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2019

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On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher S. Hassan, Özkan Öztürk, İsmai̇l Uğur Ti̇ryaki̇ Jan 2019

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.

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On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev Jan 2019

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 …

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Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda Jan 2019

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 $4g-1$.

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Po-Groups And Hypergroups In A Topos, Ali Madanshekaf, Zeinab Kanjanzadeh Jan 2019

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 …

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Cover And Contents Jan 2019

Cover And Contents

Turkish Journal of Mathematics

No abstract provided.

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Lattice Ordered Semigroups And Hypersemigroups, Niovi Kehayopulu Jan 2019

Lattice Ordered Semigroups And Hypersemigroups, Niovi Kehayopulu

Turkish Journal of Mathematics

This paper shows that many results on hypersemigroups do not need any proof as can be obtained from lattice ordered semigroups.

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Principal Parts Of A Vector Bundle On Projective Line And The Fractional Derivative, Hafiz Syed Husain, Mariam Sultana Jan 2019

Principal Parts Of A Vector Bundle On Projective Line And The Fractional Derivative, Hafiz Syed Husain, Mariam Sultana

Turkish Journal of Mathematics

This work is an exposition on computational aspects of principal parts of a vector bundle on projective line over the field of characteristic zero. Principal parts help determine the possibility of algebraically formalizing infinitesimal-neighborhoods of subschemes inside some ambient scheme. The purpose of this study is to look for the possibility of formalizing the algebraic geometric interpretation of fractional derivative. For the latter, this study follows theapproachproposedbyVasilyTarasov. The difference is that Tarasov proposeda geometric interpretation using finite order jet bundles from differential geometry. Present study proposes finite-order principal parts of the structure-sheaf of real projective line as its formal algebraic …

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Nonexistence Of Global Solutions For A Fractional System Of Strongly Coupled Integro-Differential Equations, Ahmad Mugbil Ahmad, Nasser Eddine Tatar Jan 2019

Nonexistence Of Global Solutions For A Fractional System Of Strongly Coupled Integro-Differential Equations, Ahmad Mugbil Ahmad, Nasser Eddine Tatar

Turkish Journal of Mathematics

In this paper, we study the nonexistence of nontrivial global solutions for a system of two strongly coupled fractional differential equations. Each equation involves two fractional derivatives and a nonlinear source term. The fractional derivatives are of Caputo type of subfirst orders. The nonlinear sources are nonlocal in time. They have the form of a convolution of a polynomial of the state with a (possibly singular) kernel. The system under consideration is a generalization of many interesting special systems of equations whose solutions do not exist globally in time. We establish some criteria under which no nontrivial global solutions exist. …

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Fixed-Disc Results Via Simulation Functions, Ni̇hal Özgür Jan 2019

Fixed-Disc Results Via Simulation Functions, Ni̇hal Özgür

Turkish Journal of Mathematics

In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in our results. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping.

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On Composition Factors In Modules Over Some Group Rings, Martyn Russell Dixon, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin Jan 2019

On Composition Factors In Modules Over Some Group Rings, Martyn Russell Dixon, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin

Turkish Journal of Mathematics

The aim of this paper is to prove the following result: Let G be an FC-hypercentral group and let A have a finite FG-composition series. Then A contains two FG-submodules B,C such that A = B ⊕ C, where each FG-composition factor of B has finite F -dimension and each FG-composition factor of C has infinite F -dimension. Thishasconsequencesfor FG-modules whose proper submodules all have finite F -dimensionandforthose FG-modules whose proper quotients all have finite F -dimension.

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Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives, Ramunas Garunkstis Jan 2019

Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives, Ramunas Garunkstis

Turkish Journal of Mathematics

Levinson and Montgomery proved that the Riemann zeta-function ζ(s) and its derivative have approximately the same number of nonreal zeros left of the critical line. Spira showed that ζ'(1/2+it) = 0 implies that ζ(1/2+it) = 0. Here we obtain that in small areas located to the left of the critical line and near it the functions ζ(s) and ζ'(s) have the same number of zeros. We prove our result for more general zeta-functions from the extended Selberg class S. We also consider zero trajectories of a certain family of zeta-functions from S.

