Physical Sciences and Mathematics Commons^™

Some Properties Of Gr-Multiplication Ideals, Hani Khashan

Turkish Journal of Mathematics

In this paper, we study some of the properties of gr-multiplication ideals in a graded ring R. We first characterize finitely generated gr-multiplication ideals and then give a characterization of gr-multiplication ideals by using the gr-localization of R. Finally we determine the set of gr-P-primary ideals of R when P is a gr-multiplication gr-prime ideal of R.

Q-Modules, C. Jayaram, Ünsal Teki̇r

Turkish Journal of Mathematics

In this paper we characterize Q-modules and almost Q-modules. Next we estblish some equivalent conditions for an almost Q-module to be a Q-module. Using these results, some characterizations are given for Noetherian Q-modules.

Strong Differential Subordination, Georgia Irina Oros, Gheorghe Oros

Turkish Journal of Mathematics

The concept of differential subordination was introduced in [4] by S. S. Miller and P. T. Mocanu and the concept of strong differential subordination was introduced in [1] by J. A. Antonino and S. Romaguera. This last concept was applied in the special case of Briot-Bouquet strong differential subordination. In this paper we study the strong differential subordinations in the general case, following the general theory of differential subordinations presented in [4].

Oscillation Of Higher-Order Nonlinear Delay Differential Equations With Oscillatory Coefficients, Başak Karpuz, Özkan Öcalan, Mustafa Kemal Yildiz

Turkish Journal of Mathematics

A criterion is established on the bounded solutions of type higher-order nonlinear neutral differential equations of type oscillatory or tending to zero at infinity [a(t) [x(t)+r(t)x(\kappa(t))]^{(n-1]' +p(t)F(x(\tau(t)))+q(t)G(x(\sigma(t)))= \phi(t), where t\geq t_0, n\geq 2, a,p are positive, r,q,\phi are allowed to alternate in sign infinitely many times, F,G are continuous functions, and \kappa,\tau,\sigma are strictly increasing unbounded continuous delay functions.

On The Geometry Of Null Curves In The Minkowski 4-Space, Recep Aslaner, A. İhsan Boran

Turkish Journal of Mathematics

In this paper, we study the basic results on the general study of null curves in the Minkowski 4-space R_1^4. A transversal vector bundle of a null curve in R_1^4 is constructed using a frenet Frame consisting of two real null and two space-like vectors. The null curves are characterized by using the Frenet frame.

Integral And Homothetic Indecomposability With Applications To Irreducibility Of Polynomials, Fati̇h Koyuncu, Ferruh Özbudak

Turkish Journal of Mathematics

Being motivated by some methods for construction of homothetically indecomposable polytopes, we obtain new methods for construction of families of integrally indecomposable polytopes. As a result, we find new infinite families of absolutely irreducible multivariate polynomials over any field F. Moreover, we provide different proofs of some of the main results of Gao [2].

Partial Open Book Decompositions And The Contact Class In Sutured Floer Homology, Tolga Etgü, Burak Özbağci

Turkish Journal of Mathematics

We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As an application we show that every contact three manifold (closed or with convex boundary) can be obtained by gluing tight contact handlebodies whose EH-classes are nontrivial.

Uniqueness For Meromorphic Functions And Differential Polynomials, Chao Meng

Turkish Journal of Mathematics

In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials and prove the following result: Let f and g be two transcendental meromorphic functions, \alpha be a meromorphic function such that T(r,\alpha)=o(T(r,f)+T(r,g)) and \alpha \not\equiv 0,\infty. Let a be a nonzero constant. Suppose that m,n are positive integers such that n>m+10. If \Psi_f' and \Psi_g' share ``(0,2)", then (i) if m\geq 2, then f(z)\equiv g(z); (ii) if m=1, either f(z)\equiv g(z) or f and g satisfy the algebraic equation R(f,g)\equiv 0, where R(\varpi_1,\varpi_2)=(n+1)(\varpi_1^{n+2}-\varpi_2^{n+2})-(n+2)(\varpi_1^{n+1} -\varpi_2^{n+1}). The results in this paper improve the results of Xiong-Lin-Mori …

Oscillation Of Nonlinear Neutral Delay Differential Equations Of Second-Order With Positive And Negative Coefficients, Mustafa Kemal Yildiz, Başak Karpuz, Özkan Öcalan

Turkish Journal of Mathematics

Some oscillation criteria for the following second-order neutral differential equation [x(t)\pm r(t) f( x(t-\gamma))]''+p(t) g(x(t-\alpha)) -q(t) g(x(t-\beta )) = s(t) where t\geq t_0, \gamma,\alpha,\beta \in R^+ with \alpha \geq \beta, r \in C^2([t_0,\infty ), R^+) , p,q\in C([t_0,\infty ),R^+) and f,g\in C(R,R), s\in C([ t_0,\infty),R) have been obtained. Our results are not restricted with boundedness of solutions.

