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Articles 1021 - 1050 of 2607
Full-Text Articles in Mathematics
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.
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.
Uncountably Many Nonoscillatory Bounded Solutions To Second-Order Nonlinear Neutral Dynamic Equations, Magdalena Nockowska Rosiak
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.
Companion Sequences Associated To The$R$-Fibonacci Sequence: Algebraic And Combinatorial Properties, Sadjia Abbad, Hacene Belbachir, Benali Benzaghou
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
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
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
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
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
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
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
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
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
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 …