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A Variational Study On A Natural Hamiltonian For Curves, Gözde Özkan Tükel Jan 2019

A Variational Study On A Natural Hamiltonian For Curves, Gözde Özkan Tükel

Turkish Journal of Mathematics

A variational study of finding critical points of the total squared torsion functional for curves in Euclidean 3-spaces is presented. Critical points of this functional also known as one of the natural Hamiltonians of curves are characterized by two Euler-Lagrange equations in terms of curvature and torsion of a curve. To solve these balance equations, the curvature of the critical curve is expressed by its torsion so that equations are completely solved by quadratures. Then two Killing fields along the critical curve are found for integrating the structural equations of the critical curve and this curve is expressed by quadratures …

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Extensions And Topological Conditions Of Nj Rings, Meimei Jiang, Yao Wang, Yanli Ren Jan 2019

Extensions And Topological Conditions Of Nj Rings, Meimei Jiang, Yao Wang, Yanli Ren

Turkish Journal of Mathematics

A ring $R$ is said to be NJ if $J(R)=N(R)$. This paper mainly studies the relationship between NJ rings and related rings, and investigates the Dorroh extension, the Nagata extension, the Jordan extension, and some other extensions of NJ rings. At the same time, we also prove that if $R$ is a weakly 2-primal $\alpha$-compatible ring with an isomorphism $\alpha$ of $R$, then $R[x;\alpha]$ is NJ; if $R$ is a weakly 2-primal $\delta$-compatible ring with a derivation $\delta$ of $R$, then $R[x;\delta]$ is NJ. Moreover, we consider some topological conditions for NJ rings and show for a NJ ring $R$ …

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Degenerate Maximal Hyponormal Differential Operators For The First Order, Meltem Sertbaş, Fati̇h Yilmaz Jan 2019

Degenerate Maximal Hyponormal Differential Operators For The First Order, Meltem Sertbaş, Fati̇h Yilmaz

Turkish Journal of Mathematics

In this study, all maximal hyponormal extensions are given for the degenerate first order in the Hilbert space of vector-functions on a finite interval. The extensions are defined in terms of the boundary values. The structure of the spectrum of the maximal hyponormal extensions is also investigated.

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The $X$-Coordinates Of Pell Equations And Padovan Numbers, Salah Eddine Rihane, Mohand Ouamar Hernane, Alain Togbe Jan 2019

The $X$-Coordinates Of Pell Equations And Padovan Numbers, Salah Eddine Rihane, Mohand Ouamar Hernane, Alain Togbe

Turkish Journal of Mathematics

In this paper, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=k$, where $k\in\{\pm1,\pm4\}$, which is a Padovan number, with a few exceptions that we completely characterize.

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A Neutral Relation Between Metallic Structure And Almost Quadratic $\Phi $-Structure, Si̇nem Gönül, İrem Küpeli̇ Erken, Azi̇z Yazla, Cengi̇zhan Murathan Jan 2019

A Neutral Relation Between Metallic Structure And Almost Quadratic $\Phi $-Structure, Si̇nem Gönül, İrem Küpeli̇ Erken, Azi̇z Yazla, Cengi̇zhan Murathan

Turkish Journal of Mathematics

In this paper, we give a neutral relation between metallic structure and almost quadratic metric $\phi $-structure. Considering $N$ as a metallic Riemannian manifold, we show that the warped product manifold $\mathbb{R} \times _{f}N$ has an almost quadratic metric $\phi $-structure. We define Kenmotsu quadratic metric manifolds, which include cosymplectic quadratic manifolds when $\beta =0$. Then we give nice almost quadratic metric $\phi $-structure examples. In the last section, we construct a quadratic $\phi $-structure on the hypersurface $M^{n}$ of a locally metallic Riemannian manifold $\tilde{M}^{n+1}.$

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Enveloping Algebras Of Color Hom-Lie Algebras, Abdoreza Armakan, Sergei Silvestrov, Mohammad Reza Farhangdoost Jan 2019

Enveloping Algebras Of Color Hom-Lie Algebras, Abdoreza Armakan, Sergei Silvestrov, Mohammad Reza Farhangdoost

Turkish Journal of Mathematics

In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincaré-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.

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Properties In $L_P$ Of Root Functions For A Nonlocal Problem With Involution, Leonid Kritskov, Makhmud Sadybekov, Abdizhahan Sarsenbi Jan 2019

Properties In $L_P$ Of Root Functions For A Nonlocal Problem With Involution, Leonid Kritskov, Makhmud Sadybekov, Abdizhahan Sarsenbi

Turkish Journal of Mathematics

The spectral problem $-u''(x)+\alpha u''(-x)=\lambda u(x)$, $-1$%lt; $x$ < $1$, with nonlocal boundary conditions $u(-1)=\beta u(1)$, $u'(-1)=u'(1)$, is studied in the spaces $L_p(-1,1)$ for any $\alpha\in (-1,1)$ and $\beta\ne\pm 1$. It is proved that if $r=\sqrt{(1-\alpha)/(1+\alpha)}$ is irrational then the system of its eigenfunctions is complete and minimal in $L_p(-1,1)$ for any $p>1$, but does not form a basis. In the case of a rational value of $r$, the way of supplying this system with associated functions is specified to make all the root functions a basis in $L_p(-1,1)$.