Solutions For 2n^{Th} Order Lidstone Bvp On Time Scales, Erbi̇l Çeti̇n, S. Gülşan Topal

Turkish Journal of Mathematics

In this paper, we prove the existence of solutions for nonlinear Lidstone boundary value problems by using the monotone method on time scale and also we show the existence of at least one positive solution if f is either superlinear or sublinear by the fixed point theorem in a Banach space.

A Perturbation Of M-Order Derivations On Banach Algebras, Yong-Soo Jung, Kyoo-Hong Park

Turkish Journal of Mathematics

Let \A be a unital Banach algebra and let m, 1 \leq m \leq 4, be an integer. If f: \A \to \A is an approximate m-order derivation in the sense of Hyers-Ulam-Rassias, then f: \A \to \A is an exact m-order derivation.

On Completeness Of Elementary Generalized Solutions Of A Class Of Operator-Differential Equations Of A Higher Order, Rovshan Z. Gumbataliev

Turkish Journal of Mathematics

In this paper we give definition of m-fold completeness and prove a theorem on completeness of elementary generalized solution of corresponding boundary value problems at which the equation describes the process of corrosive fracture of metals in aggressive media and the principal part of the equation has multiple characteristics.

Linear Operators That Preserve The Edgesum Of A Graph, Ian June L. Garces, Siegfred Alan C. Baluyot

Mathematics Faculty Publications

No abstract provided.

Gutt Products And Representations Of Lie Groups, Job A. Nable

Mathematics Faculty Publications

No abstract provided.

Elementary School Pre-Service Teachers’ Understandings Of Algebraic Generalizations, Jean E. Hallagan, Audrey C. Rule, Lynn F. Carlson

The Mathematics Enthusiast

It is critical for all students to learn algebra, including the ability to generalize, to function in our increasingly complex world. This pretest/intervention/posttest study of preservice elementary teachers (N = 63) in their math methods course assessed their knowledge of writing and applying algebraic generalizations using instructor-made rubrics along with analysis of work samples and reported insights. Initially, although most subjects could solve a specific case, they had considerable difficulty determining an algebraic rule. After a problemsolving- based teaching intervention, students improved in their ability to generalize, however, they encountered more difficulty with determining the algebraic generalization for items arranged …

Problem-Based Instructional Tasks, Larry Leutzinger

Faculty Publications

No abstract provided.

Strict-Dominance Solvability Of Games On Continuous Strategy Spaces, Andrew Campbell Elkington

Theses and Dissertations (Comprehensive)

The concept of strict dominance provides a technique that can be used normatively to predict the play of games based only on the assumption of individual rationality. Such predictions, unlike those based on Nash equilibria, do not depend on players’ beliefs about the behaviour of others. One strategy strictly dominates another if and only if the payoff from the first strategy is strictly greater than the payoff from the second, no matter how the opponent(s) plays. It is possible for iterated elimination of strictly dominated strategies to remove all but a single choice for each player, in which case we …

Models For On-Line Social Networks, Noor Hadi

Theses and Dissertations (Comprehensive)

On-line social networks such as Facebook or Myspace are of increasing interest to computer scientists, mathematicians, and social scientists alike. In such real-world networks, nodes represent people and edges represent friendships between them. Mathematical models have been proposed for a variety of complex real-world networks such as the web graph, but relatively few models exist for on-line social networks.

We present two new models for on-line social networks: a deterministic model we call Iterated Local Transitivity (ILT), and a random ILT model. We study various properties in the deterministic ILT model such as average degree, average distance, and diameter. We …

Simulation Studies On Estimation Of Variance Components For Multilevel Models, Sara Vakilian

Theses and Dissertations (Comprehensive)

With the presence of unequal sampling in a multilevel model, the weight inflated estimators for variance components can be biased even though the use of survey weights results in design consistent estimators of the parameters. In this thesis I will carry out a simulation study to examine the performance of current existing methods and I will examine the resampling method for correcting bias of estimators of variance components of a multilevel model with covariates. This study will be based on these three papers: “Weighting for Unequal Selection Probabilities in Multilevel Models” by D. Pfeffermann , C. J. Skinner, D.J. Holmes, …

Applications Of New Diffusion Models To Barrier Option Pricing And First Hitting Time In Finance, Keang Ly

Theses and Dissertations (Comprehensive)

The main focus of this thesis is in the application of a new family of analytical solvable diffusion models to arbitrage-free pricing exotic financial derivatives, such as barrier options. The family of diffusions is the so-called “Drifted Bessel family” having nonlinear (smile-like) local volatility with multiple adjustable parameters. In particular, the drifted Bessel-K diffusion is used to model asset (stock) price processes under a risk-neutral measure whereby discounted asset price are martingales.

