Principal Angles And Approximation For Quaternionic Projections [Dataset],
2013
University of New Mexico
Principal Angles And Approximation For Quaternionic Projections [Dataset], Terry A. Loring
Math and Statistics Datasets
We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in the matrices over the real, complex or quaternionic field (or skew field). From this we derive an algorithm to turn almost commuting projections into commuting projections that minimizes the sum of the displacements of the two projections. We quickly prove what we need using the universal real C*-algebra generated by two projections.
Counting Threshold Graphs And Finding Inertia Sets,
2013
Brigham Young University - Provo
Counting Threshold Graphs And Finding Inertia Sets, Christopher Abraham Guzman
Theses and Dissertations
This thesis is separated into two parts: threshold graphs and inertia sets. First we present an algorithmic approach to finding the minimum rank of threshold graphs and then progress to counting the number of threshold graphs with a specific minimum rank. Second, we find an algorithmic and more automated way of determining the inertia set of graphs with seven or fewer vertices using theorems and lemmata found in previous papers. Inertia sets are a relaxation of the inverse eigenvalue problem. Instead of determining all the possible eigenvalues that can be obtained by matrices with a specific zero/nonzero pattern we restrict …
Common Fundamental Domains For Lattices Of The Same Volume,
2013
Bridgewater State University
Common Fundamental Domains For Lattices Of The Same Volume, Ashley Erwin
Honors Program Theses and Projects
No abstract provided.
Variational Methods And Critical Point Theory 2013,
2013
Florida Institute of Technology
Variational Methods And Critical Point Theory 2013, Victoria Otero-Espinar, Juan J. Nieto, Donal O'Regan, Kanishka Perera
Mathematics and System Engineering Faculty Publications
[No abstract provided]
Record Linkage,
2013
Brigham Young University - Provo
Record Linkage, Stasha Ann Bown Larsen
Theses and Dissertations
This document explains the use of different metrics involved with record linkage. There are two forms of record linkage: deterministic and probabilistic. We will focus on probabilistic record linkage used in merging and updating two databases. Record pairs will be compared using character-based and phonetic-based similarity metrics to determine at what level they match. Performance measures are then calculated and Receiver Operating Characteristic (ROC) curves are formed. Finally, an economic model is applied that returns the optimal tolerance level two databases should use to determine a record pair match in order to maximize profit.
Mathematical Model Of Dynamic Protein Interactions Regulating P53 Protein Stability For Tumor Suppression,
2013
Georgia Southern University
Mathematical Model Of Dynamic Protein Interactions Regulating P53 Protein Stability For Tumor Suppression, Hua Wang, Guang Peng
Mathematical Sciences: Faculty Publications
In the field of cancer biology, numerous genes or proteins form extremely complex regulatory network, which determines cancer cell fate and cancer cell survival. p53 is a major tumor suppressor that is lost in more than 50% of human cancers. It has been well known that a variety of proteins regulate its protein stability, which is essential for its tumor suppressive function. It remains elusive how we could understand and target p53 stabilization process through network analysis. In this paper we discuss the use of random walk and stationary distribution to measure the compound effect of a network of genes …
Using Intelligent Prefetching To Reduce The Energy Consumption Of A Large-Scale Storage System,
2013
Texas State University - San Marcos
Using Intelligent Prefetching To Reduce The Energy Consumption Of A Large-Scale Storage System, Brian Romoser, Ziliang Zong, Ribel Fares, Joal Wood, Rong Ge
Mathematics, Statistics and Computer Science Faculty Research and Publications
Many high performance large-scale storage systems will experience significant workload increases as their user base and content availability grow over time. The U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) center hosts one such system that has recently undergone a period of rapid growth as its user population grew nearly 400% in just about three years. When administrators of these massive storage systems face the challenge of meeting the demands of an ever increasing number of requests, the easiest solution is to integrate more advanced hardware to existing systems. However, additional investment in hardware may significantly increase the …
Differentiation Of Solutions Of Second-Order Bvps With Integral Boundary Conditions,
2013
Nova Southeastern University
Differentiation Of Solutions Of Second-Order Bvps With Integral Boundary Conditions, Alfredo Janson, Bibi Juman
Mathematics Colloquium Series
Janson’s and Juman’s research involves differentiating solutions of boundary value problems with integral conditions, as well as showing that the resulting functions solve an associated boundary value problem—called the variational equation—with new integral boundary values.
