Mathematics Commons^™

On Burr Iii Marshal Olkin Family: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Gauss M. Cordeiro, Haitham M. Yousof, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the …

On The Modified Burr Xii-Power Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see …

The Nested Joint Clustering Via Dirichlet Process Mixture Model, Shengtong Han, Hongmei Zhang, Wenhui Sheng, Hasan Arshad

Mathematical and Statistical Science Faculty Research and Publications

This article focuses on the clustering problem based on Dirichlet process (DP) mixtures. To model both time invariant and temporal patterns, different from other existing clustering methods, the proposed semi-parametric model is flexible in that both the common and unique patterns are taken into account simultaneously. Furthermore, by jointly clustering subjects and the associated variables, the intrinsic complex shared patterns among subjects and among variables are expected to be captured. The number of clusters and cluster assignments are directly inferred with the use of DP. Simulation studies illustrate the effectiveness of the proposed method. An application to wheal size data …

Group Presentations As A Site For Collective Modeling Activity, Corey Brady, Hyunyi Jung

Mathematical and Statistical Science Faculty Research and Publications

We approach student presentations of solutions to modeling tasks as occasions for whole-class reflection on the rich conceptual work that small-group teams have done in parallel. Analyzing and interpreting these interactions can offer insights into how a classroom group negotiates a shared sense of what they have learned and what they collectively view as “newsworthy” across groups from their recent (and ongoing) model-building. We describe analytical tools to interpret a classroom’s work during presentations, and we illustrate their use in a single case. This work offers a foothold for design-based research to harness presentations to improve learning, drive instructional decisions, …

Mathematical Modeling And Classroom Discourse: A Case For Modeling-Specific Discussion Strategies, Ashley Dorlack, Hyunyi Jung, Sarah Brand, Samuel Franklin Gailliot

Mathematical and Statistical Science Faculty Research and Publications

No abstract provided.

Solving The Semidefinite Programming Relaxation Of Max-Cut Using An Augmented Lagrangian Method, Ahmed Sabah Al-Jilawi

Graduate Research Theses & Dissertations

Semidefinite programming (SDP) problems have been investigated and solved in this work. A novel approach has been introduced and validated to solve SDP relaxations of binary quadratic optimization problems. In the BiqCrunch solver, a penalty method is used to compute the solution of a semidefinite relaxation of a binary quadratic problem. This problem generates a bound on the optimal value of the original problem. A branch-and- bound approach then uses this semidefinite bound to solve the binary quadratic problems. In this study, a new approach has been developed to replace the penalty method with the augmented Lagrangian method. Also, according …

Barrier Graphs And Extremal Questions On Line, Ray, Segment, And Hyperplane Sensor Networks, Kirk Anthony Boyer

Electronic Theses and Dissertations

A sensor network is typically modeled as a collection of spatially distributed objects with the same shape, generally for the purpose of surveilling or protecting areas and locations. In this dissertation we address several questions relating to sensors with linear shapes: line, line segment, and rays in the plane, and hyperplanes in higher dimensions.

First we explore ray sensor networks in the plane, whose resilience is the number of sensors that must be crossed by an agent traveling between two known locations. The coverage of such a network is described by a particular tripartite graph, the barrier graph of the …

Companion Sequences Associated To The$R$-Fibonacci Sequence: Algebraic And Combinatorial Properties, Sadjia Abbad, Hacene Belbachir, Benali Benzaghou

Turkish Journal of Mathematics

It is well known that the companion sequence of the Fibonacci sequence is Lucas's sequence. For the generalized Fibonacci sequences, the companion sequence is not unique. Several authors proposed different definitions, and they are in a certain sense all good. Our purpose is to introduce a family of companion sequences for some generalized Fibonacci sequence: the $r$-Fibonacci sequence. We evaluate the generating functions and give some applications, and we exhibit convolution relations that generalize some known identities such as Cassini's. Afterwards, we calculate the sums of their terms using matrix methods. Next, we propose a $q$-analogue and extend the definition …

Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n

Turkish Journal of Mathematics

In this study, we solve the Diophantine equation in the title in nonnegative integers $m,n,$ and $a$. The solutions are given by $F_{1}-F_{0}=F_{2}-F_{0}=F_{3}-F_{2}=F_{3}-F_{1}=F_{4}-F_{3}=5^{0}$ and $F_{5}-F_{0}=F_{6}-F_{4}=F_{7}-F_{6}=5.$ Then we give a conjecture that says that if $a\geq 2$ and $p>7$ is prime, then the equation $F_{n}-F_{m}=p^{a}$ has no solutions in nonnegative integers $m,n.$

On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan

Turkish Journal of Mathematics

The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.

A New Solution Of Pair Matrix Equations With Arbitrary Triangular Fuzzy Numbers, Wan Suhana Wan Daud, Nazihah Ahmad, Ghassan Malkawi

Turkish Journal of Mathematics

Pair matrix equations have numerous applications in control system engineering, such as for stability analysis of linear control systems and also for reduction of nonlinear control system models. There are some situations in which the classical pair matrix equations are not well equipped to deal with the uncertainty problem during the process of stability analysis and reduction in control system engineering. Thus, this study presents a new algorithm for solving fully fuzzy pair matrix equations where the parameters of the equations are arbitrary triangular fuzzy numbers. The fuzzy Kronecker product and fuzzy $Vec$-operator are employed to transform the fully fuzzy …

Multiplication Alteration By Two-Cocycles For Bialgebras With Weak Antipode, Jose Nicanor Alonso, José Manuel Fernandez Vilaboa, Ramon Gonzalez Rodriguez

Turkish Journal of Mathematics

In this paper we introduce the theory of multiplication alteration by two-cocycles for bialgebras with weak antipode. Moreover, by the connection between two-cocycles and invertible skew pairings, we show that a special case of the double cross product of these bialgebras can be obtained as a deformation of a bialgebra with weak antipode.

A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson

Turkish Journal of Mathematics

In this article, we give sufficient conditions for the existence of solutions for a new coupled system of second-order implicit differential equations with Hadamard and Erdelyi-Kober fractional integral boundary conditions and nonlocal conditions at the boundaries in Banach space. The main result is based on a Mönch fixed point theorem combined with the measure of noncompactness of Kuratowski; an example is given to illustrate our approach.

On An Elliptic Boundary Value Problem With Critical Exponent, Khadijah Sharaf

Turkish Journal of Mathematics

We study a nonlinear critical second-order PDE with zero Dirichlet boundary condition. We prove existence and compactness results for the equation by using Bahri's method of critical points at infinity.

On The Cohen-Macaulayness Of Tangent Cones Of Monomial Curves In $\Mathbb{A}^{4}(K)$, Sefa Feza Arslan, Anargyros Katsampekis, Meli̇ssa Nalbandi̇yan

Turkish Journal of Mathematics

In this paper we give necessary and sufficient conditions for the Cohen-Macaulayness of the tangent cone of a monomial curve in 4-dimensional affine space. We particularly study the case where $C$ is a Gorenstein noncomplete intersection monomial curve and we generalize some results in the literature. Moreover, by using these results, we construct families supporting Rossi's conjecture, which is still open for monomial curves in 4-dimensional affine space.

Generalized Helices In Three-Dimensional Lie Groups, Alexander Yampolsky, Anastasiya Opariy

Turkish Journal of Mathematics

We introduce three types of helices in three-dimensional Lie groups with left-invariant metric and give their geometrical description similar to that of Lancret. We generalize the results known for the case of three-dimensional Lie groups with bi-invariant metric.

