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Multiplicative Lie Algebras, Gary L. Walls
Multiplicative Lie Algebras, Gary L. Walls
Turkish Journal of Mathematics
A multiplicative Lie algebra is a group together with a "bracket function" that satisfies the basic properties of the commutator function. This paper investigates the construction of such functions.
Null Scrolls As B-Scrolls In Lorentz-Minkowski 3-Space, Zeljka Milin Sipus, Ljiljana Primorac Gajcic, Ivana Protrka
Null Scrolls As B-Scrolls In Lorentz-Minkowski 3-Space, Zeljka Milin Sipus, Ljiljana Primorac Gajcic, Ivana Protrka
Turkish Journal of Mathematics
Null scrolls, i.e. ruled surfaces whose base curve and rulings are both lightlike (null), are Lorentzian surfaces having no Euclidean counterparts. In this work we present reparametrization of nondegenerate null scroll as a B-scroll, i.e. as a ruled surface whose rulings correspond to the binormal vectors of a base curve. We prove that the curvature of a base curve, which determines the Gaussian and mean curvature of a null scroll, is invariant under such a reparametrization. We also determine a one-parameter family of null curves on null scroll which serve as base curves for this kind of reparametrization.
Approximately Rings In Proximal Relator Spaces, Ebubeki̇r İnan
Approximately Rings In Proximal Relator Spaces, Ebubeki̇r İnan
Turkish Journal of Mathematics
This article introduces approximately rings, approximately ideals, and approximately rings of all approximately cosets by considering new operations on the set of all approximately cosets. Afterwards, some properties of approximately rings and ideals were given.
On Oscillatory And Nonoscillatory Behavior Of Solutions For A Class Of Fractional Orderdifferential Equations, Arjumand Seemab, Mujeeb Ur Rehman
On Oscillatory And Nonoscillatory Behavior Of Solutions For A Class Of Fractional Orderdifferential Equations, Arjumand Seemab, Mujeeb Ur Rehman
Turkish Journal of Mathematics
This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t) _{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
The Differential-Symbol Method Of Constructing The Quasipolynomial Solutions Of Two-Point In Time Problem For Nonhomogeneous Partial Differential Equation, Zinovii Nytrebych, Oksana Malanchuk, Volodymyr Il'kiv, Petro Pukach
The Differential-Symbol Method Of Constructing The Quasipolynomial Solutions Of Two-Point In Time Problem For Nonhomogeneous Partial Differential Equation, Zinovii Nytrebych, Oksana Malanchuk, Volodymyr Il'kiv, Petro Pukach
Turkish Journal of Mathematics
The existence of the solution of nonhomogeneous partial differential equations (PDE) of second order in time and finite or infinite order in spatial variable with quasipolynomial right-hand side is proved. This solution satisfies the homogeneous two-point in time conditions. The differential-symbol method for constructing the solution of the problem is proposed. The examples of applying this method for solving some two-point problems for PDE are suggested.
Lie Group Analysis For Initial And Boundary Value Problem Of Time-Fractional Nonlinear Generalized Kdv Partial Differential Equation, Doğan Kaya, Gulistan Iskandarova
Lie Group Analysis For Initial And Boundary Value Problem Of Time-Fractional Nonlinear Generalized Kdv Partial Differential Equation, Doğan Kaya, Gulistan Iskandarova
Turkish Journal of Mathematics
The Lie group analysis or in other word the symmetry analysis method is extended to deal with a time-fractional order derivative nonlinear generalized KdV equation. Our research in this work aims to use transformation methods and their analysis to search for exact solutions to the nonlinear generalized KdV differential equation. It is shown that this equation can be reduced to an equation with Erdelyi-Kober fractional derivative. In this study, we research the initial and boundary conditions, considering them invariant, and so we get two ordinary initial value problems, i.e. two Cauchy problems. Conservation laws for the given equation are also …
The Cissoid Of Diocles In The Lorentz-Minkowski Plane, Şenay Baydaş, Bülent Karakaş
The Cissoid Of Diocles In The Lorentz-Minkowski Plane, Şenay Baydaş, Bülent Karakaş
Turkish Journal of Mathematics
This article presents the cissoid of Diocles and the cissoid of two circles with respect to origin in the Lorentz-Minkowski plane.
