Mathematics Commons^™

On Zeros Of Certain Dirichlet Polynomials, Kajtaz H. Bllaca

Turkish Journal of Mathematics

In this article we establish the zero-free region of certain Dirichlet polynomials $L_{F, X}$ arising in approximate functional equation for functions in the Selberg class and we prove an asymptotic formula for the number of zeros of $L_{F, X}$.

On Certain Minimal Non-$\Mathfrak{Y}$-Groups For Some Classes $\Mathfrak{Y}$, Ahmet Arikan, Selami̇ Ercan

Turkish Journal of Mathematics

Let $\{\theta_n\}_{n=1}^\infty$ be a sequence of words. If there exists a positive integer $n$ such that $\theta_m(G)=1$ for every $m\geq n$, then we say that $G$ satisfies (*) and denote the class of all groups satisfying (*) by $\mathfrak{X}_{\{\theta_n\}_{n=1}^\infty}$. If for every proper subgroup $K$ of $G$, $K\in \mathfrak{X}_{\{\theta_n\}_{n=1}^\infty}$ but $G\notin\mathfrak{X}_{\{\theta_n\}_{n=1}^\infty}$, then we call $G$ a minimal non-$\mathfrak{X}_{\{\theta_n\}_{n=1}^\infty}$-group. Assume that $G$ is an infinite locally finite group with trivial center and $\theta_i(G)=G$ for all $i\geq 1$. In this case we mainly prove that there exists a positive integer $t$ such that for every proper normal subgroup $N$ of $G$, either …

Mathematics In Contemporary Society Chapter 4, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11 …

The Unimodality Of Pure O-Sequences Of Type Two In Four Variables, Bernadette Boyle

Mathematics Faculty Publications

Since the 1970's, great interest has been taken in the study of pure O-sequences, which, due to Macaulay's theory of inverse systems, have a bijective correspondence to the Hilbert functions of Artinian level monomial algebras. Much progress has been made in classifying these according to their shape. Macaulay's theorem immediately gives us that all Artinian algebras in two variables have unimodal Hilbert functions. Furthermore, it has been shown that all Artinian level monomial algebras of type two in three variables have unimodal Hilbert functions. This paper will classify all Artinian level monomial algebras of type two in four variables into …

Pure Injective And *-Pure Injective Lca Groups, Peter Loth

Mathematics Faculty Publications

No abstract provided.

The Logical System Of Frege’S Grundgesetze : A Rational Reconstruction, Méven Cadet, Marco Panza

MPP Published Research

This paper aims at clarifying the nature of Frege's system of logic, as presented in the first volume of the Grundgesetze . We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.

Pruebas Entimemáticas Y Pruebas Canónicas En La Geometría Plana De Euclides, Marco Panza, Abel Lassalle Casanave

MPP Published Research

Dado que la aplicación del Postulado I.2 no es uniforme en Elementos, ¿de qué manera debería ser aplicado en la geometría plana de Euclides? Además de legitimar la pregunta misma desde la perspectiva de una filosofía de la práctica matemática, nos proponemos esbozar una perspectiva general de análisis conceptual de textos matemáticos que involucra una noción ampliada de la teoría matemática como sistema de autorizaciones o potestades y una noción de prueba que depende del auditorio.

Since the application of Postulate I.2 in the Elements is not uniform, one could wonder in what way should it be applied in Euclid’s …

Comparative Analysis Of Various Continuous-Time Deterministic Models Of Tumor-Immune Interactions, Robert Paul Childress

Mathematics Theses - Archive

Cancer is historically a leading cause of death in the United States. In 2013,cancer was the second leading cause of death with 584,881 deaths \cite{CDC}.Having solely been responsible for 22.5\% of all deaths in 2013 alone \cite{CDC},obtaining as complete an understanding as possible of cancer is obviously necessitated.I investigate deterministic ordinary differential equation models of increasingcomplexity simulating avascular tumor growth and interactions with the innate immuneresponse. After first establishing a baseline of tumor growth limited only by theavailability of local nutrients, I compare the effects on said growth of the nativeimmune system response, chemotherapy, immunotherapy, and various combinations ofthe aforementioned …

Some Multivariate Process Capability Indices, Rachel Lee Goodwin

Mathematics Dissertations - Archive

Process capability indices (PCIs) play an important role in the field of Statistical Process Control. Prior to the last 25 years, PCIs had been formulated to assess the quality of a single product characteristic. Product quality, however, is typically dependent on several related variables. Therefore, there is a great need for multivariate process capability indices (MPCIs). The quality of a product is almost always determined from sample data. Thus, it is imperative that an MPCI has a corresponding confidence interval. In that way, conclusions may be drawn regarding the capability of the process that makes that product. Of the MPCIs …

Numerical Solutions Of American Options With Dividends Using Finite Difference Methods, Nsoki Mavinga, Chi Zhang , '15

Mathematics & Statistics Faculty Works

We study the Black-Scholes model for American options with dividends. We cast the problem as a free-boundary problem for heat equations and use transformations to rewrite the problem in linear complementarity form. We use explicit and implicit finite difference methods to obtain numerical solutions. We implement and test the methods on a particular example in MATLAB. The effects of dividend payments on option pricing are also considered.

Positivity Of Equivariant Gromov–Witten Invariants, D. Anderson, Linda Chen

Mathematics & Statistics Faculty Works

We show that the equivariant Gromov–Witten invariants of a projective homogeneous space G/P exhibit Graham-positivity: when expressed as polynomials in the positive roots, they have nonnegative coefficients.