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On Linear Dynamics Of Sets Of Operators, Mohamed Amouch, Otmane Benchiheb Jan 2019

On Linear Dynamics Of Sets Of Operators, Mohamed Amouch, Otmane Benchiheb

Turkish Journal of Mathematics

Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$. The concept of hypercyclicity for a subset of $\mathcal{B}(X)$ was introduced in [1]. In this work, we introduce the notion of hypercyclic criterion for a subset of $\mathcal{B}(X)$. We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.

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On Product Complex Finsler Manifolds, Hongchuan Xia, Qian Wei Jan 2019

On Product Complex Finsler Manifolds, Hongchuan Xia, Qian Wei

Turkish Journal of Mathematics

Let $(M, F)$ be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds $(M_1, F_1)$ and $(M_2, F_2)$ with $F=\sqrt{f(K, H)}$ and $K=F_1^2$, $H=F_2^2$. In this paper, we prove that $(M, F)$ is a weakly Käahler-Finsler (resp. weakly complex Berwald) manifold if and only if $(M_1, F_1)$ and $(M_2, F_2)$ are both weakly Kähler-Finsler (resp. weakly complex Berwald) manifolds, which is independent of the choice of function $f$. Meanwhile, we prove that $(M, F)$ is a complex Landsberg manifold if and only if either $(M_1, F_1)$ and $(M_2, F_2)$ are both complex Landsberg manifolds and $f=c_1K+c_2H$ with …

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Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala Jan 2019

Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala

Turkish Journal of Mathematics

Let $(\beta_n)_{n\ge 2}$ be a sequence of nonnegative real numbers and $\delta$ be a positive real number. We introduce the subclass $\mathcal{A}(\beta_n,\delta)$ of analytic functions, with the property that the Taylor coefficients of the function $f$ satisfies $\sum_{n\ge2}^{\infty}\beta_n a_n \le \delta$, where $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$. The class $\mathcal{A}(\beta_n,\delta)$ contains nonunivalent functions for some choices of $(\beta_n)_{n\ge 2}$. In this paper, we provide some general properties of functions belonging to the class $\mathcal{A}(\beta_n,\delta)$, such as the radii of univalence, distortion theorem, and invariant property. Furthermore, we derive the best approximation of an analytic function in such class by using the semiinfinite quadratic programming. …

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Some General Results On Fractional Banach Sets, Faruk Özger Jan 2019

Some General Results On Fractional Banach Sets, Faruk Özger

Turkish Journal of Mathematics

The gamma function which is expressed by an improper integral is used to establish the fractional difference operators and fractional Banach sets. In this study, we achieve some comprehensive and complementary results related to characterizations of the matrix classes of fractional Banach sets. We also obtain some identities or inequalities for the Hausdorff measure of noncompactness of the corresponding matrix operators, and finally find the necessary and sufficient conditions for those matrix operators to be compact.

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A Bernstein-Type Theorem For $\Xi$-Submanifolds Withflat Normal Bundle In The Euclidean Spaces, Xu-Yong Jiang, He-Jun Sun, Peibiao Zhao Jan 2019

A Bernstein-Type Theorem For $\Xi$-Submanifolds Withflat Normal Bundle In The Euclidean Spaces, Xu-Yong Jiang, He-Jun Sun, Peibiao Zhao

Turkish Journal of Mathematics

$\xi$-Submanifolds in the Euclidean spaces are a natural extension of self-shrinkers and a generalization of $\lambda$-hypersurfaces. Moreover, $\xi$-submanifolds are expected to take the place of submanifolds with parallel mean curvature vector. In this paper, we establish a Bernstein-type theorem for $\xi$-submanifolds in the Euclidean spaces. More precisely, we prove that an $n$-dimensional smooth graphic $\xi$-submanifold with flat normal bundle in $\mathbb{R}^{n+p}$ is an affine $n$-plane.

