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On The Geometry Of Tangent Bundle Of A Hypersurface In $%%Tcimacro{\U{211d} }%%Beginexpansion\Mathbb{R}%Endexpansion^{N+1}$, Semra Yurttançikmaz
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, Nesli̇han Uyanik, Shi̇geyoshi̇ Owa
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", Niovi Kehayopulu
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, Keiju Sono
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, Salah Mecheri, Aissa Nasli Bakir
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, Gülseren Çi̇çek, Eli̇mhan N. Mahmudov
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, Erdal İmamoğlu
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, Ratan Kumar Giri, Debajyoti Choudhuri
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, Damian Maingi
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, Xiaoyuan Yang, Ran Li, Yufeng Lu
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, Emre Kirli, Dursun Irk
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 $L_{2}(R^{2})$, Mussakan Muratbekov, Madi Muratbekov, Ainash Suleimbekova
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, Ahmad Al Salman
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, Siham Aouissi, Mohamed Talbi, Daniel C. Mayer, Moulay Chrif Ismaili
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.
Some New Representations Of Hikami's Second-Order Mock Theta Function $\Mathfrak{D}_5(Q)$, Qiuxia Hu
Some New Representations Of Hikami's Second-Order Mock Theta Function $\Mathfrak{D}_5(Q)$, Qiuxia Hu
Turkish Journal of Mathematics
In this paper, a second-order mock theta function $\mathfrak{D}_5(q)$ given by Hikami [11] is studied. By using basic hypergeometric transformation formulae, we attain some new representations of Hikami's mock theta function $\mathfrak{D}_5(q)$. Meanwhile, dual nature of bilateral series associated to mock theta function $\mathfrak{D}_5(q)$ is also discussed.
On Estimation Of The Number Of Eigenvalues Of The Magnetic Schrödinger Operator In A Three-Dimensional Layer, Araz R. Aliyev, Elshad H. Eyvazov, Shahin Sh. Rajabov
On Estimation Of The Number Of Eigenvalues Of The Magnetic Schrödinger Operator In A Three-Dimensional Layer, Araz R. Aliyev, Elshad H. Eyvazov, Shahin Sh. Rajabov
Turkish Journal of Mathematics
In this paper, we study the magnetic Schrödinger operator in a three-dimensional layer. We obtain an estimate for the number of eigenvalues of this operator lying to the left of the essential spectrum threshold. We show that the magnetic Schrödinger operator to the left of the continuous spectrum threshold can have only a finite number of eigenvalues of infinite multiplicity.
A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan
A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan
Turkish Journal of Mathematics
In this paper, we obtain the existence--uniqueness of solution to the second-order linear Fredholm integro-differential equation (FIDE) with Dirichlet boundary condition by hybridizable discontinuous Galerkin (HDG) method. A key property of these methods is to eliminate all internal degrees of freedom and to construct a linear system that only includes globally coupled unknowns at the element interfaces. After designing and implementing HDG algorithm, we provide some necessary and sufficient conditions based on the stabilization parameter and kernel function to guarantee the existence-uniqueness of the approximate solution. Then, some numerical examples are carried out to assess the performance of the present …
Secondary Constructions Of (Non)-Weakly Regular Plateaued Functions Over Finite Fields, Si̇hem Mesnager, Ferruh Özbudak, Ahmet Sinak
Secondary Constructions Of (Non)-Weakly Regular Plateaued Functions Over Finite Fields, Si̇hem Mesnager, Ferruh Özbudak, Ahmet Sinak
Turkish Journal of Mathematics
Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We can distinguish two kinds of constructions of plateaued functions: secondary constructions and primary constructions. The first method uses already known functions to obtain new functions while the latter do not need to use previously constructed functions to obtain new functions. In this work, the first secondary constructions of (non)weakly regular plateaued (vectorial) functions are presented over the finite fields of odd characteristics. We also introduce some recursive constructions of (non)weakly regular …
Diameter Estimate For A Class Of Compact Generalized Quasi-Einstein Manifolds, Deng Yihua
Diameter Estimate For A Class Of Compact Generalized Quasi-Einstein Manifolds, Deng Yihua
Turkish Journal of Mathematics
In this paper, we discuss the lower diameter estimate for a class of compact generalized quasi-Einstein manifolds which are closely related to the conformal geometry. Using the Bochner formula and the Hopf maximum principle, we get a gradient estimate for the potential function of the manifold. Based on the gradient estimate, we get the lower diameter estimate for this class of generalized quasi-Einstein manifolds.
