Mathematics Commons^™

Xenakis' Combination Of Music And Mathematics, Janelle Anderson

The Journal of Undergraduate Research

My interest in using mathematics in music composition stems from the works of the contemporary composer Iannis Xenakis. As a physics and music education major I am able to combine both fields of study for this topic. Although Xenakis wrote many orchestral compositions it is his vocal music that I have concentrated on as I too am a singer. Graphic representation and new music notation are among the methods used to analyze his music. I found that his first choral work was called “Nuits,” which I proceeded to analyze. I also found myself interested in the analysis of a more …

2011-2012 Unlv Mcnair Journal, Cyndy Anang, Sajar Camara, Pamela Cornejo, Carla Antonieta Farcello, Ilse Anahi Garcia, Natiera Magnuson, William L. Mccurdy, Lorena Munoz, Maxym V. Myroshnychenko, Ricardo Rios, Theodore Waldeck, Barbara Wallen, Ana Zuniga, Brenda M. Aguilar, Tiffany Alexandra Alvarez, Daniel N. Erosa, Paige C. Espinosa, Carla Antonieta Farcello, Julienne Jochel Paraiso, Nathaniel Derek Phillipps, Carmen Vallin, Jacent N. Wamala, Ernesto Zamora-Ramos

McNair Journal

Journal articles based on research conducted by undergraduate students in the McNair Scholars Program

Table of Contents

Biography of Dr. Ronald E. McNair

Statements:

Dr. Neal J. Smatresk, UNLV President

Dr. Juanita P. Fain, Vice President of Student Affairs

Dr. William W. Sullivan, Associate Vice President for Retention and Outreach

Mr. Keith Rogers, Deputy Executive Director of the Center for Academic Enrichment and Outreach

McNair Scholars Institute Staff

Mathematics In The Age Of Technology: There Is A Place For Technology In The Mathematics Classroom, Helen Crompton

Teaching & Learning Faculty Publications

In today’s world of ubiquitous computing there are a number of technologies available to K-12 educators for teaching and learning mathematics. However, Koehler and Mishra (2008) have described how teaching and learning with such technologies presents a “wicked problem,” as it can involve a number of variables, independent of each other and contextually bound, that need to be brought together. This article highlights the advantages technology offers for mathematics education and looks at some of the reasons behind the poor uptake, such as teacher beliefs and lack of training. A number of solutions are offered to address these issues, including …

Daemon Decay And Cosmic Inflation, Emil Prodanov

Articles

Quantum tunneling in Reissner--Nordstroem geometry is studied and the tunneling rate is determined. A possible scenario for cosmic inflation, followed by reheating phases and subsequent radiation-domination expansion, is proposed.

Computer Monitored Problem Solving Dialogues, Lisa Dion, Jeremy Jank, Nicole Rutt

Symposium on Research and Creative Expression (SORCE)

This project looks over the shoulder at students collaboratively engaged in a math problem-solving activity. One task we looked at was mechanically classifying the students current activity or knowledge state, of which we have identified 15 different categories. We have produced an automatic classifier that examines student sentences and is 55% accurate in identifying utterances as containing certain bits of knowledge or evidence of certain activities. The classifier was built from a corpus of student-written reports. Treating each sentence as a bag of words, we built vector space models of the word co-occurrence matrix using both non-negative matrix factorization (NMF) …

Non-Contiguous Pattern Avoidance In Binary Trees, Michael Dairyko, Samantha Tyner, Casey Wynn

Symposium on Research and Creative Expression (SORCE)

We consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by modifying a known algorithm that counts binary trees avoiding a single contiguous tree pattern. Next, we use this algorithm to prove several theorems about the generating function whose nth coefficient gives the number of n-leaf trees avoiding a pattern. In addition, we investigate and structurally explain the recurrences that arise from these generating functions. Finally, we examine the enumeration of binary trees avoiding multiple tree patterns.

Modeling Infectious Diseases : Two Strain Diseases In Metapopulations, Daniel Rossi, Sydney Philipps, Rachel Vonarb

Symposium on Research and Creative Expression (SORCE)

Infectious diseases often mutate and are carried between regions. We consider a mathematical model which begins to account for these factors. We assume two disjoint populations that only occasionally comingle, and two strains of a disease present in these populations. Of interest are the equations describing the dynamics of this system, the conditions under which epidemics will occur, and the long term behavior of the system under various initial conditions. We find that in many ways this system is similar to a simpler one-population model. However, we find evidence that there may be conditions under which both disease strains can …

Properties Of Rd-Projective And Rd-Injective Modules, Lixin Mao

Turkish Journal of Mathematics

In this paper, we first study RD-projective and RD-injective modules using, among other things, covers and envelopes. Some new characterizations for them are obtained. Then we introduce the RD-projective and RD-injective dimensions for modules and rings. The relations between the RD-homological dimensions and other homological dimensions are also investigated.

Krull Dimension Of Types In A Class Of First-Order Theories, Domenico Zambella

Turkish Journal of Mathematics

We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula---plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-companion is strongly minimal. We also prove that the length of any increasing sequence of prime types is bounded, so every formula has finite Krull dimension.

Some Properties Of Associate And Presimplifiable Rings, Manal Ghanem

Turkish Journal of Mathematics

In this paper we study some properties of associate and presimplifiable rings. We give a characterization of the associate (resp., domainlike) pullback P of R_1 \rightarrow{R_3} \leftarrow{R_2}, where R_1 and R_2 are two presimplifiable (resp., domainlike) rings. We prove that R is presimplifiable ring if and only if the factor ring R/{nil(R)} is presimplifiable and the ideal nil(R) is presimplifiable. Then we investigate the associate and presimplifiable property of the dual rings {R[x]/\langle{x^2}\rangle} and its modules through the base ring R and its modules.

