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Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore 2017 Utah State University

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

All Graduate Plan B and other Reports

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log2(α)3 + 16.5log2(α)2 + 6log ...


Stable Cohomology Of Local Rings And Castelnuovo-Mumford Regularity Of Graded Modules, Luigi Ferraro 2017 University of Nebraska-Lincoln

Stable Cohomology Of Local Rings And Castelnuovo-Mumford Regularity Of Graded Modules, Luigi Ferraro

Dissertations, Theses, and Student Research Papers in Mathematics

This thesis consists of two parts:

1) A bimodule structure on the bounded cohomology of a local ring (Chapter 1),

2) Modules of infinite regularity over graded commutative rings (Chapter 2).

Chapter 1 deals with the structure of stable cohomology and bounded cohomology. Stable cohomology is a $\mathbb{Z}$-graded algebra generalizing Tate cohomology and first defined by Pierre Vogel. It is connected to absolute cohomology and bounded cohomology. We investigate the structure of the bounded cohomology as a graded bimodule. We use the information on the bimodule structure of bounded cohomology to study the stable cohomology algebra as a ...


Classification Results Of Hadamard Matrices, Gregory Allen Schmidt 2017 University of Tennessee, Knoxville

Classification Results Of Hadamard Matrices, Gregory Allen Schmidt

Masters Theses

In 1893 Hadamard proved that for any n x n matrix A over the complex numbers, with all of its entries of absolute value less than or equal to 1, it necessarily follows that

|det(A)| ≤ nn/2 [n raised to the power n divided by two],

with equality if and only if the rows of A are mutually orthogonal and the absolute value of each entry is equal to 1 (See [2], [3]). Such matrices are now appropriately identified as Hadamard matrices, which provides an active area of research in both theoretical and applied fields of the sciences ...


Π-Operators In Clifford Analysis And Its Applications, Wanqing Cheng 2017 University of Arkansas, Fayetteville

Π-Operators In Clifford Analysis And Its Applications, Wanqing Cheng

Theses and Dissertations

In this dissertation, we studies Π-operators in different spaces using Clifford algebras. This approach generalizes the Π-operator theory on the complex plane to higher dimensional spaces. It also allows us to investigate the existence of the solutions to Beltrami equations in different spaces.

Motivated by the form of the Π-operator on the complex plane, we first construct a Π-operator on a general Clifford-Hilbert module. It is shown that this operator is an L^2 isometry. Further, this can also be used for solving certain Beltrami equations when the Hilbert space is the L^2 space of a measure space. This ...


Optimal Dual Fusion Frames For Probabilistic Erasures, Patricia Mariela Morillas 2017 Universidad Nacional de San Luis and CONICET, Argentina

Optimal Dual Fusion Frames For Probabilistic Erasures, Patricia Mariela Morillas

Electronic Journal of Linear Algebra

For any fixed fusion frame, its optimal dual fusion frames for reconstruction is studied in case of erasures of subspaces. It is considered that a probability distribution of erasure of subspaces is given and that a blind reconstruction procedure is used, where the erased data are set to zero. It is proved that there are always optimal duals. Sufficient conditions for the canonical dual fusion frame being either the unique optimal dual, a non-unique optimal dual, or a non optimal dual, are obtained. The reconstruction error is analyzed, using the optimal duals in the probability model considered here and using ...


College Algebra, Trigonometry, And Precalculus (Clayton), Chaogui Zhang, Scott Bailey, Billie May, Jelinda Spotorno, Kara Mullen 2017 Clayton State University

College Algebra, Trigonometry, And Precalculus (Clayton), Chaogui Zhang, Scott Bailey, Billie May, Jelinda Spotorno, Kara Mullen

Mathematics Grants Collections

This Grants Collection for College Algebra, Trigonometry, and Precalculus was created under a Round Five ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

  • Linked Syllabus
  • Initial Proposal
  • Final Report


Foundations For College Algebra, Da'Mon Andrews, Antre' Drummer 2017 East Georgia State College

Foundations For College Algebra, Da'mon Andrews, Antre' Drummer

Mathematics Grants Collections

This Grants Collection for Biochemistry was created under a Round Seven ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

  • Linked Syllabus
  • Initial Proposal
  • Final Report


Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg 2017 University of St Thomas

Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg

Linear Algebra

No abstract provided.