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Turkish Journal of Mathematics
In this research article, a novel $\Phi$-fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach' and Perov's fixed point theorems. While the $\Phi$-fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity …
Zero-Divisor Graphs Of Partial Transformation Semigroups, Kemal Toker
Zero-Divisor Graphs Of Partial Transformation Semigroups, Kemal Toker
Turkish Journal of Mathematics
Let $\mathcal P_{n}$ be the partial transformation semigroup on $X_{n}=\{1,2,\ldots ,n\}$. In this paper, we find the left zero-divisors, right zero-divisors and two sided zero-divisors of $\mathcal P_{n}$, and their numbers. For $n \geq 3$, we define an undirected graph $\Gamma(\mathcal P_{n})$ associated with $\mathcal P_{n}$ whose vertices are the two sided zero-divisors of $\mathcal P_{n}$ excluding the zero element $\theta$ of $\mathcal P_{n}$ with distinct two vertices $\alpha$ and $\beta$ joined by an edge in case $\alpha\beta=\theta =\beta\alpha$. First, we prove that $\Gamma(\mathcal P_{n})$ is a connected graph, and find the diameter, girth, domination number and the degrees of …
Axes In Non-Associative Algebras, Louis Rowen, Yoav Segev
Axes In Non-Associative Algebras, Louis Rowen, Yoav Segev
Turkish Journal of Mathematics
Fusion rules are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to axial algebras, introduced recently by Hall, Rehren and Shpectorov. Axial algebras, in turn, are closely related to $3$-transposition groups and Vertex operator algebras. In this paper we consider fusion rules for semisimple idempotents, following Albert in the power-associative case. We examine the notion of an axis in the non-commutative setting and show that the dimension $d$ of any algebra $A$ generated by a pair $a,b$ of (not necessarily Jordan) axes of respective types $(λ,δ)$ and $(λ',δ')$ must be at …
Finite Groups With Three Non-Abelian Subgroups, Bijan Taeri, Fatemeh Tayanloo Beyg
Finite Groups With Three Non-Abelian Subgroups, Bijan Taeri, Fatemeh Tayanloo Beyg
Turkish Journal of Mathematics
We characterize finite groups with exactly two nonabelian proper subgroups. When $G$ is nilpotent, we show that $G$ is either the direct product of a minimal nonabelian $p$-group and a cyclic $q$-group or a $2$-group. When $G$ is nonnilpotent supersolvable group, we obtain the presentation of $G$. Finally, when $G$ is nonsupersolvable, we show that $G$ is a semidirect product of a $p$-group and a cyclic group.
Global Existence And Blow-Up Of Solutions For Parabolic Equations Involving The Laplacian Under Nonlinear Boundary Conditions., Anass Lamaizi, Abdellah Zerouali, Omar Chakrone, Belhadj Karim
Global Existence And Blow-Up Of Solutions For Parabolic Equations Involving The Laplacian Under Nonlinear Boundary Conditions., Anass Lamaizi, Abdellah Zerouali, Omar Chakrone, Belhadj Karim
Turkish Journal of Mathematics
This paper is concerned with the existence and blow-up of solutions to the following linear parabolic equation: $ ~~ u_t - \Delta u +u = 0 \quad \text{ in } \Omega \times (0,T) $, under nonlinear boundary condition in a bounded domain $ \Omega \subset \mathbb{R}^n $, $n \geq 1$, with smooth boundary. We obtain a threshold result for the global existence of solutions, next we shall prove the existence time $T$ of solution is finite when the initial energy satisfies certain condition.
