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On $H$-Antimagicness Of Cartesian Product Of Graphs, Martin Baca, Andrea Semanicova-Fenovcikova, Muhammad Awais Umar, Des Welyyanti
On $H$-Antimagicness Of Cartesian Product Of Graphs, Martin Baca, Andrea Semanicova-Fenovcikova, Muhammad Awais Umar, Des Welyyanti
Turkish Journal of Mathematics
A graph $G=(V(G),E(G))$ admits an $H$-covering if every edge in $E$ belongs to a~subgraph of $G$ isomorphic to $H$. A graph $G$ admitting an $H$-covering is called {\it $(a,d)$-$H$-antimagic} if there is a bijection $f:V(G)\cup E(G) \to \{1,2,\dots, V(G) + E(G) \}$ such that, for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H$-weights, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e),$ constitute an arithmetic progression with the initial term $a$ and the common difference $d$. In this paper we provide some sufficient conditions for the Cartesian product of graphs to be $H$-antimagic. We use partitions subsets of integers …
Worst-Case Large Deviations Upper Bounds For I.I.D. Sequencesunder Ambiguity, Mustafa Ç. Pinar
Worst-Case Large Deviations Upper Bounds For I.I.D. Sequencesunder Ambiguity, Mustafa Ç. Pinar
Turkish Journal of Mathematics
An introductory study of large deviations upper bounds from a worst-case perspective under parameter uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging min‒max (or max‒min) problems that admit some simplifications and some explicit results, mostly in the case of the normal probability law.
A Comparative Study Of Gauss‒Laguerre Quadrature And An Open Type Mixed Quadrature By Evaluating Some Improper Integrals, Pritikanta Patra, Debasish Das, Rajani Ballav Dash
A Comparative Study Of Gauss‒Laguerre Quadrature And An Open Type Mixed Quadrature By Evaluating Some Improper Integrals, Pritikanta Patra, Debasish Das, Rajani Ballav Dash
Turkish Journal of Mathematics
An open type mixed quadrature rule is constructed blending the anti-Gauss 3-point rule with Steffensen's 4-point rule. The analytical convergence of the mixed rule is studied. An adaptive integration scheme is designed based on the mixed quadrature rule. A comparative study of the mixed quadrature rule and the Gauss‒Laguerre quadrature rule is given by evaluating several improper integrals of the form $\int\limits_{0}^{\infty}e^{-x}f(x)dx$. The advantage of implementing mixed quadrature rule in developing an efficient adaptive integration scheme is shown by evaluating some improper integrals.
Various Centroids And Some Characterizations Of Catenary Rotation Hypersurfaces, Dong-Soo Kim, Young Ho Kim, Dae Won Yoon
Various Centroids And Some Characterizations Of Catenary Rotation Hypersurfaces, Dong-Soo Kim, Young Ho Kim, Dae Won Yoon
Turkish Journal of Mathematics
We study positive $C^1$ functions $z=f(x), x=(x_1,\cdots, x_n)$ defined on the $n$-dimensional Euclidean space $ \mathbb R^{n}$. For $x=(x_1,\cdots, x_n)$ with nonzero numbers $x_1, \cdots, x_n$, we consider the rectangular domain $I(x)=I(x_1)\times \cdots \times I(x_n)\subset \mathbb R^{n}$, where $I(x_i)= [0, x_i]$ if $x_i>0$ and $I(x_i)= [x_i,0]$ if $x_i
On The Dimension Of Vertex Labeling Of $K$-Uniform Dcsl Of An Even Cycle, Nageswara Rao Karrey, Germina Kizhekekunnel Augustine
On The Dimension Of Vertex Labeling Of $K$-Uniform Dcsl Of An Even Cycle, Nageswara Rao Karrey, Germina Kizhekekunnel Augustine
Turkish Journal of Mathematics
In this paper, we discuss the lower bound for the dcsl index $ \delta_k $ of a $k$-uniform dcsl of even cycle $ C_{2n},\ n\geq 2 $, in terms of the dimension of a poset and prove that $dim({\mathscr{F}})\leq \delta_k(C_{2n}) $, where ${\mathscr{F}}$ is the range of any $k$-uniform dcsl $ f $ of $ C_{2n},\ n\geq 2 $.
