A Contiguous Extension Of Dixon's Theorem For A Terminating ${}_4f_3(1)$ Series With Applications,
2021
TÜBİTAK
A Contiguous Extension Of Dixon's Theorem For A Terminating ${}_4f_3(1)$ Series With Applications, Mohammad Idris Qureshi, Richard Bruce Paris, Shakir Hussain Malik
Turkish Journal of Mathematics
We derive a summation formula for the terminating hypergeometric series \[{}_4F_3\left[\!\!\begin{array}{c}-m,a,b,1+c\\1+a+m,1+a-b,c\end{array}\!\!;1\right],\] where $m$ denotes a nonnegative integer. Using this summation formula, we establish a reduction formula for the Srivastava-Daoust double hypergeometric function with arguments $z$ and $-z$. Special cases of this reduction formula lead to several reduction formulas for the hypergeometric functions ${}_{p+1}F_p$ with quadratic arguments when $p=2,3$ and 4 by employing series rearrangement techniques. A general double series identity involving a bounded sequence of arbitrary complex numbers is also given.
On Characterization Of Tripotent Matrices In Triangular Matrix Rings,
2021
TÜBİTAK
On Characterization Of Tripotent Matrices In Triangular Matrix Rings, Tuğba Peti̇k
Turkish Journal of Mathematics
Let $\mathfrak{R}$ be a ring with identity $1$ whose tripotents are only $-1$, $0$, and $1$. It is characterized the structure of tripotents in $\mathcal{T}(\mathfrak{R})$ which is the ring of triangular matrices over $\mathfrak{R}$. In addition, when $\mathfrak{R}$ is finite, it is given number of the tripotents in $\mathcal{T}_{n}( \mathfrak{R})$ which is the ring of $n\times n$ dimensional triangular matrices over $\mathfrak{R}$ with $n$ being a positive integer.
2-Absorbing $\Phi$-$\Delta$-Primary Ideals,
2021
TÜBİTAK
2-Absorbing $\Phi$-$\Delta$-Primary Ideals, Sanem Yavuz, Serkan Onar, Bayram Ali̇ Ersoy, Ünsal Teki̇r, Suat Koç
Turkish Journal of Mathematics
This paper aims to introduce 2-absorbing $\phi$-$\delta$-primary ideals over commutative rings which unify the concepts of all generalizations of 2-absorbing and 2-absorbing primary ideals. Let $A $be a commutative ring with a nonzero identity and $\mathcal{I(A)}$ be the set of all ideals of $A$. Suppose that $\delta:\mathcal{I(A)}\rightarrow\mathcal{I(A)}$ is an expansion function and $\phi:\mathcal{I(A)}\rightarrow\mathcal{I(A)}% \cup\left\{ \emptyset\right\} $ is a reduction function. A proper ideal $Q\ $of $A\ $is said to be a 2-absorbing $\phi$-$\delta$-primary if whenever $abc\in Q-\phi(Q)$,\ where $a,b,c\in R,\ $then either $ab\in Q$ or $ac\in\delta(Q)$ or $bc\in\delta(Q). $Various examples, properties, and characterizations of this new class of ideals are …
Count Of Genus Zero $J$-Holomorphic Curves In Dimensions Four And Six,
2021
TÜBİTAK
Count Of Genus Zero $J$-Holomorphic Curves In Dimensions Four And Six, Ahmet Beyaz
Turkish Journal of Mathematics
The abstract should provide clear information about the research and the results obtained, and should not exceed 200 words. The abstract should not contain citations. An application of Gromov--Witten invariants is that they distinguish the deformation types of symplectic structures on a smooth manifold. In this manuscript, it is proven that the use of Gromov--Witten invariants in the class of embedded $J$-holomorphic spheres is restricted. This restriction is in the sense that they cannot distinguish the deformation types of symplectic structures on $X_1\times S^2$ and $X_2\times S^2$ for two minimal, simply connected, symplectic $4$-manifolds $X_1$ and $X_2$ with $b_2^+(X_1)>1$ …
Bilinear Multipliers Of Small Lebesgue Spaces,
2021
TÜBİTAK
Bilinear Multipliers Of Small Lebesgue Spaces, Öznur Kulak, Ahmet Turan Gürkanli
Turkish Journal of Mathematics
Let $G$ be a compact abelian metric group with Haar measure $\lambda $ and $% \hat{G}$ its dual with Haar measure $\mu $. Assume that$~1 < p_{i}
Some Qualitative Results For Functional Delay Dynamic Equations On Time Scales,
2021
TÜBİTAK