How The Use Of Subjectivist Instructional Strategies In Teaching Multiple Sections Of An Eighth Grade Algebra Class In Guyana Relates To Algebra Achievement And Attitude Changes Toward Mathematics, Jennifer Hoyte 2017 Florida International University

How The Use Of Subjectivist Instructional Strategies In Teaching Multiple Sections Of An Eighth Grade Algebra Class In Guyana Relates To Algebra Achievement And Attitude Changes Toward Mathematics, Jennifer Hoyte

FIU Electronic Theses and Dissertations

In Guyana, South America, the Ministry of Education seeks to provide universal, inclusive education that prepares its citizens to take their productive places in society and to creatively solve complex, real-world problems. However, with frequent national assessments that are used to place students in high school, college or into jobs, teachers resort to using familiar strategies such as lecture, recitation and test drilling. Despite their efforts, over 56% of students are failing the Grade 6 assessments, 43% failing 10th grade Mathematics and over 60% failing college algebra courses. Such performance has been linked to students’ lower academic self-concept and their ...


Solutions Of The System Of Operator Equations $Bxa=B=Axb$ Via The *-Order, Mehdi Vosough, Mohammad Sal Moslehian 2017 Ferdowsi University of Mashhad

Solutions Of The System Of Operator Equations $Bxa=B=Axb$ Via The *-Order, Mehdi Vosough, Mohammad Sal Moslehian

Electronic Journal of Linear Algebra

In this paper, some necessary and sufficient conditions are established for the existence of solutions to the system of operator equations $BXA=B=AXB$ in the setting of bounded linear operators on a Hilbert space, where the unknown operator $X$ is called the inverse of $A$ along $B$. After that, under some mild conditions, it is proved that an operator $X$ is a solution of $BXA=B=AXB$ if and only if $B \stackrel{*}{ \leq} AXA$, where the $*$-order $C\stackrel{*}{ \leq} D$ means $CC^*=DC^*, C^*C=C^*D$. Moreover, the general solution of the equation above is obtained ...


Zero Forcing Propagation Time On Oriented Graphs, Adam Berliner, Chassidy Bozeman, Steve Butler, Minerva Catral, Leslie Hogben, Brenda Kroschel, Jephian C.H. Lin, Nathan Warnberg, Michael Young 2017 Saint Olaf College

Zero Forcing Propagation Time On Oriented Graphs, Adam Berliner, Chassidy Bozeman, Steve Butler, Minerva Catral, Leslie Hogben, Brenda Kroschel, Jephian C.H. Lin, Nathan Warnberg, Michael Young

Mathematics Publications

Zero forcing is an iterative coloring procedure on a graph that starts by initially coloring vertices white and blue and then repeatedly applies the following rule: if any blue vertex has a unique (out-)neighbor that is colored white, then that neighbor is forced to change color from white to blue. An initial set of blue vertices that can force the entire graph to blue is called a zero forcing set. In this paper we consider the minimum number of iterations needed for this color change rule to color all of the vertices blue, also known as the propagation time ...


Recursive Robust Pca Or Recursive Sparse Recovery In Large But Structured Noise, Chenlu Qiu, Namrata Vaswani, Brian Lois, Leslie Hogben 2017 Iowa State University

Recursive Robust Pca Or Recursive Sparse Recovery In Large But Structured Noise, Chenlu Qiu, Namrata Vaswani, Brian Lois, Leslie Hogben

Namrata Vaswani

This paper studies the recursive robust principal components analysis problem. If the outlier is the signal-of-interest, this problem can be interpreted as one of recursively recovering a time sequence of sparse vectors, St, in the presence of large but structured noise, Lt. The structure that we assume on Lt is that Lt is dense and lies in a low-dimensional subspace that is either fixed or changes slowly enough. A key application where this problem occurs is in video surveillance where the goal is to separate a slowly changing background (Lt) from moving foreground objects (St) on-the-fly. To solve the above ...


Recursive Robust Pca Or Recursive Sparse Recovery In Large But Structured Noise, Chenlu Qiu, Namrata Vaswani, Brian Lois, Leslie Hogben 2017 Iowa State University

Recursive Robust Pca Or Recursive Sparse Recovery In Large But Structured Noise, Chenlu Qiu, Namrata Vaswani, Brian Lois, Leslie Hogben

Namrata Vaswani

This paper studies the recursive robust principal components analysis problem. If the outlier is the signal-of-interest, this problem can be interpreted as one of recursively recovering a time sequence of sparse vectors, St, in the presence of large but structured noise, Lt. The structure that we assume on Lt is that Lt is dense and lies in a low-dimensional subspace that is either fixed or changes slowly enough. A key application where this problem occurs is in video surveillance where the goal is to separate a slowly changing background (Lt) from moving foreground objects (St) on-the-fly. To solve the above ...