Module Classes And The Lifting Property, Muhammet Tamer Koşan

Turkish Journal of Mathematics

Let R be a ring. A collection of R-modules containing the zero module and closed under isomorphisms will be denoted by X. An R-module M is said to be X-lifting if for every X-submodule N of M there exists A \leq N such that M=A \oplus B and N \cap B is small in B [11]. In the present paper, we consider the question: Can we characterize X-lifting modules via objects of the class X?

Universal Inequalities And Bounds For Weighted Eigenvalues Of The Schrödinger Operator On The Heisenberg Group, Hejun Sun

Turkish Journal of Mathematics

For a bounded domain \Omega in the Heisenberg group H^n, we investigate the Dirichlet weighted eigenvalue problem of the Schrödinger operator - \Delta_{H^n} +V, where \Delta_{H^n} is the Kohn Laplacian and V is a nonnegative potential. We establish a Yang-type inequality for eigenvalues of this problem. It contains the sharpest result for \Delta_{H^n} in [17] of Soufi, Harrel II and Ilias. Some estimates for upper bounds of higher order eigenvalues and the gaps of any two consecutive eigenvalues are also derived. Our results are related to some previous results for the Laplacian \Delta and the Schrödinger operator -\Delta+V on a …

Hypersurfaces With Constant Mean Curvature In A Real Space Form, Shichang Shu, Sanyang Liu

Turkish Journal of Mathematics

Let M^n be an n\(n \geq 3)-dimensional complete connected and oriented hypersurface in M^{n+1}(c)(c \geq 0) with constant mean curvature H and with two distinct principal curvatures, one of which is simple. We show that (1) if c=1 and the squared norm of the second fundamental form of M^n satisfies a rigidity condition (1.3), then M^n is isometric to the Riemannian product S^1(\sqrt{1-a^2}) \times S^{n-1}(a); (2) if c=0, H \neq 0 and the squared norm of the second fundamental form of M^n satisfies S \geq n^2H^2/(n-1), then M^n is isometric to the Riemannian product S^{n-1}(a)\times R or S^1(a) \times R^{n-1}

On Generalized Witt Algebras In One Variable, Ki Bong Nam, Jonathan Pakianathan

Turkish Journal of Mathematics

We study a class of infinite dimensional Lie algebras called generalized Witt algebras (in one variable). These include the classical Witt algebra and the centerless Virasoro algebra as important examples. We show that any such generalized Witt algebra is a semisimple, indecomposable Lie algebra which does not contain any abelian Lie subalgebras of dimension greater than one. We develop an invariant of these generalized Witt algebras called the spectrum, and use it to show that there exist infinite families of nonisomorphic, simple, generalized Witt algebras and infinite families of nonisomorphic, nonsimple, generalized Witt algebras. We develop a machinery that can …

On The Uniqueness Of Strongly Flat Covers Of Cyclic Acts, Majid Ershad, Roghaieh Khosravi

Turkish Journal of Mathematics

In [1], strongly flat covers of cyclic acts are discussed and it is asked if strongly flat covers are unique. From this point of view, in this paper we give numerous classes of monoids over which strongly flat covers of cyclic acts are unique.

Weingarten Quadric Surfaces In A Euclidean 3-Space, Min Hee Kim, Dae Won Yoon

Turkish Journal of Mathematics

In this paper, we study quadric surfaces in a Euclidean 3-space. Furthermore, we classify quadric surfaces in a Euclidean 3-space in terms of the Gaussian curvature and the mean curvature.

Covers And Envelopes With Respect To A Semidualizing Module, Xiaoguang Yan, Xiaosheng Zhu

Turkish Journal of Mathematics

Let R be a commutative ring and C be a semidualizing R-module. For a given class of R-modules Q, we define a class Q_C by M \in Q_C \Leftrightarrow Hom_R(C,M) \in Q. We prove that if Q \subseteq (R) is a Kaplansky class and closed under direct sums, then Q_C^{\bot} is special preenveloping. As corollaries, we can show that p_C^{n \bot} and f_C^{n \bot} are both special preenveloping. Finally, we show that I_C^n is covering, I_C^{n \bot} is enveloping and special preenveloping provided R is Noetherian.

Some Results On G-Frames In Hilbert Spaces, Abdolaziz Abdollahi, Elham Rahimi

Turkish Journal of Mathematics

In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H. We further give necessary and sufficient conditions on g-Bessel sequences {\Lambda_i \in L (H,H_i) : i \in J} and {\Gamma_i \in L(H,H_i): i \in J} and operators L_1, L_2 on H so that {\Lambda_iL_1+\Gamma_iL_2: …

Conjugate Convolution And Characterizations Of Inner Amenable Locally Compact Groups, Bahram Mohammadzadeh

Turkish Journal of Mathematics

For locally compact group G, we give some characterizations of inner amenability of G by conjugate convolution operations. Moreover, we study multiples of positive elements in group algebra L^1(G), whenever G is inner amenable.

An Exploration Of Modeling Techniques For The Study Of The Dynamics Of E-Mail Viruses, Karin Weule

Theses, Dissertations and Culminating Projects

We analyze real data sets from two e-mail viruses, the Magistr.b and the Sircam.a to explore how we can use mathematical models to predict the behavior described by the data. Analysis of the data is conducted primarily with computer programming in MatLab. We focus mainly on the use of two continuous models commonly used in the study of biological diseases, the SIS and the SIR models. A discrete modeling approach using agent-based simulations is also explored and revealed to be potentially useful in developing a compartmentalized model that incorporates both SIS and SIR model behavior. The theory behind the continuous …