Some Qualitative Results For Functional Delay Dynamic Equations On Time Scales, Hali̇s Can Koyuncuoğlu
Turkish Journal of Mathematics
Let $\mathbb{T}$ be a nonempty, closed, and arbitrary set of real numbers, namely a time scale, and consider the following delay dynamical equation% \[ x^{\Delta}\left( t\right) =a\left( t\right) x\left( t\right) +f\left( t,x\left( \mathbb{\vartheta}\left( t\right) \right) \right) ,\text{ }t\in\mathbb{T}, \] where $\mathbb{\vartheta}$ stands for the abstract delay function. The main goal of this study is three-fold: obtaining the existence of an equi-bounded solution, proving the asymptotic stability of the zero solution, and showing the existence of a periodic solution based on new periodicity concept on time scales for the given delayed equation under certain conditions. In our analysis, we propose an …
On The Geometry Of Tangent Bundle Of A Hypersurface In $%%Tcimacro{\U{211d} }%%Beginexpansion\Mathbb{R}%Endexpansion^{N+1}$,
2021
TÜBİTAK
On The Geometry Of Tangent Bundle Of A Hypersurface In $%%Tcimacro{\U{211d} }%%Beginexpansion\Mathbb{R}%Endexpansion^{N+1}$, Semra Yurttançikmaz
Turkish Journal of Mathematics
In this paper, tangent bundle $TM$ of the hypersurface $M$ in $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n+1}$ has been studied. For hypersurface $M$ given by immersion $f:M\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n+1},$ considering the fact that $F=df:TM\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2n+2}$ is also immersion, $TM$ is treated as a submanifold of $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2n+2}.$ Firstly, an induced metric which is called rescaled induced metric has been defined on $TM,$ and the Levi-Civita connection has been calculated for this metric. Next, curvature tensors of tangent bundle $TM$ have been obtained. Finally, the orthonormal …
Some Applications Of Fractional Calculus For Analytic Functions,
2021
TÜBİTAK
Some Applications Of Fractional Calculus For Analytic Functions, Nesli̇han Uyanik, Shi̇geyoshi̇ Owa
Turkish Journal of Mathematics
For analytic functions $f\left( z\right) $ in the class $A_{n},$ fractional calculus (fractional integrals and fractional derivatives) $D_{z}^{\lambda }f\left( z\right) $ of order $\lambda $ are introduced. Applying $% D_{z}^{\lambda }f\left( z\right) $ for $f\left( z\right) \in A_{n},$ we introduce the interesting subclass $A_{n}\left( \alpha _{m},\beta ,\rho ,\lambda \right) $ of $A_{n}.$ The object of this paper is to discuss some properties of $f\left( z\right) $ concerning $D_{z}^{\lambda }f\left( z\right) .$
On The Paper ``A Study On (Strong) Order-Congruences In Ordered Semihypergroups",
2021
TÜBİTAK
On The Paper ``A Study On (Strong) Order-Congruences In Ordered Semihypergroups", Niovi Kehayopulu
Turkish Journal of Mathematics
Throughout the paper in the title by Jian Tang, Yanfeng Luo and Xiangyun Xie in Turk J Math 42 (2018) the following lemma has been used. Lemma: Let $(S,*)$ be a semihypergroup and $\rho$ an equivalence relation on S. Then $(i)$ If $\rho$ is a congruence, then $(S/\rho,\otimes)$ is a semihypergroup with respect to the hyperoperation $(a)_\rho\otimes (b)_\rho=\bigcup\limits_{c\in a*b} {(c)_\rho}$. $(ii)$ If $\rho$ is a strong congruence, then $(S/\rho,\otimes)$ is a semigroup with respect to the operation $(a)_\rho\otimes (b)_\rho=(c)_\rho$ for all $c\in a*b$.} The property (i) of the paper is certainly wrong as $\bigcup\limits_{c\in a*b} {(c)_\rho}$ is a subset of …
Moments And Zero Density Estimates For Dirichlet $L$-Functions,
2021
TÜBİTAK
Moments And Zero Density Estimates For Dirichlet $L$-Functions, Keiju Sono
Turkish Journal of Mathematics
In this paper, we estimate the density of zeros of primitive Dirichlet $L$-functions in the half-plane $\Re (s)>1/2$, under the assumption of a plausible conjecture on high moments of Dirichlet $L$-functions on the critical line. We conditionally improve the results of Huxley [9], Jutila [13], Heath-Brown [5, 6] and Bourgain [1].
