Mathematics Commons^™

Type I General Exponential Class Of Distributions, Gholamhossein G. Hamedani, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new family of continuous distributions and study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments and hazard function are also presented. We estimate the model parameters by the maximum likelihood method and assess its performance based on biases and mean squared errors in a simulation study framework.

Mathematically Predicting The Aleut Tribe Population Using Archaeological Data, Jack Conrad Kiefer Ii, Paden Allen Thompson

Research on Capitol Hill

Sanak Island, located off the southern Alaska Peninsula, was home to the native Aleut peoples for thousands of years. Their hunter-gatherer society depended heavily on the arctic and marine ecosystem for food resources.

In 2015, a team of archaeologists from Idaho State and Utah State universities went to the island and collected data about the Aleut population size and their diet.

This study constructed a dynamical model to mathematically predict the Aleut population over time in order to gain insights into how food resources affected the Aleut people’s ability to survive.

Connecting The Arcs Motivational Model To Game Design For Mathematics Learning, Mario J. Toussaint, Victoria Brown

Transformations

Students’ performance in mathematics at all levels of education have not markedly improved for the past few decades. Stakeholders at tertiary institutions have been attempting to remedy this situation by implementing various types of intervention programs designed to increase students’ success in mathematics courses. Technology has been the primary method adopted by many educators to foster student engagement in mathematics. This paper describes an intervention program that uses the ARCS model to develop a serious game intended to increase students’ motivation and engagement in a mathematics course.

Data Analysis Of The Effectiveness Of The L-Sections Of Ma 112, Mil'yonta Williams

Summer Community of Scholars Posters (RCEU and HCR Combined Programs)

No abstract provided.

On Oscillation Of Integro-Differential Equations, Said R. Grace, Ağacik Zafer

Turkish Journal of Mathematics

We study the oscillatory behavior of solutions for integro-differential equations of the form $$x'(t) = e(t) -\int_0^t (t-s)^{\alpha-1}k(t, s)f(s, x(s))\, {\rm ds},\quad t\geq 0,$$ where $0

On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems, Tüba Gülşen, Etibar Sadi Panakhov

Turkish Journal of Mathematics

In this study, we discuss the inverse spectral problem for the energy-dependent Schrödinger equation on a finite interval. We construct an isospectrality problem and obtain some relations between constants in boundary conditions of the problems that constitute isospectrality. Above all, we obtain degeneracy of $ K(x,t)-K_{0}{ (x,t)}$ and $L(x,t)-L_{0} (x,t)$ by using a different approach. Some of the main results of our study coincide with results reported by Jodeit and Levitan. However, the method to obtain degeneracy is completely different. Furthermore, we consider all above results for the nonisospectral case.

Reducing Subspaces Of Toeplitz Operators On Dirichlet Type Spaces Of The Bidisk, Hongzhao Lin

Turkish Journal of Mathematics

The reducing subspaces of Toeplitz operators $T_{z_1^N}$(or $T_{z_2^N}$), $T_{z_1^Nz_2^N}$, and $T_{z_1^Nz_2^M}$ on Dirichlet type spaces of the bidisk ${\mathcal{D}}_\alpha({{{\mathbb{D}}}^{2}})$ are described, which extends the results for the corresponding operators on the Bergman space of the bidisk.

Two-Dimensional Generalized Discrete Fourier Transform And Related Quasi-Cyclic Reed‒Solomon Codes, Majid Mazrooei, Lale Rahimi, Najme Sahami

Turkish Journal of Mathematics

Using the concept of the partial Hasse derivative, we introduce a generalization of the classical 2-dimensional discrete Fourier transform, which will be called 2D-GDFT. Begining with the basic properties of 2D-GDFT, we proceed to study its computational aspects as well as the inverse transform, which necessitate the development of a faster way to calculate the 2D-GDFT. As an application, we will employ 2D-GDFT to construct a new family of quasi-cyclic linear codes that can be assumed to be a generalization of Reed‒Solomon codes.

Field Of Values Of Perturbed Matrices And Quantum States, Madjid Khakshour, Gholamreza Aghamollaei, Alemeh Sheikhhosseini

Turkish Journal of Mathematics

In this paper, the notion of the pseudofield of values of matrices is introduced and studied. The relationship between quantum states and the field of values of matrices is mentioned. The notion of the pseudopolynomial numerical hull, as a generalization of the pseudofield of values, of matrices is introduced and some properties of this notion are investigated.

Remarks On The Zero Toeplitz Product Problem In The Bergman And Hardy Spaces, Mübari̇z Tapdigoğlu Garayev, Mehmet Gürdal

Turkish Journal of Mathematics

In this article, we are interested in the zero Toeplitz product problem: for two symbols $f,g\in L^{\infty}\left( \mathbb{D},dA\right) ,$\ if the product $T_{f}T_{g}$\ is identically zero on $L_{a}^{2}\left( \mathbb{D}\right), $\ then can we claim $T_{f}$\ or $T_{g}$\ is identically zero? We give a particular solution of this problem. A new proof of one particular case of the zero Toeplitz product problem in the Hardy space $H^{2}\left( \mathbb{D}% \right) $ is also given.