Closed-form spectral expansions for barrier option values are derived within the Bessel-K family of models. This follow from the closed-form spectral expansions for the transition probability …

First-Passage Time Models With A Stochastic Time Change In Credit Risk, Hui Li

Theses and Dissertations (Comprehensive)

Many authors have used a time-changed Brownian motion as a model of log-stock returns. Using a Levy process as a stochastic time change, one obtains well known asset price models such as the variance gamma (VG) and normal inverse Gaussian (NIG) models. Following on the heels of these asset price models, it is natural to extend structural credit models by using a time-changed geometric Brownian motion and other jump-diffusion processes to model the value of a firm. To avoid the difficulties that arise in computing the associated first passage time distribution and in analogy to the time-changed Markov chain models, …

Mathematical Modeling Of Quantum Dots With Generalized Envelope Functions Approximations And Coupled Partial Differential Equations, Dmytro Sytnyk

Theses and Dissertations (Comprehensive)

No abstract provided.

Multiple Linear Regression Model Of Visceral Leishmaniasis In Bihar, India, Darren Sheets

Mathematics Theses

Visceral Leishmaniasis (VL) is one of the world's worst parasitic killers, second only to Malaria, claiming nearly 500,000 lives each year. The disease attacks the spleen, liver, and bone marrow, and if left untreated is nearly always fatal. Whilst the disease is found all around the world, it is primarily prevalent in developing countries, in particular India. The most affected state in India is Bihar, where the disease is endemic. While other research has been conducted with emphasis on the effect of climate variables on the disease incidence rate, this analysis focuses on socio-economic variables such as literacy rate, housing …

Complementary Responses To Mean And Variance Modulations In The Perfect Integrate-And-Fire Model, Joanna R. Wares, Todd W. Troyer

Department of Math & Statistics Faculty Publications

In the perfect integrate-and-fire model (PIF), the membrane voltage is proportional to the integral of the input current since the time of the previous spike. It has been shown that the firing rate within a noise free ensemble of PIF neurons responds instantaneously to dynamic changes in the input current, whereas in the presence of white noise, model neurons preferentially pass low frequency modulations of the mean current. Here, we prove that when the input variance is perturbed while holding the mean current constant, the PIF responds preferentially to high frequency modulations. Moreover, the linear filters for mean and variance …

Biology In Mathematics At The University Of Richmond, Lester Caudill

Department of Math & Statistics Faculty Publications

In an effort to meet the needs of science students for modeling skills, three new courses have been created at the University of Richmond: Scientific Calculus I and II, and Mathematical Models in Biology and Medicine. The courses are described, and lessons learned and future directions are discussed.

A Nonlinear Extremal Problem On The Hardy Space, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

We relate some classical extremal problems on the Hardy space to norms of truncated Toeplitz operators and complex symmetric operators

Teacher Knowledge And Statistics: What Types Of Knowledge Are Used In The Primary Classroom?, Tim Burgess

The Mathematics Enthusiast

School curricula are increasingly advocating for statistics to be taught through investigations. Although the importance of teacher knowledge is acknowledged, little is known about what types of teacher knowledge are needed for teaching statistics at the primary school level. In this paper, a framework is described that can account for teacher knowledge in relation to statistical thinking. This framework was applied in a study that was conducted in the classrooms of four second-year teachers, and was used to explore the teacher knowledge used in teaching statistics through investigations. As a consequence, descriptions of teacher knowledge are provided and give further …

Enhancing Statistics Instruction In Elementary Schools: Integrating Technology In Professional Development, Maria Meletiou-Mavrotheris, Efi Paparistodemou, Despina Stylianou

The Mathematics Enthusiast

The research discussed in this article comes from an ongoing multifaceted program for the teaching and learning of early statistical reasoning in Cyprus. The initial stage of the program was concerned with the design of a line of instructional materials for the development of statistical reasoning. Central to this design was the functional integration with existing core curricular ideas of the recently developed dynamic statistics software Tinkerplots@, which provides young students with the opportunity to model and investigate real world problems of statistics. Next, professional development seminars for the teaching of statistics with the use of Tinkerplots® were designed and …

Keeping Up-To-Date With Bayes (Abstract), Kristin Duncan

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Bayes’ theorem, a rule for updating probabilities as new information is obtained, may be over two centuries old but it has been the driving force behind many of the most significant recent advances in statistics and other sciences.

2009 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.