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Converse Theorems In Lyapunov's Second Method And Applications For Fractional Order Systems, Javier Gallegos, Manuel Duarte-Mermoud Jan 2019

Converse Theorems In Lyapunov's Second Method And Applications For Fractional Order Systems, Javier Gallegos, Manuel Duarte-Mermoud

Turkish Journal of Mathematics

We establish a characterization of the Lyapunov and Mittag-Leffler stability through (fractional) Lyapunov functions, by proving converse theorems for Caputo fractional order systems. A hierarchy for the Mittag-Leffler order convergence is also proved which shows, in particular, that fractional differential equation with derivation order lesser than one cannot be exponentially stable. The converse results are then applied to show that if an integer order system is (exponentially) stable, then its corresponding fractional system, obtained from changing its differentiation order, is (Mittag-Leffler) stable. Hence, available integer order control techniques can be disposed to control nonlinear fractional systems. Finally, we provide examples …

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On The Cover Ideals Of Chordal Graphs, Nursel Erey Jan 2019

On The Cover Ideals Of Chordal Graphs, Nursel Erey

Turkish Journal of Mathematics

The independence complex of a chordal graph is known to be shellable which is equivalent to the fact that cover ideal of a chordal graph has linear quotients. We use this result to obtain recursive formulas for the Betti numbers of cover ideals of chordal graphs. Moreover, we give a new proof of such result which yields different shellings of the independence complex.

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A Circulant Functional Equation For The Additive Function And Its Stability, Vichian Laohakosol, Watcharapon Pimsert, Kanet Ponpetch Jan 2019

A Circulant Functional Equation For The Additive Function And Its Stability, Vichian Laohakosol, Watcharapon Pimsert, Kanet Ponpetch

Turkish Journal of Mathematics

A general solution of a matrix functional equation involving circulant matrices of the additive function is determined, and its stability is established.

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The Perceived Appeal, Challenge, And Learning Choice For Gifted And Talented Students In Advanced Placement Mathematics Courses, Emma Marie Denise Biggs Jan 2019

The Perceived Appeal, Challenge, And Learning Choice For Gifted And Talented Students In Advanced Placement Mathematics Courses, Emma Marie Denise Biggs

Theses and Dissertations

The Advanced Placement program has undergone many changes since its post Sputnik surge when it was designed to accelerate learners. The number of students enrolled in AP courses has swelled, demographics of participants have diversified, and course curriculums and designs have altered. The homogenous Ivy League bound population of gifted and talented students who made up the initial 1,299 students enrolled in the program has morphed into a heterogeneous population of over 2,800,000 students with many learning needs. With the increase in the testing culture of the United States, the focus in education has shifted towards closing the achievement gap …

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Chemometric Applications In Fire Debris Analysis: Likelihood Ratios From Naive Bayes And Frequency Of Component And Pyrolysis Product Occurrence, Anuradha Akmeemana Jan 2019

Chemometric Applications In Fire Debris Analysis: Likelihood Ratios From Naive Bayes And Frequency Of Component And Pyrolysis Product Occurrence, Anuradha Akmeemana

Electronic Theses and Dissertations

One of the major challenges in fire investigation is the determination of the cause of fire. The fire can be accidental or intentional. The determination of ignitable liquid residue (ILR) from fire debris helps the process and this process is called fire debris analysis in forensic science. This is one of the most complex areas in the field of forensics because of the evaporation of the ILR from the debris and the interference of the substrate matrix with the ILR if present. In the present, the final decisions in fire debris analysis are based on categorical statements and it only …

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A Statistical Analysis And Machine Learning Of Genomic Data, Jongyun Jung Jan 2019

A Statistical Analysis And Machine Learning Of Genomic Data, Jongyun Jung

All Graduate Theses, Dissertations, and Other Capstone Projects

Machine learning enables a computer to learn a relationship between two assumingly related types of information. One type of information could thus be used to predict any lack of informaion in the other using the learned relationship. During the last decades, it has become cheaper to collect biological information, which has resulted in increasingly large amounts of data. Biological information such as DNA is currently analyzed by a variety of tools. Although machine learning has already been used in various projects, a flexible tool for analyzing generic biological challenges has not yet been made. The recent advancements in the DNA …

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Adaptive Smoothing Parameter In Kernel Density Estimation And Parameter Estimation In Normal Mixture Distributions, Sabiha Mahzabeen Jan 2019

Adaptive Smoothing Parameter In Kernel Density Estimation And Parameter Estimation In Normal Mixture Distributions, Sabiha Mahzabeen

All Graduate Theses, Dissertations, and Other Capstone Projects

Kernel density estimation is a widely used tool in nonparametric density estimation procedures. Choice of a kernel function and a smoothing parameter are two important issues in implementing kernel density estimation procedures. In this paper, four different kernel functions are considered in implementing an adaptive selection procedure in choosing the smoothing parameter. In simulation, a skewed bimodal density which is a mixture of two normal distributions is considered along with the standard normal and the standard exponential densities. In skewed bimodal data, parameter estimation is also explored in the context of the parameter estimation in mixtures of normal distributions. Maximum …

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