The Localization Theorem For Finite-Dimensional Compact Group Actions, Ali̇ Arslan Özkurt, Mehmet Onat

Turkish Journal of Mathematics

The localization theorem is known for compact $G$-spaces, where $G$ is a compact Lie group. In this study, we show that the localization theorem remains true for finite-dimensional compact group actions, and Borel's fixed point theorem holds not only for torus actions but for arbitrary finite-dimensional compact connected abelian group actions.

Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai

Turkish Journal of Mathematics

It is well known that the transformation semigroup on a nonempty set $X$, which is denoted by $T(X)$, is regular, but its subsemigroups do not need to be. Consider a finite ordered set $X=(X;\leq)$ whose order forms a path with alternating orientation. For a nonempty subset $Y$ of $X$, two subsemigroups of $T(X)$ are studied. Namely, the semigroup $OT(X,Y)=\{\alpha\in T(X)\mid \alpha~\text{is order-preserving and }X\alpha\subseteq Y\}$ and the semigroup $OS(X,Y)=\{\alpha\in T(X)\mid\alpha$ is order-preserving and $Y\alpha \subseteq Y\}$. In this paper, we characterize ordered sets having a coregular semigroup $OT(X,Y)$ and a coregular semigroup $OS(X,Y)$, respectively. Some characterizations of regular semigroups $OT(X,Y)$ …

The Order Supergraph Of The Power Graph Of A Finite Group, Asma Hamzeh, Ali Reza Ashrafi

Turkish Journal of Mathematics

The power graph $\mathcal{P}(G)$ is a graph with group elements as a vertex set and two elements are adjacent if one is a power of the other. The order supergraph $\mathcal{S}(G)$ of the power graph $\mathcal{P}(G)$ is a graph with vertex set $G$ in which two elements $x, y \in G$ are joined if $o(x) o(y)$ or $o(y) o(x)$. The purpose of this paper is to study certain properties of this new graph together with the relationship between $\mathcal{P}(G)$ and $\mathcal{S}(G)$.

Combinatorial Enumeration Of Cyclic Covers Of $\Mathbb{P}^{1}$, Alberto Besana, Cristina Martinez Ramirez

Turkish Journal of Mathematics

We study plane algebraic curves defined over a field $k$ of arbitrary characteristic that are ramified coverings of the projective line $\mathbb{P}^{1}(k)$ branched over a given configuration of distinct points by their ramification type specified by a partition of $d$ the degree of the covering. We enumerate them by using the combinatorics of partitions and its connection to the representation theory of the symmetric group.

Compactness And Duality On Poletsky?Stessin Hardy Spaces Of Complex Ellipsoids, Si̇bel Şahi̇n

Turkish Journal of Mathematics

In the first part of this study, we characterize the compact subspaces of $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ and their relation to the vanishing Carleson measures. In the second part, we discuss the dual complement of the complex ellipsoid and give a duality result for $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ spaces in the sense of Grothendieck?K\"{o}the?da Silva.

Solutions Of The Björling Problem For Timelike Surfaces In The Lorentz-Minkowski Space, Seher Kaya, Rafael Lopez

Turkish Journal of Mathematics

We give a number of new examples of timelike minimal surfaces in the Lorentz-Minkowski space. Our method consists of solving the Björling problem by prescribing a circle or a helix as the core curve $\alpha$ and rotating with constant angular speed the unit normal vector field in the normal plane to $\alpha$. As particular cases, we exhibit new examples of timelike minimal surfaces invariant by a uniparametric group of helicoidal motions.

Normality And Quotient In Crossed Modules Over Groupoids And Double Groupoids, Osman Mucuk, Serap Demi̇r

Turkish Journal of Mathematics

We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures, and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give some examples of these objects.

Coefficients Inequalities For Classes Of Meromorphic Functions, Jacek Dziok, Maslina Darus, Janusz Sokol

Turkish Journal of Mathematics

A typical problem in the theory of analytic functions is to study a functional made up of combinations of coefficients of the original function. Usually, there is a parameter over which the extremal value of the functional is needed. One of the important functionals of this type is the Fekete-Szegö functional defined on the class of analytic functions. In this paper we transfer the Fekete-Szegö problem to some classes of meromorphic functions.

Derivations, Generalized Derivations, And *-Derivations Of Period $2$ In Rings, Hesham Nabiel

Turkish Journal of Mathematics

The aim of this article is to discuss the existence of certain kinds of derivations and *-derivations that are of period 2. Moreover, we obtain the form of generalized reverse derivations and generalized left derivations of period $2$.

Relative Stable (Co)Homology, Chaoling Huang, Li Yuan

Turkish Journal of Mathematics

For a fixed precovering class $\mathcal{X}$ and a fixed preenveloping class $\mathcal{Y}$, we first introduce the notions of relative stable cohomology $\widetilde{Ext}_{\mathcal{X}}(-,\ -)$ and relative stable homology $\widetilde{Tor}_{\mathcal{X}\mathcal{Y}}(-,\ -)$. Then we consider their properties and, more importantly, we study the stable (co)homology under the case of $\mathcal{P}(R)$, $\mathcal{F}(R)$, and $\mathcal{I}(R)$ and the case of $\mathcal{P}_C(R)$, $\mathcal{F}_C(R)$, and $\mathcal{I}_C(R)$. Finally, we generalize relative stable (co)homology from the case of $R$-modules to the case of $R$-complexes.