A Short Note On Some Arithmetical Properties Of The Integer Part Of $\Alpha P$, Yildirim Akbal
A Short Note On Some Arithmetical Properties Of The Integer Part Of $\Alpha P$, Yildirim Akbal
Turkish Journal of Mathematics
Let $\alpha>0$ be an irrational number. We study some of the arithmetical properties of $\{ \fl{\alpha p}\}_{p=2}^{\infty}$, where $p$ denotes a prime number and $\fl{x}$ denotes the largest integer not exceeding $x$.
On A Nonnegativity Principle With Applications To A Certain Multitermfractional Boundary Value Problem, Noureddine Ferfar, Said Mazouzi
On A Nonnegativity Principle With Applications To A Certain Multitermfractional Boundary Value Problem, Noureddine Ferfar, Said Mazouzi
Turkish Journal of Mathematics
The main object of the present paper is to state and prove a general nonnegativity principle in the framework of multiterm fractional differential equations, which we use to investigate some iterative monotone sequences of lower and upper solutions to a certain fractional eigenvalue problem. The obtained results can be easily extended to fractional differential equations of distributed orders since the latter are the natural extension of multiterm fractional differential equations.
Solutions To Nonlinear Second-Order Three-Point Boundary Value Problems Of Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Solutions To Nonlinear Second-Order Three-Point Boundary Value Problems Of Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we consider existence criteria of three positive solutions of three-point boundary value problems for $p$-Laplacian dynamic equations on time scales. To show our main results, we apply the well-known Leggett-Williams fixed point theorem. Moreover, we present some results for the existence of single and multiple positive solutions for boundary value problems on time scales, by applying fixed point theorems in cones. The conditions we used in the paper are different from those in [Dogan A. On the existence of positive solutions for the one-dimensional $ p $-Laplacian boundary value problems on time scales. Dynam Syst Appl 2015; …
Legendre Wavelet Solution Of High Order Nonlinear Ordinary Delay Differential Equations, Sevi̇n Gümgüm, Demet Özdek, Gökçe Özaltun
Legendre Wavelet Solution Of High Order Nonlinear Ordinary Delay Differential Equations, Sevi̇n Gümgüm, Demet Özdek, Gökçe Özaltun
Turkish Journal of Mathematics
The purpose of this paper is to illustrate the use of the Legendre wavelet method in the solution of high-order nonlinear ordinary differential equations with variable and proportional delays. The main advantage of using Legendre polynomials lies in the orthonormality property, which enables a decrease in the computational cost and runtime. The method is applied to five differential equations up to sixth order, and the results are compared with the exact solutions and other numerical solutions when available. The accuracy of the method is presented in terms of absolute errors. The numerical results demonstrate that the method is accurate, effectual …
Star-Likeness Associated With The Exponential Function, Adiba Naz, Sumit Nagpal, V. Ravichandran
Star-Likeness Associated With The Exponential Function, Adiba Naz, Sumit Nagpal, V. Ravichandran
Turkish Journal of Mathematics
Given a domain $\Omega$ in the complex plane $\mathbb{C}$ and a univalent function $q$ defined in an open unit disk $\mathbb{D}$ with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions $\Psi(\Omega,q)$ so that the differential subordination $\psi(p(z),zp'(z),z^2p''(z);z)\prec h(z)$ implies $p(z)\prec q(z)$, where $p$ is an analytic function in $\mathbb{D}$ with $p(0)=1$, $\psi:\mathbb{C}^3\times \mathbb{D}\to\mathbb{C}$ and $\Omega=h(\mathbb{D})$. This paper investigates the properties of this class for $q(z)=e^z$. As application, several sufficient conditions for normalized analytic functions $f$ to be in the subclass of star-like functions associated with the exponential function are obtained.