Relationships Between The Completion Problems For Various Classes Of Matrices, Leslie Hogben 2017 Iowa State University

Relationships Between The Completion Problems For Various Classes Of Matrices, Leslie Hogben

Leslie Hogben

No abstract provided.


On Higman`S Conjecture, A. Vera-López, J. M. Arregi, M. A. García-Sánchez, L. Ormaetxea 2017 Universidad del Pais Vasco

On Higman`S Conjecture, A. Vera-López, J. M. Arregi, M. A. García-Sánchez, L. Ormaetxea

Electronic Journal of Linear Algebra

Let Gn be the subgroup of GLn(q) consisting of the upper unitriangular matrices of size nxn over Fq. In 1960, G. Higman conjectured that the number of conjugacy classes of Gn, denoted by r(Gn), was given by a polynomial in q with integer coefficients. This has been verified for nn, r(Gn) can be expressed in terms of r(Gi), with i


Discovery Learning Plus Direct Instruction Equals Success: Modifying American Math Education In The Algebra Classroom, Sean P. Ferrill Mr. 2017 Seattle Pacific University

Discovery Learning Plus Direct Instruction Equals Success: Modifying American Math Education In The Algebra Classroom, Sean P. Ferrill Mr.

Honors Projects

In light of both high American failure rates in algebra courses and the significant proportion of innumerate American students, this thesis examines a variety of effective educational methods in mathematics. Constructivism, discovery learning, traditional instruction, and the Japanese primary education system are all analyzed to incorporate effective education techniques. Based on the meta-analysis of each of these methods, a hybrid method has been constructed to adapt in the American Common Core algebra classroom.


Elimination For Systems Of Algebraic Differential Equations, Richard Gustavson 2017 The Graduate Center, City University of New York

Elimination For Systems Of Algebraic Differential Equations, Richard Gustavson

All Dissertations, Theses, and Capstone Projects

We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, if the given system of differential equations has a solution. We first look solely at the ``algebraic data" of ...


On Skew-Symmetric Matrices Related To The Vector Cross Product In R^7, P. D. Beites, A. P. Nicolás, José Vitória 2017 University of Beira Interior

On Skew-Symmetric Matrices Related To The Vector Cross Product In R^7, P. D. Beites, A. P. Nicolás, José Vitória

Electronic Journal of Linear Algebra

A study of real skew-symmetric matrices of orders $7$ and $8$, defined through the vector cross product in $\mathbb{R}^7$, is presented. More concretely, results on matrix properties, eigenvalues, (generalized) inverses and rotation matrices are established.


A Transformation That Preserves Principal Minors Of Skew-Symmetric Matrices, Abderrahim BOUSSAIRI, Brahim CHERGUI 2017 Faculté des Sciences Ain chock

A Transformation That Preserves Principal Minors Of Skew-Symmetric Matrices, Abderrahim Boussairi, Brahim Chergui

Electronic Journal of Linear Algebra

It is well known that two $n\times n$ symmetric matrices have equal corresponding principal minors of all orders if and only if they are diagonally similar. This result cannot be extended to arbitrary matrices. The aim of this work is to give a new transformation that preserves principal minors of skew-symmetric matrices.


The Recognition Problem For Table Algebras And Reality-Based Algebras, Allen Herman, Mikhail Muzychuk, Bangteng Xu 2017 University of Regina

The Recognition Problem For Table Algebras And Reality-Based Algebras, Allen Herman, Mikhail Muzychuk, Bangteng Xu

EKU Faculty and Staff Scholarship

Given a finite-dimensional noncommutative semisimple algebra A over C with involution, we show that A always has a basis B for which ( A , B ) is a reality-based algebra. For algebras that have a one-dimensional representation δ , we show that there always exists an RBA-basis for which δ is a positive degree map. We characterize all RBA-bases of the 5-dimensional noncommutative semisimple algebra for which the algebra has a positive degree map, and give examples of RBA-bases of C ⊕ M n ( C ) for which the RBA has a positive degree map, for all n ≥ 2


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