A Study Of The Tubular Surfaces Constructed By Thespherical Indicatrices In Euclidean $3-$Space, Fatma Ateş, Erdem Kocakuşakli, İsmai̇l Gök, Yusuf Yayli
A Study Of The Tubular Surfaces Constructed By Thespherical Indicatrices In Euclidean $3-$Space, Fatma Ateş, Erdem Kocakuşakli, İsmai̇l Gök, Yusuf Yayli
Turkish Journal of Mathematics
A basic goal of this paper is to investigate the tubular surface constructed by the spherical indicatrices of any spatial curve in the Euclidean $3-$ space. This kind of tubular surface is designed for the alternative moving frame $\{N,C,W\}$ in conjunction with finding a relationship between the tubular surfaces and their special curves, such as geodesic curves, asymptotic curves, and minimal curves. The minimal curve $\gamma $ on a surface is defined by the property that its fundamental coefficients satisfy Eq. (3.7) along the curve $\gamma $. At the end of this article, we exemplify these curves on the tubular …
Second Hankel Determinant For Certain Subclasses Of Bi-Univalent Functions Involving Chebyshev Polynomials, Hali̇t Orhan, Evri̇m Toklu, Ekrem Kadioğlu
Second Hankel Determinant For Certain Subclasses Of Bi-Univalent Functions Involving Chebyshev Polynomials, Hali̇t Orhan, Evri̇m Toklu, Ekrem Kadioğlu
Turkish Journal of Mathematics
In this paper our purpose is to find the upper bound estimate for the second Hankel determinant $ a_{2}a_{4}-a_{3}^{2} $ for functions defined by convolution belonging to the class $\mathcal{N}_{\sigma}^{\mu,\delta}(\lambda,t)$ by using Chebyshev polynomials.
Existence Of Maximal Ideals In Leavitt Path Algebras, Songül Esi̇n, Müge Kanuni̇ Er
Existence Of Maximal Ideals In Leavitt Path Algebras, Songül Esi̇n, Müge Kanuni̇ Er
Turkish Journal of Mathematics
Let $E$ be an arbitrary directed graph and let $L$ be the Leavitt path algebra of the graph $E$ over a field $K$. The necessary and sufficient conditions are given to assure the existence of a maximal ideal in $L$ and also the necessary and sufficient conditions on the graph that assure that every ideal is contained in a maximal ideal are given. It is shown that if a maximal ideal $M$ of $L$ is nongraded, then the largest graded ideal in $M$, namely $gr(M)$, is also maximal among the graded ideals of $L$. Moreover, if $L$ has a unique …
Second Hankel Determinant For A Subclass Of Analytic Bi-Univalent Functions Defined By Subordination, Ahmad Motamednezhad, Teodor Bulboaca, Ebrahim Analouei Adegani, Nesa Dibagar
Second Hankel Determinant For A Subclass Of Analytic Bi-Univalent Functions Defined By Subordination, Ahmad Motamednezhad, Teodor Bulboaca, Ebrahim Analouei Adegani, Nesa Dibagar
Turkish Journal of Mathematics
In this work with a different technique we obtain upper bounds of the functional $\left a_2a_4-a_3^2\right $ for functions belonging to a comprehensive subclass of analytic bi-univalent functions, which is defined by subordinations in the open unit disk. Moreover, our results extend and improve some of the previously known ones.
