Physical Sciences and Mathematics Commons^™

Study On Algebras With Retractions And Planes Over A Dvr., Prosenjit Das Dr.

Doctoral Theses

Aim:The main aim of this thesis is to study the following problems:1. For a Noetherian ring R, to find a set of minimal sufficient fibre conditions for an R-algebra with a retraction to R to be an A1-fibration over R.2. To investigate sufficient conditions for a factorial A1-form, with a retraction to the base ring, to be A1.3. To investigate whether planes of the form b(X, Y)Zn – a(X, Y) are co- ordinate planes in the polynomial ring in three variables X, Y and Z over a discrete valuation ring.The 1st problem will be discussed in Chapter 3 entitled Codimension- …

Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola

Dartmouth Scholarship

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We …

Invariant And Coinvariant Spaces For The Algebra Of Symmetric Polynomials In Non-Commuting Variables, Francois Bergeron, Aaron Lauve

Mathematics and Statistics: Faculty Publications and Other Works

We analyze the structure of the algebra K⟨x⟩Sn of symmetric polynomials in non-commuting variables in so far as it relates to K[x]Sn, its commutative counterpart. Using the "place-action" of the symmetric group, we are able to realize the latter as the invariant polynomials inside the former. We discover a tensor product decomposition of K⟨x⟩Sn analogous to the classical theorems of Chevalley, Shephard-Todd on finite reflection groups.

Résumé. Nous analysons la structure de l'algèbre K⟨x⟩Sn des polynômes symétriques en des variables non-commutatives pour obtenir des analogues des résultats classiques concernant la structure de l'anneau K[x]Sn des polynômes symétriques en des variables …

Characterizing Preservice Teachers’ Mathematical Understanding Of Algebraic Relationships, Leah A. Nillas

Leah A. Nillas

Minimal Circuits For Very Incompletely Specified Boolean Functions, Richard Strong Bowen

HMC Senior Theses

In this report, asymptotic upper and lower bounds are given for the minimum number of gates required to compute a function which is only partially specified and for which we allow a certain amount of error. The upper and lower bounds match. Hence, the behavior of these minimum circuit sizes is completely (asymptotically) determined.

Assessing The Impact Of A Computer-Based College Algebra Course, Ningjun Ye

Dissertations

USM piloted the Math Zone in Spring 2007, a computer-based program in teaching MAT 101and MAT 099 in order to improve student performance. This research determined the effect of the re-design of MAT 101 on student achievements in comparison to a traditional approach to the same course. Meanwhile, the study investigated possible effects of the Math Zone program on students’ attitude toward studying mathematics.

This study shows that there was no statistically significant difference on MAT101 final exam scores between the Math Zone students and the Classroom students in Fall 2007, Spring 2008 and Fall 2008. At the same time, …

The Co-Universal C*-Algebra Of A Row-Finite Graph, Aidan Sims

Faculty of Informatics - Papers (Archive)

Let $E$ be a row-finite directed graph. We prove that there exists a $C^*$-algebra $\Cr{E}$ with the following co-universal property: given any $C^*$-algebra $B$ generated by a Toeplitz-Cuntz-Krieger $E$-family in which all the vertex projections are nonzero, there is a canonical homomorphism from $B$ onto $\Cr{E}$. We also identify when a homomorphism from $B$ to $\Cr{E}$ obtained from the co-universal property is injective. When every loop in $E$ has an entrance, $\Cr{E}$ coincides with the graph $C^*$-algebra $C^*(E)$, but in general, $\Cr{E}$ is a quotient of $C^*(E)$. We investigate the properties of $\Cr{E}$ with emphasis on the utility of co-universality …

Phase Transition On The Toeplitz Algebra Of The Affine Semigroup Over The Natural Numbers, Marcelo Laca, Iain F. Raeburn

Faculty of Informatics - Papers (Archive)

We show that the group of orientation-preserving affine transformations of the rational numbers is quasi-lattice ordered by its subsemigroup N⋊N^×. The associated Toeplitz C^∗-algebra T(N⋊N^×) is universal for isometric representations which are covariant in the sense of Nica. We give a presentation of T(N⋊N^×) in terms of generators and relations, and use this to show that the C^∗-algebra QN recently introduced by Cuntz is the boundary quotient of in the sense of Crisp and Laca. The Toeplitz algebra T …

An Investigation Of Kurosh's Theorem, Keith Anthony Earl

Theses Digitization Project

The purpose of this project will be an exposition of the Kurosh Theorem and the necessary and suffcient condition that A must be algebraic and satisfy a P.I. to be locally finite.

Incidence Functions, Yiyu Liao

Open Access Theses & Dissertations

In the mid 1960's, the incidence algebra was introduced in the seminal paper of Gian-Carlo Rota. He addressed the importance of the Mobius function in combinatorics. In particular, the incidence algebra of a locally finite poset plays an essentially unifying role in the theory of the Mobius function. One of the significant generalizations is the incidence algebra of a Mobius category introduced by Pierre Leroux. With the help from Mobius category, it was exciting to be able to extend the combinatorial results more broadly than just on posets. Before attempting to study this generalization of the Mobius function, we have …

Fraction Competency And Algebra Success, Coretta Thomas

LSU Master's Theses

Abstract In this thesis, I investigated the importance of fraction competence to success in algebra. I studied 107 of the students whom I teach. These students were all enrolled in Algebra I. A fraction pretest and an algebra pretest were given at the beginning of the 2009-2010 school year. A comparison was done to study the connection between the fraction pretest score and the semester grade as well as the algebra pretest score and the semester grade. The strongest correlation was between the fraction pretest and the semester grade. This supported the theory that fraction competence is a strong predictor …

Qed Corrections Of Order Α(Zα)²EF To The Hyperfine Splitting Of P1/2 And P3/2 States In Hydrogenlike Ions, Ulrich D. Jentschura, Vladimir A. Yerokhin

Physics Faculty Research & Creative Works

The hyperfine structure (HFS) of a bound electron is modified by the self-interaction of the electron with its own radiation field. This effect is known as the self-energy correction. In this work, we discuss the evaluation of higher order self-energy corrections to the HFS of bound P states. These are expressed in a semianalytic expansion involving powers of Zα and ln(Zα), where Z is the nuclear charge number and α is the fine-structure constant. We find that the correction of relative order α (Zα)² involves only a single logarithm ln(Zα) for P_1/2 states [but no term of order …

Proposed Problems Of Mathematics (Vol. Ii), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The first book of “Problèmes avec et sans … problèmes!” was published in Morocco in 1983. I collected these problems that I published in various Romanian or foreign magazines (amongst which: “Gazeta Matematică”, magazine which formed me as problem solver, “American Mathematical Monthly”, “Crux Mathematicorum” (Canada), “Elemente der Mathematik” (Switzerland), “Gaceta Matematica” (Spain), “Nieuw voor Archief” (Holland), etc. while others are new proposed problems in this second volume.

These have been created in various periods: when I was working as mathematics professor in Romania (1984-1988), or co-operant professor in Morocco (1982-1984), or emigrant in the USA (1990-1997). I thank to …