Minimum Rank Problems For Cographs,
2013
Brigham Young University - Provo
Minimum Rank Problems For Cographs, Nicole Andrea Malloy
Theses and Dissertations
Let G be a simple graph on n vertices, and let S(G) be the class of all real-valued symmetric nxn matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The smallest rank achieved by a matrix in S(G) is called the minimum rank of G, denoted mr(G). The maximum nullity achieved by a matrix in S(G) is denoted M(G). For each graph G, there is an associated minimum rank class, MR(G) consisting of all matrices A in S(G) with rank A = mr(G). Although no restrictions are applied to the diagonal entries of …
Peakon, Pseudo-Peakon, And Cuspon Solutions For Two Generalized Camassa- Holm Equations,
2013
Zhejiang Normal University
Peakon, Pseudo-Peakon, And Cuspon Solutions For Two Generalized Camassa- Holm Equations, Jibin Li, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we study peakon, cuspon, and pseudo-peakon solutions for two generalized Camassa-Holm equations. Based on the method of dynamical systems, the two generalized Camassa-Holm equations are shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, pseudo-peakons, and periodic cusp solutions. In particular, the pseudo-peakon solution is for the first time proposed in our paper. Moreover, when a traveling system has a singular straight line and a heteroclinic loop, under some parameter conditions, there must be peaked solitary wave solutions appearing.
Estimating Norms Of Commutators [Dataset],
2013
University of New Mexico
Estimating Norms Of Commutators [Dataset], Terry A. Loring, Freddy Vides
Math and Statistics Datasets
We find estimates on the norm of a commutator of the form [f(x),y] in terms of the norm of [x,y], assuming that x and y are bounded linear operators on Hilbert space, with x normal and with spectrum within the domain of f. In particular we discuss |[x^2,y]| and |[x^{1/2},y]| for 0leq x leq 1. For larger values of delta = |[x,y]| we can rigorous calculate the best possible upper bound |[f(x),y]| leq eta_f(delta) for many f. In other cases we have conducted numerical experiments that strongly suggest that we have in many cases found the correct formula for the …
Estimating Norms Of Commutators,
2013
University of New Mexico
Estimating Norms Of Commutators, Terry A. Loring, Freddy Vides
Branch Mathematics and Statistics Faculty and Staff Publications
We find estimates on the norm of a commutator of the form $[f(x),y]$ in terms of the norm of $[x,y]$, assuming that $x$ and $y$ are bounded linear operators on Hilbert space, with $x$ normal and with spectrum within the domain of $f$. In particular we discuss $\|[x^2,y]\|$ and $\|[x^{1/2},y]\|$ for $0\leq x \leq 1$. For larger values of $\delta = \|[x,y]\|$ we can rigorous calculate the best possible upper bound $\|[f(x),y]\| \leq \eta_f(\delta)$ for many $f$. In other cases we have conducted numerical experiments that strongly suggest that we have in many cases found the correct formula for the …
Why 20? Why 40? A Possible Explanation Of A Special Role Of 20 And 40 In Traditional Number Systems,
2013
The University of Texas at El Paso
Why 20? Why 40? A Possible Explanation Of A Special Role Of 20 And 40 In Traditional Number Systems, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Both historical and linguistic evidence shows that numbers 20 and 40 played a special role in many traditional numerical systems. The fact that, e.g., the same number 20 appears in unrelated cultures such as Romans and Mayans is an indication that this number must have a general explanation related to human experience. In this paper, we provide a possible explanation of 20 and 40 along these lines: namely, we show that these numbers can be identified as the smallest sample sizes for which we can extract statistically significant information.
Ua66 Ogden College Of Science & Engineering Newsletter,
2013
Western Kentucky University
Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean
Ogden College of Science & Engineering Publications
No abstract provided.