A Third-Order P-Laplacian Boundary Value Problem On An Unbounded Domain, Samuel Azubuike Iyase, Ogbu Famous Imaga
A Third-Order P-Laplacian Boundary Value Problem On An Unbounded Domain, Samuel Azubuike Iyase, Ogbu Famous Imaga
Turkish Journal of Mathematics
In this work, we apply Leray-Schauder continuation principle to establish the existence of at least one solution to the third order p-Laplacian boundary value problem on an unbounded domain of the form \begin{equation*} (w(t) \varphi_{p}( u^{\prime\prime}(t)))^{\prime} = K ( t, u(t) , u^{\prime}(t), u^{\prime\prime}(t) ) , t \in ( 0, \infty) \end{equation*} \begin{equation*} u(0)= 0, \, u^{\prime} (0) = \sum^{m}_{i=1} \alpha _{i} \int_{0}^{\xi_{i}} u(t) dt, \, \lim_{t \rightarrow\infty} ( w(t)\varphi_{p} ( u^{\prime \prime} (t)) = 0 \end{equation*} under the nonresonant condition $ \sum_{i=1}^{m} \alpha_{i} \xi^{2} \neq 2. $
Finite Topological Type Of Complete Finsler Gradient Shrinking Ricci Solitons, Mohamad Yar Ahmadi, Sina Hedayatian
Finite Topological Type Of Complete Finsler Gradient Shrinking Ricci Solitons, Mohamad Yar Ahmadi, Sina Hedayatian
Turkish Journal of Mathematics
In the present work it is shown that on a Finslerian space, a forward complete gradient shrinking Ricci soliton has finite topological type, provided either the Ricci scalar is bounded above or the Ricci scalar is bounded from below and injectivity radius is bounded away from zero.
Practical Stability Analysis Of Perturbed Fuzzy Control System Related To Unperturbed Fuzzy Control System, Coşkun Yakar, Betül Özbay Eli̇büyük
Practical Stability Analysis Of Perturbed Fuzzy Control System Related To Unperturbed Fuzzy Control System, Coşkun Yakar, Betül Özbay Eli̇büyük
Turkish Journal of Mathematics
The behavior of solutions of a perturbed fuzzy control system with respect to an original unperturbed fuzzy control system is investigated. Notions of practical stability, asymptotic stability and instability are introduced. Sufficient conditions of stability properties are given with the help of Lyapunov-like functions.
A Semi-Symmetric Metric Connection On Almost Contact B-Metric Manifolds, Şenay Bulut
A Semi-Symmetric Metric Connection On Almost Contact B-Metric Manifolds, Şenay Bulut
Turkish Journal of Mathematics
The object of the present paper is to study a semisymmetric metric connection on an almost contact $B-$metric manifold. We deduce a relation between the Levi-Civita connection and the semisymmetric metric connection on the considered manifold. We determined the class of the torsion tensor corresponding to the semisymmetric connection. We study Ricci-like solitons on almost contact $B-$metric manifolds with the semisymmetric connection. Finally, we give some examples to considered manifolds with the semisymmetric connection.
On The Paper "Regular Equivalence Relations On Ordered $*$-Semihypergroups", Niovi Kehayopulu
On The Paper "Regular Equivalence Relations On Ordered $*$-Semihypergroups", Niovi Kehayopulu
Turkish Journal of Mathematics
If $(S,\circ,\le)$ is an ordered hypersemigroup, an equivalence relation $\rho$ on $S$ is called congruence if $(a,b)\in\rho$ implies $(a\circ x, b\circ x)\in\rho$ and $(x\circ a, x\circ b)\in\rho$ for every $x\in S$; in the sense that for every $u\in a\circ x$ there exists $v\in b\circ x$ such that $(u,v)\in\rho$ and for every $u\in x\circ a$ there exists $v\in x\circ b$ such that $(u,v)\in\rho$. It has been proved in Turk J Math 2021(5) [On the paper "A study on (strong) order-congruences in ordered semihypergroups"] that if $S$ is an ordered hypersemigroup, then there exists a congruence $\rho$ on $S$ such that $S/\rho$ …