On $(K,N)$ Power Quasi-Normal Operators,
2021
TÜBİTAK
On $(K,N)$ Power Quasi-Normal Operators, Salah Mecheri, Aissa Nasli Bakir
Turkish Journal of Mathematics
The aim of this paper is to present certain basic properties of some classes of nonnormal operators defined on a complex separable Hilbert space. Both of the normality of their integer powers and their relations with isometries are established. The ascent of such operators as well as other important related results are also established. The decomposition of such operators, their restrictions on invariant subspaces, and some spectral properties are also presented.
Optimization Of Mayer Functional In Problems With Discrete And Differential Inclusions And Viability Constraints,
2021
TÜBİTAK
Optimization Of Mayer Functional In Problems With Discrete And Differential Inclusions And Viability Constraints, Gülseren Çi̇çek, Eli̇mhan N. Mahmudov
Turkish Journal of Mathematics
This paper derives the optimality conditions for a Mayer problem with discrete and differential inclusions with viable constraints. Applying necessary and sufficient conditions of problems with geometric constraints, we prove optimality conditions for second order discrete inclusions. Using locally adjoint mapping, we derive Euler-Lagrange form conditions and transversality conditions for the optimality of the discrete approximation problem. Passing to the limit, we establish sufficient conditions to the optimal problem with viable constraints. Conditions ensuring the existence of solutions to the viability problems for differential inclusions of second order have been studied in recent years. However, optimization problems of second-order differential …
Sparse Polynomial Interpolation With Bernstein Polynomials,
2021
TÜBİTAK
Sparse Polynomial Interpolation With Bernstein Polynomials, Erdal İmamoğlu
Turkish Journal of Mathematics
We present an algorithm for interpolating an unknown univariate polynomial $f$ that has a $t$ sparse representation ($t
Reduced Limit Approach To Semilinear Pdes Involving The Fractional Laplacian With Measure Data,
2021
TÜBİTAK
Reduced Limit Approach To Semilinear Pdes Involving The Fractional Laplacian With Measure Data, Ratan Kumar Giri, Debajyoti Choudhuri
Turkish Journal of Mathematics
We study the following partial differential equation (PDE) \begin{align} \begin{split} (-\Delta)^s u + g(x,u) & = \mu\,\,\mbox{in}\,\,\Omega,\\ u & = 0\,\,\mbox{in}\,\,\mathbb{R}^N\setminus\Omega,\label{eqn_abs} \end{split} \end{align} where $(-\Delta)^s$ is the fractional Laplacian operator, $\Omega$ is a bounded domain in $\mathbb{R}^N$ with $\partial\Omega$ being the boundary of $\Omega$, $g(.,.)$ is a nonlinear function defined over $\Omega\times\mathbb{R}$. Let $(\mu_n)_n$ be a sequence of measure in $\Omega$. Assume that there exists a solution $u_n$ with data $\mu_n$, i.e. $u_n$ satisfies the equation (0.1) with $\mu=\mu_n$. We further assume that the sequence of measures weakly converges to $\mu$, while $(u_n)_n$ converges to $u$ in $L^1(\Omega)$. In general, …
Indecomposable Vector Bundles Via Monads On A Cartesian Product Of Projective Spaces,
2021
TÜBİTAK
Indecomposable Vector Bundles Via Monads On A Cartesian Product Of Projective Spaces, Damian Maingi
Turkish Journal of Mathematics
The existence of monads on products of projective spaces $P^{a_1}\times\cdots\times\ P^{a_n}$ is nontrivial. In this paper, we construct monads over the polycyclic variety $P^{2n+1}\times\ P^{2n+1}$, we prove that cohomology vector bundle associated to these monads is simple. We also construct a monad on $P^1\times P^1\times\ P^2$. We also study the vector bundles associated to monads and prove stability and simplicity.