The Effects Of Standards-Based Grading On Student Performance In Algebra 2,
2013
Western Kentucky University
The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales
Dissertations
The use of standards-based grading in American public schools is increasing, offering students, parents, and teachers a new way of measuring and communicating about student achievement and performance. Parents indicate an appreciation for this method of grading, and students at the elementary grades (K-6) have improved standardized test scores in reading and math as a result of its implementation. This study seeks to determine whether standards-based grading has the same effect on students at the high school level (grades 9-12) by comparing end-of-course test scores and posttest scores of Algebra 2 students enrolled in a standards-based graded classroom with to …
Pomona College
Extended Book Review: Mathematics In Popular Culture: Essays On Appearances In Film, Fiction, Games, Television And Other Media, Edited By Jessica K. Sklar And Elizabeth S. Sklar; Loving+Hating Mathematics: Challenging The Myths Of Mathematical Life, By Reuben Hersh And Vera John-Steiner; Mathematicians: An Outer View Of The Inner World, By Mariana Cook, Gizem Karaali
Pomona Faculty Publications and Research
I was delighted to have the opportunity to review three books on a topic near and dear to my heart. In recent years it has become a passion of mine to think of and speak about the place of mathematics in the real world, in the world of those who are not doing mathematics for a living. I care about the applications and the implications of mathematics, but more than that, I care about the feelings and the impressions attached to it. Often math anxiety or skepticism comes up; the latter may be due to how frequently others (mis)use statistics, …
Deformations Associated With Rigid Algebras,
2013
Loyola University Chicago
Deformations Associated With Rigid Algebras, M Gerstenhaber, Anthony Giaquinto
Mathematics and Statistics: Faculty Publications and Other Works
The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional algebra may be absolutely rigid in the classical deformation theory for single algebras while depending essentially on some parameters. Two examples studied here, the function field of a sphere with four marked points and the first Weyl algebra, show, however, that the existence of these parameters may be made evident by the cohomology of a diagram (presheaf) of algebras constructed from the original. The Cohomology Comparison Theorem asserts, on the other …
Weak Covering Properties And Selection Principles,
2013
Boise State University
Weak Covering Properties And Selection Principles, L. Babinkostova, B. A. Pansera, Marion Scheepers
Mathematics Faculty Publications and Presentations
No convenient internal characterization of spaces that are productively Lindelöf is known. Perhaps the best general result known is Alsterʼs internal characterization, under the Continuum Hypothesis, of productively Lindelöf spaces which have a basis of cardinality at most ℵ1. It turns out that topological spaces having Alsterʼs property are also productively weakly Lindelöf. The weakly Lindelöf spaces form a much larger class of spaces than the Lindelöf spaces. In many instances spaces having Alsterʼs property satisfy a seemingly stronger version of Alsterʼs property and consequently are productively X, where X is a covering property stronger than the …
Finding The Best Function: A Way To Explain Calculus Of Variations To Engineering And Science Students,
2013
The University of Texas at El Paso
Finding The Best Function: A Way To Explain Calculus Of Variations To Engineering And Science Students, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical problems, we need to find the most appropriate function: e.g., we need to find a control strategy u(t) that leads to the best performance of a system, we need to find the shape of the car which leads to the smallest energy losses, etc. Optimization over an unknown function can be described by the known Euler-Lagrange equations. The traditional way of deriving Euler-Lagrange equations when explaining them to the engineering and science students is, however, somewhat over-complicated. We provide a new, simpler way to deriving these equations, a way in which we directly use the fact that …
Dialect Or A New Language: A Possible Explanation Of The 70% Mutual Intelligibility Threshold,
2013
The University of Texas at El Paso
Dialect Or A New Language: A Possible Explanation Of The 70% Mutual Intelligibility Threshold, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In most cases, linguists have a consensus on when people from different regions speak two different dialects of the same language (and can, thus, understand each other reasonably well) or two different languages (in this case, their mutual intelligibility is limited). In most cases, this intuitive consensus corresponds to a 70% mutual intelligibility threshold: if at least 70% of the words from one region are understandable to people from another region, then these are two dialects, otherwise these are two different languages. In this paper, we provide a possible explanation for this 70% threshold.