Onthe Global $L^{P}$ Boundedness Of A General Classof $H$-Fourier Integral Operators, Chafika Amel Aitemrar, Abderrahmane Senoussaoui
Onthe Global $L^{P}$ Boundedness Of A General Classof $H$-Fourier Integral Operators, Chafika Amel Aitemrar, Abderrahmane Senoussaoui
Turkish Journal of Mathematics
In this paper, we study the $L^{p}$-boundedness of a class of semiclassical Fourier integral operators.
Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations, Feifei Du, Lynn Erbe, Baoguo Jia, Allan Peterson
Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations, Feifei Du, Lynn Erbe, Baoguo Jia, Allan Peterson
Turkish Journal of Mathematics
In this paper we study the Caputo and Riemann--Liouville nabla $(q,h)$-fractional difference equation and obtain the following two main results: Assume $0
Spectral Expansion For The Singular Dirac System With Impulsive Conditions, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Spectral Expansion For The Singular Dirac System With Impulsive Conditions, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.
Evaluations Of Some Terminating Hypergeometric $_2f_1(2)$ Series With Applications, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
Evaluations Of Some Terminating Hypergeometric $_2f_1(2)$ Series With Applications, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
Turkish Journal of Mathematics
Explicit expressions for the hypergeometric series $_2F_1(-n, a; 2a\pm j;2)$ and $_2F_1(-n, a; -2n \pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for $ j \leq 5$ derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating $_3F_2(2)$ series and the confluent hypergeometric function $_1F_1(x)$.
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Turkish Journal of Mathematics
The aim of this paper is to estimate the shape of an unknown part of the boundary of a geometrical domain. The identification technique used to estimate this part is the observation of the solution of a diffusion problem on the known part of this boundary. This technique is based on the sentinels theory.
Quantitative Voronovskaya- And Grüss-Voronovskaya-Type Theorems By The Blending Variant Of Szã¡Sz Operators Including Brenke-Type Polynomials, Purshottam Narain Agrawal, Behar Baxhaku, Ruchi Chauhan
Quantitative Voronovskaya- And Grüss-Voronovskaya-Type Theorems By The Blending Variant Of Szã¡Sz Operators Including Brenke-Type Polynomials, Purshottam Narain Agrawal, Behar Baxhaku, Ruchi Chauhan
Turkish Journal of Mathematics
The present paper aims to investigate a class of linear positive operators by combining Szász-Jain operators and Brenke polynomials and studies their approximation properties. We also prove quantitative Voronovskaya-type results and establish Grüss-Voronovskaja-type theorem. Furthermore, we show the rate of convergence for Szász-Jain-Brenke operators to functions having derivative of bounded variation and not having derivative of bounded variation by illustrative graphics using MATLAB.
On $N$-Absorbing $\Delta$-Primary Ideals, Gülşen Ulucak, Ünsal Teki̇r, Suat Koç
On $N$-Absorbing $\Delta$-Primary Ideals, Gülşen Ulucak, Ünsal Teki̇r, Suat Koç
Turkish Journal of Mathematics
Let $R$ be a commutative ring with nonzero identity and $n$ be a positive integer. In this paper, we study the concepts of $n$-absorbing $\delta $-primary ideals and weakly $n$-absorbing $\delta$-primary ideals, which are the generalizations of $\delta$-primary ideals and weakly $\delta$-primary ideals, respectively. We introduce the concepts of $n$-absorbing $\delta$-primary ideals and weakly $n$-absorbing $\delta$-primary ideals. Moreover, we give many properties of these new types of ideals and investigate the relations between these structures.