Resonance Problems For Nonlinear Elliptic Equations With Nonlinear Boundary Conditions, Nsoki Mavinga, M. N. Nkashama

Mathematics & Statistics Faculty Works

We study the solvability of nonlinear second order elliptic partial differential equations with nonlinear boundary conditions where we impose asymptotic conditions on both nonlinearities in the differential equation and on the boundary in such a way that resonance occurs at a generalized eigenvalue; which is an eigenvalue of the linear problem in which the spectral parameter is both in the differential equation and on the boundary. The proofs are based on some variational techniques and topological degree arguments.

Prognostic Value Of Estimating Functional Capacity With The Use Of The Duke Activity Status Index In Stable Patients With Chronic Heart Failure, Justin L. Grodin, Muhammad Hammadah, Yiying Fan, Stanley L. Hazen, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

BACKGROUND: Over the years, several methods have been developed to reliably quantify functional capacity in patients with heart failure. Few studies have investigated the prognostic value of these assessment tools beyond cardiorenal prognostic biomarkers in stable patients with chronic heart failure. METHODS AND RESULTS: We administered the Duke Activity Status Index (DASI) questionnaire, a self-assessment tool comprising 12 questions for estimating functional capacity, to 1,700 stable nonacute coronary syndrome patients with history of heart failure who underwent elective diagnostic coronary angiography with 5-year follow-up of all-cause mortality. In a subset of patients (n = 800), B-type natriuretic peptide (BNP) was …

Rayleigh Approximation To Ground State Of The Bose And Coulomb Glasses, Shawn D. Ryan, V. Mityushev, V. M. Vinokur, L. Berlyand

Mathematics and Statistics Faculty Publications

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our …

Algebraic And Numerical Exploration Of Free Energies For Materials With Memory, John Murrough Golden, Giovambattista Amendola, Mauro Fabrizio

Articles

Abstract. We study the forms of a range of free energy functionals for materials with memory for two types of strain history, namely sinusoidal and ex- ponential behaviours. The work deals with discrete spectrum materials, which are those with relaxation functions given by sums of decaying exponentials.

Hamiltonian Approach To Internal Wave-Current Interactions In A Two-Media Fluid With A Rigid Lid, Alan Compelli, Rossen Ivanov

Articles

We examine a two-media 2-dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface with wind generated surface waves but considered bounded above by a lid by an assumption that surface waves have negligible amplitude. An internal wave driven by gravity which propagates in the positive x-direction acts as a free common interface between the media. The current is such that it is zero at the flatbed but a negative constant, due to an assumption that surface winds blow in the negative x-direction, at the lid. We are concerned …

On The Characterization Of Prime Sets Of Polynomials By Congruence Conditions, Arvind Suresh

CMC Senior Theses

This project is concerned with the set of primes modulo which some monic, irreducible polynomial over the integers has a root, called the Prime Set of the polynomial. We completely characterise these sets for degree 2 polynomials, and develop sufficient machinery from algebraic number theory to show that if the Galois group of a monic, irreducible polynomial over the integers is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer.

Calculus For Everyone, Sandra Kingan, Brooklyn College Library And Academic It

Open Educational Resources

Professor Kingan’s motivation for writing her free Calculus I textbook was to help address the departments high failure rates in Calculus. Along with another CUNY initiative to offer Calculus workshops in advance of taking the course, Kingan’s concise textbook in Calculus I offers students inside and outside of CUNY an opportunity to prepare for Calculus I at their own pace. She also believes that by providing free access to this material she could help to overcome some of the inequity students experience when Calculus is not offered in their high school. The textbook was written specifically for this pilot project. …

Bifurcation And Dynamics Of A Normal Form Map, Reza Khoshsiar Ghaziani

Turkish Journal of Mathematics

This paper investigates the dynamics and stability properties of a so-called planar truncated normal form map. This kind of map is widely used in the applied context, especially in normal form coefficients of n-dimensional maps. We determine analytically the border collision bifurcation curves that characterize the dynamic behaviors of the system. We first analyze stability of the fixed points and the existence of local bifurcations. Our analysis shows the presence of a rich variety of local bifurcations, namely stable fixed points, periodic cycles, quasiperiodic cycles that are constraints to stable attractors called invariant closed curves, and chaos, where dynamics of …

Quadratic Recursive Towers Of Function Fields Over $\Mathbb{F}_2$, Henning Stichtenoth, Seher Tutdere

Turkish Journal of Mathematics

Let $\FF=(F_n)_{n\geq 0}$ be a quadratic recursive tower of algebraic function fields over the finite field $\F_2$, i.e. $\FF$ is a recursive tower such that $[F_n:F_{n-1}]=2$ for all $n\geq 1$. For any integer $r\geq 1$, let $\beta_r(\FF):=\lim_{n\to \infty} B_r(F_n)/g(F_n)$, where $B_r(F_n)$ is the number of places of degree $r$ and $g(F_n)$ is the genus, respectively, of $F_n/\F_2$. In this paper we give a classification of all rational functions $f(X,Y)\in \F_2(X,Y)$ that may define a quadratic recursive tower $\FF$ over $\F_2$ with at least one positive invariant $\beta_r(\FF)$. Moreover, we estimate $\beta_1(\FF)$ for each such tower.