrices And Their Generalizations, Florentin Smarandache, W.B Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers. In this book the authors introduce the new notion of superbimatrices and generalize it to super trimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerized world. The main difference between simple bimatrices and super bimatrices is that in case of simple bimatrices we have only one type of product defined on them, whereas in case …
Rees Products Of Posets And Inequalities, Tricia Muldoon Brown
Rees Products Of Posets And Inequalities, Tricia Muldoon Brown
University of Kentucky Doctoral Dissertations
In this dissertation we will look at properties of two different posets from different perspectives. The first poset is the Rees product of the face lattice of the n-cube with the chain. Specifically we study the Möbius function of this poset. Our proof techniques include straightforward enumeration and a bijection between a set of labeled augmented skew diagrams and barred signed permutations which label the maximal chains of this poset. Because the Rees product of this poset is Cohen-Macaulay, we find a basis for the top homology group and a representation of the top homology group over the symmetric …
Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy
Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Through this book, for the first time we represent every finite group in the form of a graph. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group. This study is innovative because through this description one can immediately look at the graph and say the number of elements in the group G which are self-inversed. Also study of different properties like the subgroups of a group, normal subgroups of a group, p-sylow subgroups of a group and conjugate elements of a group …
Transformée En Échelle De Signaux Stationnaires, Daniel Alpay, Mamadou Mboup
Transformée En Échelle De Signaux Stationnaires, Daniel Alpay, Mamadou Mboup
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the scale transform of a discrete time signal we define a new family of linear systems. We focus on a particular case related to function theory in the bidisk.
Generalized Q-Functions And Dirichlet-To-Neumann Maps For Elliptic Differential Operators, Daniel Alpay, Jussi Behrndt
Generalized Q-Functions And Dirichlet-To-Neumann Maps For Elliptic Differential Operators, Daniel Alpay, Jussi Behrndt
Mathematics, Physics, and Computer Science Faculty Articles and Research
The classical concept of Q-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be interpreted as a generalized Q-function. For couplings of uniformly elliptic second order differential expression on bounded and unbounded domains explicit Krein type formulas for the difference of the resolvents and trace formulas in an H2-framework are obtained.
The Schur Transformation For Nevanlinna Functions: Operator Representations, Resolvent Matrices, And Orthogonal Polynomials, Daniel Alpay, A. Dijksma, H. Langer
The Schur Transformation For Nevanlinna Functions: Operator Representations, Resolvent Matrices, And Orthogonal Polynomials, Daniel Alpay, A. Dijksma, H. Langer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at ∞, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation p times we find a Nevanlinna function np which is a fractional linear transformation of the given function n. The main results concern the effect of this transformation to the realizations of n and np, by which we …
Krein Systems, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich
Krein Systems, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich
Mathematics, Physics, and Computer Science Faculty Articles and Research
In the present paper we extend results of M.G. Krein associated to the spectral problem for Krein systems to systems with matrix valued accelerants with a possible jump discontinuity at the origin. Explicit formulas for the accelerant are given in terms of the matrizant of the system in question. Recent developments in the theory of continuous analogs of the resultant operator play an essential role.