Pythagorean Triples Containing Generalized Lucas Numbers, Zafer Şi̇ar, Refi̇k Keski̇n
Pythagorean Triples Containing Generalized Lucas Numbers, Zafer Şi̇ar, Refi̇k Keski̇n
Turkish Journal of Mathematics
Let $P$ and $Q$ be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: $U_{0}(P,Q)=0,U_{1}(P,Q)=1,$ and $ U_{n+1}(P,Q)=PU_{n}(P,Q)+QU_{n-1}(P,Q)$ for $n\geq 1$ and $ V_{0}(P,Q)=2,V_{1}(P,Q)=P,$ and $V_{n+1}(P,Q)=PV_{n}(P,Q)+QV_{n-1}(P,Q)$ for $n\geq 1,$ respectively. In this paper, we assume that $P$ and $Q$ are relatively prime odd positive integers and $P^{2}+4Q>0.$ We determine all indices $n$ such that $U_{n}=(P^{2}+4Q)x^{2}.$ Moreover, we determine all indices $n$ such that $(P^{2}+4Q)U_{n}=x^{2}.$ As a result, we show that the equation $V_{n}^{2}(P,1)+V_{n+1}^{2}(P,1)=x^{2}$ has solution only for $n=2,$ $P=1,$ $x=5$ and $V_{n+1}^{2}(P,-1)=V_{n}^{2}(P,-1)+x^{2}$ has no solutions. Moreover, we solve some Diophantine equations.
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Turkish Journal of Mathematics
In this paper, the authors study some subordination and superordination properties for classes of $p$-valent meromorphic, analytic, and univalent functions associated with a linear operator $\mathfrak{L}_{p,\lambda}^{m,\ell}(a,c,\mu)$ of the Erdélyi-Kober type. Connections with several earlier results are also pointed out.
A New Proof Of A Harnack Inequality For The Curve Shortening Flow, Mihai Bailesteanu
A New Proof Of A Harnack Inequality For The Curve Shortening Flow, Mihai Bailesteanu
Turkish Journal of Mathematics
We offer a new approach for determining Harnack quantities for the curve shortening flow and we show how, following this procedure, one can obtain Hamilton's Harnack inequality for this flow $\kappa_t+\frac{1}{2t}\kappa\geq\frac{\kappa_s^2}{\kappa}$, where $\kappa$ is the curvature of the curve being deformed by the flow.
Convergence And Gundy's Decomposition For Noncommutative Quasi-Martingales, Congbian Ma, Ping Li, Youliang Hou
Convergence And Gundy's Decomposition For Noncommutative Quasi-Martingales, Congbian Ma, Ping Li, Youliang Hou
Turkish Journal of Mathematics
In this paper, we prove the bilaterally almost uniformly convergence of bounded $L_1(\mathcal{M})$-noncommutative quasi-martingales. We also prove Gundy's decomposition for noncommutative quasi-martingales. As an application, we prove that every relatively weakly compact quasi-martingale difference sequence in $L_1(\mathcal{M},\tau)$ whose sequence of norms is bounded away from zero is 2-co-lacunary.
Unconditional Wavelet Bases In Lebesgue Spaces, Yan Zhang, Yun Zhang Li
Unconditional Wavelet Bases In Lebesgue Spaces, Yan Zhang, Yun Zhang Li
Turkish Journal of Mathematics
In this paper, we prove that an orthonormal wavelet basis associated with a general isotropic expansive matrix must be an unconditional basis for all $L^{p}$(ℝ${}^{d})$ with $1$<$p$<$\infty$, provided the wavelet functions satisfy some usual conditions.
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Turkish Journal of Mathematics
Rotation minimizing (RM) vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even when the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed into a Riemannian manifold are studied when the ambient manifold is the Euclidean 3-space, the hyperbolic 3-space, and a Kähler manifold.
On The $J$-Reflexive Operators, Parviz Sadat Hosseini, Bahmann Yousefi
On The $J$-Reflexive Operators, Parviz Sadat Hosseini, Bahmann Yousefi
Turkish Journal of Mathematics
A bounded linear operator $T$ on a Banach space $X$ is $J$-reflexive if every bounded operator on $X$ that leaves invariant the sets $J(T,x)$ for all $x$ is contained in the closure of $orb(T)$ in the strong operator topology. We discuss some properties of $J$-reflexive operators. We also give and prove some necessary and sufficient conditions under which an operator is $J$-reflexive. We show that isomorphisms preserve $J$-reflexivity and some examples are considered. Finally, we extend the $J$-reflexive property in terms of subsets.
