Mathematics Commons^™

On Distribution Of Upper Marginal Records In Bivariate Random Sequences, Gülder Kemalbay, İsmi̇han Bayramoğlu

Turkish Journal of Mathematics

The theory of record values has been extensively studied in the statistical literature. However, there are not many papers devoted to the theory of records for bivariate and multivariate random sequences. This paper presents the marginal record values and record times in extended sequence of bivariate random vectors. The joint distributions of some upper marginal records are derived. Some results on joint probability mass function of upper record time vectors and distribution function of upper record value vectors are given via copula functions. Moreover, the numerical and graphical applications of considered upper records using flood data and prediction of rainfall …

Construction Of Higher Groupoids Via Matched Pairs Actions, Koray Yilmaz, Erdal Ulualan

Turkish Journal of Mathematics

In this work, we construct a relationship between matched pairs and triples of groupoids. Given two 3-groupoids with a common edge, we construct a triple groupoid by using the matched pairs actions.

Third-Order Boundary Value Transmission Problems, Eki̇n Uğurlu

Turkish Journal of Mathematics

In this paper, we consider some third-order operators with transmission conditions. In particular, it is shown that such operators are formally symmetric in the corresponding Hilbert spaces and we introduce the resolvent operators associated with the differential operators. After showing that the eigenvalues of the problems are real and discrete we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data.

Relationships Between Category Theory And Functional Programming With An Application, Alper Odabaş, Eli̇s Soylu

Turkish Journal of Mathematics

The most recent studies in mathematics are concerned with objects, morphisms, and the relationship between morphisms. Prominent examples can be listed as functions, vector spaces with linear transformations, and groups with homomorphisms. Category theory proposes and constitutes new structures by examining objects, morphisms, and compositions. Source and target of a morphism in category theory corresponds to input and output in programming language. Thus, a connection can be obtained between category theory and functional programming languages. From this point, this paper constructs a small category implementation in a functional programming language called Haskell.

On A New Generalization Of Telephone Numbers, Urszula Bednarz, Ma?Gorzata Wo?Owiec-Musia?

Turkish Journal of Mathematics

In this paper we introduce a new generalization of telephone numbers. We give the generating function, direct formulae, and matrix generators for these numbers. Moreover, we present their interpretations and we prove some properties of these numbers connected with congruences.

On The Distance Formulae In The Generalized Taxicab Geometry, Harun Bariş Çolakoğlu

Turkish Journal of Mathematics

In this paper, we first determine the generalized taxicab distance formulae between a point and a line and two parallel lines in the real plane, then we determine the generalized taxicab distance formulae between a point and a plane, two parallel planes, a point and a line, two parallel lines and two skew lines in three dimensional space, giving also the relations between these formulae and their well-known Euclidean analogs. Finally, we give the generalized taxicab distance formulae between a point and a plane, a point and a line and two skew lines in $n$-dimensional space, by generalizing the concepts …

On The Solvability Of The Main Boundary Value Problems For A Nonlocal Poisson Equation, Valery Karachik, Abdizhahan Sarsenbi, Batirkhan Turmetov

Turkish Journal of Mathematics

Solvability of the main boundary value problems for the nonlocal Poisson equation is studied. Existence and uniqueness theorems for the considered problems are obtained. The necessary and sufficient solvability conditions for all problems are given and integral representations for the solutions are constructed.

On The Exponential Diophantine Equation $P_N^X+P_{N+1}^X=P_M$, Salah Eddine Rihane, Bernadette Faye, Florian Luca, Alain Togbe

Turkish Journal of Mathematics

In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables $(m, n, x)$, where $P_k$ is the $k$th term of the Pell sequence.

The Spectral Expansion For The Hahn-Dirac System On The Whole Line, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna

Turkish Journal of Mathematics

We consider the singular Hahn-Dirac system defined by $ -\frac{1}{q}D_{-\omega q^{-1},q^{-1}}y_{2}+p\left( x\right) y_{1} =\lambda y_{1}, $ $D_{\omega,q}y_{1}+r\left( x\right) y_{2} & =\lambda y_{2}, $ where $\lambda$ is a complex spectral parameter and $p$ and $r$ are real-valued functions defined on $(-\infty,\infty)$ and continuous at $\omega_{0}$. We prove the existence of a spectral function for such a system. We also prove the Parseval equality and the spectral expansion formula in terms of the spectral function for this system on the whole line.

On Null Submanifolds Of Generalized Robertson-Walker Space Forms, Fortune Massamba, Mohamed H. A. Hamed, Samuel Ssekajja

Turkish Journal of Mathematics

We investigate totally umbilical $r$-null submanifolds of generalized Robertson-Walker space forms. Using generalized Newton transformations, we obtain new geometric configurations for the mean curvature functions which generalize many well-known results on null geometry.

A New General Subclass Of $M$-Fold Symmetric Bi-Univalent Functionsgiven By Subordination, Arzu Akgül

Turkish Journal of Mathematics

In a recent work, Orhan et al. (Afrika Matematika, 2016) defined a subclass of analytic bi-univalent one-fold symmetric functions. The main purpose of this paper is to generalize and improve the results of Orhan et al.