The Kernel Spaces And Fredholmness Of Truncated Toeplitz Operators,
2021
TÜBİTAK
The Kernel Spaces And Fredholmness Of Truncated Toeplitz Operators, Xiaoyuan Yang, Ran Li, Yufeng Lu
Turkish Journal of Mathematics
In this paper, we study some conditions about invertible and Fredholm truncated Toeplitz operators which have unique symbols. For $f\in L^\infty$, if $A_f$ is a Fredholm operator, then $f _E\neq 0$ for any $E\subset \mathbb{T}$ with $ E >0$. Moreover \textnormal {ind} $(A_f)=0.$ In particular, if $A_f$ is invertible in $\mathfrak{L}(K_u^2)$, then $f$ is invertible in $L^\infty$. Besides, we give some results about the kernel spaces of truncated Toeplitz operators. For $f \in L^\infty$, we obtain the necessary and sufficient condition that the defect operator $I-A_f^*A_f$ of truncated Toeplitz operator $A_f$ meeting some conditions is compact on the model space …
A Fourth Order One Step Method For Numerical Solution Of Good Boussinesq Equation,
2021
TÜBİTAK
A Fourth Order One Step Method For Numerical Solution Of Good Boussinesq Equation, Emre Kirli, Dursun Irk
Turkish Journal of Mathematics
In this paper, we investigate the numerical solution of "good" Boussinesq equation by using the quartic B-spline Galerkin method for space discretization and the fourth order one-step method for time discretization.The proposed numerical scheme is analyzed for truncation error. Four test problems are studied. The accuracy and efficiency are measured by computing error norm $L_{\infty }$ and the order of convergence for the proposed method. The results of numerical experiments confirm that the proposed method has a higher accuracy.
Bounded Invertibility And Separability Of A Parabolic Type Singular Operator In The Space $L_{2}(R^{2})$,
2021
TÜBİTAK
Bounded Invertibility And Separability Of A Parabolic Type Singular Operator In The Space $L_{2}(R^{2})$, Mussakan Muratbekov, Madi Muratbekov, Ainash Suleimbekova
Turkish Journal of Mathematics
In this paper, we consider the operator of parabolic type $$ Lu=\frac{\partial u}{\partial t}-\frac{\partial^{2}u}{\partial x^{2}}+q(x)u, $$ in the space $L_{2}(R^{2})$ with a greatly growing coefficient at infinity. The operator is originally defined on $C_{0}^{\infty}(R^{2})$, where $C_{0}^{\infty}(R^{2})$ is the set of infinitely differentiable and compactly supported functions. \noindent Assume that the coefficient $q(x)$ is a continuous function in $R=(-\infty, \infty)$, and it can be a strongly increasing function at infinity. \noindent The operator $L$ admits closure in space $L_{2}(R^{2})$, and the closure is also denoted by $L$. \noindent In the paper, we proved the bounded invertibility of the operator $L$ in …
Singular Integral Operators And Maximal Functions With Hardy Space Kernels,
2021
TÜBİTAK
Singular Integral Operators And Maximal Functions With Hardy Space Kernels, Ahmad Al Salman
Turkish Journal of Mathematics
In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on $L^{p},1
3-Principalization Over S_3-Fields,
2021
TÜBİTAK
3-Principalization Over S_3-Fields, Siham Aouissi, Mohamed Talbi, Daniel C. Mayer, Moulay Chrif Ismaili
Turkish Journal of Mathematics
Let $p\equiv 1\,(\mathrm{mod}\,9)$ be a prime number and $\zeta_3$ be a primitive cube root of unity. Then $k=\mathbb{Q}(\sqrt[3]{p},\zeta_3)$ is a pure metacyclic field with group $\mathrm{Gal}(k/\mathbb{Q})\simeq S_3$. In the case that $k$ possesses a $3$-class group $C_{k,3}$ of type $(9,3)$, the capitulation of $3$-ideal classes of $k$ in its unramified cyclic cubic extensions is determined, and conclusions concerning the maximal unramified pro-$3$-extension $k_3^{(\infty)}$, that is the $3$-class field tower of $k$, are drawn.