On Expansions Of Prime And 2-Absorbing Hyperideals In Multiplicative Hyperrings, Gülşen Ulucak

Turkish Journal of Mathematics

In this paper, we study $ \delta $-primary and 2-absorbing $ \delta $-primary hyperideals which are the extended classes of prime and 2-absorbing hyperideals, respectively. Assume that $R$ is a commutative multiplicative hyperring with nonzero identity. We call $ I \in \mathcal{I*(R)}$ a $\delta $-primary hyperideal if $a,b\in R$ and $a\circ b\subseteq I$ imply either $a\in I$ or $b\in \delta (I)$ and also, $ I $ is called 2-absorbing $\delta $-primary hyperideal if $a,b,c\in R $ and $a\circ b\circ c \subseteq I$ imply $a\circ b\subseteq I$ or $b\circ c\subseteq \delta (I)$ or $a\circ c\subseteq \delta (I)$. Moreover, we give the …

Convolutionproperties For A Family Of Analytic Functions Involving $Q$-Analogue Ofruscheweyh Differential Operator, Khurshid Ahmad, Muhammad Arif, Jin Lin Liu

Turkish Journal of Mathematics

The main object of the present paper is to investigate convolution properties for a new subfamily of analytic functions that are defined by $q$ -analogue of Ruscheweyh differential operator. Several consequences of the main results are also given.

The Frequency Function And Its Connections To The Lebesgue Points And The Hardy-Littlewood Maximal Function, Faruk Temur

Turkish Journal of Mathematics

The aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function $\mathcal{T}$, and further to investigate its relations to the Hardy-Littlewood maximal function $\mathcal{M}$, and to the Lebesgue points. We surmount the intricate issue of measurability of $\mathcal{T}f$ by approaching it with a sequence of carefully constructed auxiliary functions for which measurability is easier to prove. After this, we give analogues of the recent results on the discrete frequency function. We then connect the points of discontinuity of $\mathcal{M}f$ for $f$ simple to the zeros …

An Involution Of Reals, Discontinuous On Rationals, And Whose Derivative Vanishes A.E., Abdurrahman Muhammed Uludağ, Hakan Ayral

Turkish Journal of Mathematics

We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.

Some Sufficient Conditions For A Group To Be Abelian, Gary Walls

Turkish Journal of Mathematics

A group is said to satisfy a word $w$ in the symbols $\{x, x^{-1}, y, y^{-1} \}$ provided that if the 'x' and 'y' are replaced by arbitrary elements of the group then the equation $w=1$ is satisfied. This paper studies certain equations in words, as above, which together with other conditions imply that groups which satisfy these equations and conditions must be abelian.

Some Applications Of Differential Subordination For Certain Starlike Functions, Rahim Kargar, Lucyna Trojnar Spelina

Turkish Journal of Mathematics

Let $\mathcal{S}^*(q_c)$ denote the class of functions $f$ analytic in the open unit disc $\Delta$, normalized by the condition $f(0)=0=f'(0)-1$ and satisfying the following inequality $\left \left(\frac{zf'(z)}{f(z)}\right)^2-1\right < c \quad (z\in\Delta, 0

The Matrix-Valued Numerical Range Over Finite Fields, Edoardo Ballico

Turkish Journal of Mathematics

In this paper we define and study the matrix-valued $k\times k$ numerical range of $n\times n$ matrices using the Hermitian product and the product with $n\times k$ unitary matrices $U$ (on the right with $U$, on the left with its adjoint $U^\dagger = U^{-1}$). For all $i, j=1,\dots ,k$ we study the possible $(i,j)$-entries of these $k\times k$ matrices. Our results are for the case in which the base field is finite, but the same definition works over $\mathbb {C}$. Instead of the degree $2$ extension $\mathbb {R}\hookrightarrow \mathbb {C}$ we use the degree $2$ extension $\mathbb {F} _q\hookrightarrow \mathbb …