Uncountably Many Nonoscillatory Bounded Solutions To Second-Order Nonlinear Neutral Dynamic Equations, Magdalena Nockowska Rosiak

Turkish Journal of Mathematics

This work is devoted to the study of the existence of uncountably many nonoscillatory bounded solutions to second-order nonlinear neutral dynamic equations by means of the Darbo fixed point theorem. We construct assumptions without sign conditions on the nonlinear part of the equation. Moreover, we prove the necessary condition for the existence of an asymptotically zero solution to the problem under consideration.

Gait And Postural Analysis In Healthy Young Adults And People With Parkinson's Disease, Aisha Joy Chen

CGU Theses & Dissertations

Postural analysis is the study of how the position of the body in any mode interacts with internal and external forces. This type of analysis is typically used to assess potential abnormalities in the balance control system and to understand how the balance control system changes with time. However, compared to other medical fields of study, postural analysis is relatively new [1]. In fact, although widely used in clinical and research studies, postural assessment methods are scientifically inaccurate, and some data collection methods are relatively expensive. A better understanding of the human balance control system could lead to more accurate …

Convergence In A Disk Stacking Model On The Cylinder, Christophe Golé, Stéphane Douady

Mathematics Sciences: Faculty Publications

We study an iterative process modeling growth of phyllotactic patterns, wherein disks are added one by one on the surface of a cylinder, on top of an existing set of disks, as low as possible and without overlap. Numerical simulations show that the steady states of the system are spatially periodic, lattices-like structures called rhombic tilings. We present a rigorous analysis of the dynamics of all configurations starting with closed chains of 3 tangent, non-overlapping disks encircling the cylinder. We show that all these configurations indeed converge to rhombic tilings. Surprisingly, we show that convergence can occur in either …

Zeros Of The Dedekind Zeta-Function, Mashael Alsharif

Electronic Theses and Dissertations

H. L. Montgomery proved a formula for sums over two sets of nontrivial zeros of the Riemann zeta-function. Assuming the Riemann Hypothesis, he used this formula and Fourier analysis to prove an estimate for the proportion of simple zeros of the Riemann zeta-function. We prove a generalization of his formula for the nontrivial zeros of the Dedekind zeta-function of a Galois number field, and use this formula and Fourier analysis to prove an estimate for the proportion of distinct zeros, assuming the Generalized Riemann Hypothesis.

Totally Acyclic Complexes, Holly M. Zolt

College of Graduate Studies: Theses & Dissertations

We consider the following question: when is every exact complex of injective modules a totally acyclic one? It is known, for example, that over a commutative Noetherian ring of finite Krull dimension this condition is equivalent with the ring being Iwanaga-Gorenstein. We give equivalent characterizations of the condition that every exact complex of injective modules (over arbitrary rings) is totally acyclic. We also give a dual result giving equivalent characterizations of the condition that every exact complex of flat modules is F-totally acyclic over an arbitrary ring.

Edge Colorings Of Graphs On Surfaces And Star Edge Colorings Of Sparse Graphs, Katherine M. Horacek

Graduate Theses, Dissertations, and Problem Reports (ETD)

In my dissertation, I present results on two types of edge coloring problems for graphs.

For each surface Σ, we define ∆(Σ) = max{∆(G)| G is a class two graph with maximum degree ∆(G) that can be embedded in Σ}. Hence Vizing’s Planar Graph Conjecture can be restated as ∆(Σ) = 5 if Σ is a sphere. For a surface Σ with characteristic χ(Σ) ≤ 0, it is known ∆(Σ) ≥ H(χ(Σ))−1, where H(χ(Σ)) is the Heawood number of the surface, and if the Euler char- acteristic χ(Σ) ∈ {−7, −6, . . . , −1, 0}, ∆(Σ) is already …

Teachers' Reflection On Their Beliefs And Question-Asking Practices During Mathematics Instruction, Kaili Takiyah Hardamon

Wayne State University Dissertations

Teachers’ daily instructional practices are a critical component in creating a rich and meaningful educational experience for students. Thus, factors that inform instructional practices are of particular importance and interest to education researchers and other stakeholders. Beliefs about teaching and learning are a known factor influencing teachers’ instructional practices (Ernest, 1989). This study focused on a specific instructional practice, question-asking, which has a profound impact on students’ experience with mathematics (Weiland, Hudson, and Amador (2014). Understanding the relationship between teachers’ beliefs and practice helps to make sense of teachers’ decision-making processes, particularly as they choose questions to ask students during …

Characterizations Of Certain Recently Introduced Discrete Distributions, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of certain recently introduced discrete distributions are presented to complete, in some way, the works cited in the References.

A Gene Based Approach To Test Genetic Association Based On An Optimally Weighted Combination Of Multiple Traits., Jianjun Zhang, Qiuying Sha, Guanfu Liu, Xuexia Wang

Michigan Tech Publications, Part 1

There is increasing evidence showing that pleiotropy is a widespread phenomenon in complex diseases for which multiple correlated traits are often measured. Joint analysis of multiple traits could increase statistical power by aggregating multiple weak effects. Existing methods for multiple trait association tests usually study each of the multiple traits separately and then combine the univariate test statistics or combine p-values of the univariate tests for identifying disease associated genetic variants. However, ignoring correlation between phenotypes may cause power loss. Additionally, the genetic variants in one gene (including common and rare variants) are often viewed as a whole that affects …