A New General Subclass Of Analytic Bi-Univalent Functions, Serap Bulut
A New General Subclass Of Analytic Bi-Univalent Functions, Serap Bulut
Turkish Journal of Mathematics
In a very recent work, Şeker [Seker B. On a new subclass of bi-univalent functions defined by using Salagean operator. Turkish Journal of Mathematics 2018; 42: 2891-2896] defined two subclasses of analytic bi-univalent functions by means of Salagean differential operator and he obtained the initial Taylor-Maclaurin coefficient estimates for functions belonging to these classes. The main purpose of this paper is to improve the results obtained by Şeker in the aforementioned study. For this purpose, we define a general subclass of bi-univalent functions.
An Inequality On Diagonal $F$-Thresholds Over Standard-Graded Complete Intersection Rings, Jinjia Li
An Inequality On Diagonal $F$-Thresholds Over Standard-Graded Complete Intersection Rings, Jinjia Li
Turkish Journal of Mathematics
In a recent paper, De Stefani and N\'{u}\~{n}ez-Betancourt proved that for a standard-graded $F$-pure $k$-algebra $R$, its diagonal $F$-threshold $c(R)$ is always at least $-a(R)$, where $a(R)$ is the $a$-invariant. In this paper, we establish a refinement of this result in the setting of complete intersection rings.
Some Remarks On Generalized Kirk's Process In Banach Spaces And Application, Abdelkader Dehici
Some Remarks On Generalized Kirk's Process In Banach Spaces And Application, Abdelkader Dehici
Turkish Journal of Mathematics
In this work, we establish a common fixed point result for mappings satisfying a controllable punctual inequality and we study the convergence (resp. weak convergence) of the generalized Kirk's process associated with them. In addition, our results are applied to investigate the convergence (resp. weak convergence) of Kuhfittig's iterative process to the solution of a nonlinear system of functional equations.
Value Sets Of Folding Polynomials Over Finite Fields, Ömer Küçüksakalli
Value Sets Of Folding Polynomials Over Finite Fields, Ömer Küçüksakalli
Turkish Journal of Mathematics
Let $k$ be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra $\mf{g}$. We find the cardinality of the value sets of the folding polynomials $P_\mf{g}^k(\mb{x}) \in \Z[\mb{x}]$ of arbitrary rank $n \geq 1$, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.
A New Comprehensive Subclass Of Analytic Bi-Close-To-Convex Functions, Serap Bulut
A New Comprehensive Subclass Of Analytic Bi-Close-To-Convex Functions, Serap Bulut
Turkish Journal of Mathematics
In a very recent work, Şeker and Sümer Eker [On subclasses of bi-close-to-convex functions related to the odd-starlike functions. Palestine Journal of Mathematics 2017; 6: 215-221] defined two subclasses of analytic bi-close-to-convex functions related to the odd-starlike functions in the open unit disk $\mathbb{U}$. The main purpose of this paper is to generalize and improve the results of Şeker and Sümer Eker (in the aforementioned study) defining a comprehensive subclass of bi-close-to-convex functions. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to this new class.
On Image Summand Coinvariant Modules And Kernel Summand Invariant Modules, Derya Keski̇n Tütüncü, Yosuke Kuratomi, Yoshiharu Shibata
On Image Summand Coinvariant Modules And Kernel Summand Invariant Modules, Derya Keski̇n Tütüncü, Yosuke Kuratomi, Yoshiharu Shibata
Turkish Journal of Mathematics
In this paper we introduce the concept of im-summand coinvariance and im-small coinvariance; that is, a module $M$ over a right perfect ring is said to be im-summand (im-small) coinvariant if, for any endomorphism $\varphi$ of $P$ such that ${\rm Im} \varphi$ is a direct summand (a small submodule) of $P$, $\varphi (\ker \nu) \subseteq \ker \nu$, where $(P, \nu)$ is the projective cover of $M$. We first give some fundamental properties of im-summand coinvariant modules and im-small coinvariant modules, and we prove that, for modules $M$ and $N$ over a right perfect ring such that $N$ is a small …
On Distribution Of Upper Marginal Records In Bivariate Random Sequences, Gülder Kemalbay, İsmi̇han Bayramoğlu
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
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
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
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?
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
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
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
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
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
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
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.