Further Results On The Join Graph Of A Finite Group, Zahra Bahrami, Bijan Taeri

Turkish Journal of Mathematics

Let $G$ be a finite group which is not cyclic of prime power order. The join graph $\Delta(G)$ is an undirected simple whose vertices are the proper subgroups of $G$, which are not contained in the Frattini subgroup $\Phi(G)$ of $G$ and two vertices $H$ and $K$ are joined by an edge if and only if $G=\langle H,K\rangle$. We classify finite groups whose join graphs have domination number $\leq 2$ and independence number $\leq 3$. We show that $\Delta(G)\cong \Delta(A_4)$ if and only if $G\cong A_4$. We also show that if the independence number of $\Delta(G)$ is less than $15$, …

Relative Ranks Of Some Partial Transformation Semigroups, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik

Turkish Journal of Mathematics

Let $P_{n}$, $T_{n}$, $I_{n}$, and $S_{n}$ be the partial transformation semigroup, the (full) transformation semigroup, the symmetric inverse semigroup, and the symmetric group on $X_{n}=\{1,\ldots ,n \}$, respectively. For $1\leq r\leq n-1$, let $PK_{n,r}$ be the subsemigroup consisting $\alpha\in P_{n}$ such that $ \im\alpha \leq r$ and let $SPK_{n,r}=PK_{n,r}\setminus T_{n}$. In this paper, we first examine the subsemigroup $I_{n,r}=I_{n}\cup PK_{n,r}$ and we find the necessary and sufficient conditions for any nonempty subset of $PK_{n,r}$ to be a (minimal) relative generating set of the subsemigroup $I_{n,r}$ modulo $I_{n}$. Then we examine the subsemigroups $PI_{n,r}= SI_{n}\cup PK_{n,r}$ and $SI_{n,r}=SI_{n}\cup SPK_{n,r}$ for $1\leq …

A Convergent Two-Level Linear Scheme For The Generalizedrosenau-Kdv-Rlw Equation, Ayhan Aydin

Turkish Journal of Mathematics

A new convergent two-level finite difference scheme is proposed for the numerical solution of initial value problem of the generalized Rosenau--KdV--RLW equation. The new scheme is second-order, linear, conservative, and unconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solution is studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence of the scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating the solitary wave graph of the equation. Wave generation subject to initial Gaussian condition has …

On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher S. Hassan, Özkan Öztürk, İsmai̇l Uğur Ti̇ryaki̇

Turkish Journal of Mathematics

In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.

On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev

Turkish Journal of Mathematics

We investigate the Schrödinger operator $L(q)$ in $L_{2}\left( \mathbb{R}^{d}\right) \ (d\geq1)$ with the complex-valued potential $q$ that is periodic with respect to a lattice $\Omega.$ Besides, it is assumed that the Fourier coefficients $q_{\gamma}$ of $q$ with respect to the orthogonal system $\{e^{i\left\langle \gamma x\right\rangle }:\gamma\in\Gamma\}$ vanish if $\gamma$ belongs to a half-space, where $\Gamma$ is the lattice dual to $\Omega.$ We prove that the Bloch eigenvalues are $\mid\gamma+t\mid^{2}$ for $\gamma\in\Gamma,$ where $t$ is a quasimomentum and find explicit formulas for \ the Bloch functions. Moreover, we investigate the multiplicity of the Bloch eigenvalue and consider necessary and sufficient conditions …

Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda

Turkish Journal of Mathematics

We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater than or equal to $4g-1$.

Po-Groups And Hypergroups In A Topos, Ali Madanshekaf, Zeinab Kanjanzadeh

Turkish Journal of Mathematics

This paper deals with two constructions in topos theory: po-groups and hypergroups. After a deep analysis of these, we restrict our attention to find a hypergroup associated to a po-group $G$ in a topos $\mathcal{E}$. The method that we use here is based on the Mitchell--B$\acute{{\rm e}}$nabou language. Then, we show that on the negative and positive cones of a po-group $G$ in $\mathcal{E},$ the left and right translations are hyperhomomorphisms in $\mathcal{E}.$ Our aim is to find two faithful and left exact functors from the category of po-groups in $\mathcal{E}$ to the (smallest in some sense) finitely complete category …