Prime-Valent Arc-Transitivebasic Graphs With Order $4p$ Or $4p^2$, Hailin Liu
Prime-Valent Arc-Transitivebasic Graphs With Order $4p$ Or $4p^2$, Hailin Liu
Turkish Journal of Mathematics
A graph $\Ga$ is called $G$-basic if $G$ is quasiprimitive or bi-quasiprimitive on the vertex set of $\Ga$, where $G\leq\Aut\Ga$. In this paper, we complete the classification of $r$-valent arc-transitive basic graphs with order $4p$ or $4p^2$, where $p$ and $r$ are odd primes.
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Nisar
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Nisar
Turkish Journal of Mathematics
The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.
Invariant Subspaces Of Operators Quasi-Similar To L-Weakly And M-Weaklycompact Operators, Erdal Bayram
Invariant Subspaces Of Operators Quasi-Similar To L-Weakly And M-Weaklycompact Operators, Erdal Bayram
Turkish Journal of Mathematics
Let T be an L-weakly compact operator defined on a Banach lattice E without order continuous norm. We prove that the bounded operator S defined on a Banach space X has a nontrivial closed invariant subspace if there exists an operator in the commutant of S that is quasi-similar to T. Additively, some similar and relevant results are extended to a larger classes of operators called super right-commutant. We also show that quasi-similarity need not preserve L-weakly or M-weakly compactness.
On Product And Golden Stuctures And Harmonicity, Sadetti̇n Erdem
On Product And Golden Stuctures And Harmonicity, Sadetti̇n Erdem
Turkish Journal of Mathematics
In this work, almost product and almost golden structures are studied. Conditions for those structures being integrable and parallel are investigated. Moreover, the harmonicity of a map between almost product or almost golden manifolds with pure or hyperbolic metric is discussed under certain conditions.
On Oscillation Of Integro-Differential Equations, Said R. Grace, Ağacik Zafer
On Oscillation Of Integro-Differential Equations, Said R. Grace, Ağacik Zafer
Turkish Journal of Mathematics
We study the oscillatory behavior of solutions for integro-differential equations of the form $$x'(t) = e(t) -\int_0^t (t-s)^{\alpha-1}k(t, s)f(s, x(s))\, {\rm ds},\quad t\geq 0,$$ where $0
On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems, Tüba Gülşen, Etibar Sadi Panakhov
On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems, Tüba Gülşen, Etibar Sadi Panakhov
Turkish Journal of Mathematics
In this study, we discuss the inverse spectral problem for the energy-dependent Schrödinger equation on a finite interval. We construct an isospectrality problem and obtain some relations between constants in boundary conditions of the problems that constitute isospectrality. Above all, we obtain degeneracy of $ K(x,t)-K_{0}{ (x,t)}$ and $L(x,t)-L_{0} (x,t)$ by using a different approach. Some of the main results of our study coincide with results reported by Jodeit and Levitan. However, the method to obtain degeneracy is completely different. Furthermore, we consider all above results for the nonisospectral case.
Reducing Subspaces Of Toeplitz Operators On Dirichlet Type Spaces Of The Bidisk, Hongzhao Lin
Reducing Subspaces Of Toeplitz Operators On Dirichlet Type Spaces Of The Bidisk, Hongzhao Lin
Turkish Journal of Mathematics
The reducing subspaces of Toeplitz operators $T_{z_1^N}$(or $T_{z_2^N}$), $T_{z_1^Nz_2^N}$, and $T_{z_1^Nz_2^M}$ on Dirichlet type spaces of the bidisk ${\mathcal{D}}_\alpha({{{\mathbb{D}}}^{2}})$ are described, which extends the results for the corresponding operators on the Bergman space of the bidisk.