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Dissipative Canonical Type Differential Operators For First Order, Ruki̇ye Öztürk Mert, Zameddi̇n İsmai̇lov, Pembe İpek Al
Dissipative Canonical Type Differential Operators For First Order, Ruki̇ye Öztürk Mert, Zameddi̇n İsmai̇lov, Pembe İpek Al
Turkish Journal of Mathematics
In this paper, using the Calkin-Gorbachuk method, the general form of all maximally dissipative extensions of the minimal operator generated by the first order linear symmetric canonical type quasi-differential expression in the weighted Hilbert space of vector functions has been found. Also, the spectrum set of these extensions has been investigated.
Conceptions On Topological Transitivity In Products And Symmetric Products, Anahi Rojas, Franco Barragan, Sergio Macías
Conceptions On Topological Transitivity In Products And Symmetric Products, Anahi Rojas, Franco Barragan, Sergio Macías
Turkish Journal of Mathematics
Having a finite number of topological spaces $X_i$ and functions $f_i : X_i \to X_i$, and considering one of the following classes of functions: exact, transitive, strongly transitive, totally transitive, orbit-transitive, strictly orbittransitive, $\omega$-transitive, mixing, weakly mixing, mild mixing, chaotic, exactly Devaney chaotic, minimal, backward minimal, totally minimal, $TT_{++}$, scattering, Touhey or an $F$ -system, in this paper, we study dynamical behaviors of the systems $(X_i,f_i)$, $(\prod X_i,\prod f_i)$, $(\mathcal{F}_n(\prod X_i),\mathcal{F}_n(\prod f_i))$, and $(\mathcal{F}_n(X_i),\mathcal{F}_n(f_i))$.
On Connected Tetravalent Normal Edge-Transitive Cayley Graphs Of Non-Abelian Groups Of Order 5p2, Soghra Khazaei, Hesam Sharifi
On Connected Tetravalent Normal Edge-Transitive Cayley Graphs Of Non-Abelian Groups Of Order 5p2, Soghra Khazaei, Hesam Sharifi
Turkish Journal of Mathematics
Our aim in this paper is to investigate graph automorphism and group automorphism determining all connected tetravalent normal edge transitive Cayley graphs on non-Abelian groups of order 5p2 with respect to tetravalent sets and same-order elements, where p is a prime number and its Sylow p-subgroup is cyclic.
Some Results Of K-Frames And Their Multipliers, Mitra Shamsabadi, Ali Akbar Arefijamaal
Some Results Of K-Frames And Their Multipliers, Mitra Shamsabadi, Ali Akbar Arefijamaal
Turkish Journal of Mathematics
K-frames are strong tools for the reconstruction of elements from range of a bounded linear operator K on a separable Hilbert space H. In this paper, we study some properties of K-frames and introduce the K-frame multipliers. We also focus on representing elements from the range of K by K-frame multipliers.
A New Method For Obtaining The Inconsistent Elements In A Decision Table Based On Dominance Principle, Yasemen Uçan, Ahmet Topal, Ni̇lgün Güler Bayazit
A New Method For Obtaining The Inconsistent Elements In A Decision Table Based On Dominance Principle, Yasemen Uçan, Ahmet Topal, Ni̇lgün Güler Bayazit
Turkish Journal of Mathematics
In this study,using only the dominance relation,we propose a set defining inconsistent elements in the decision table. Then, we show the accuracy of our proposition with an example. We also express the computational complexity comparisons of the proposed method with general method in terms of the number of set intersection operations and the real number comparison operations.
Geodesic Motions In So(2,1), İsmet Ayhan
Geodesic Motions In So(2,1), İsmet Ayhan
Turkish Journal of Mathematics
In this study,we have considered the rotational motions of a particle around the origin of the unit 2-sphere $S_2^2$ with constant angular velocity in semi-Euclidean 3-spacewithindextwo $E^3_2$, namely geodesic motions of $SO(2,1)$. Then we have obtained the vector and the matrix representations of the spherical rotations around the origin of a particle on $S_2^2$. Furthermore, we consider some relations between semi-Riemann spaces $SO(2,1)$ and $T_1S_2^2$ such as diffeomorphism and isometry. We have obtained the system of differential equations giving geodesics of Sasaki semi-Riemann manifold $(T_1S_2^2,g^S)$ . Moreover, we consider the stationary motion of a particle on $S_2^2$ corresponding to one …
Bounds For A New Subclass Of Bi-Univalent Functions Subordinate To The Fibonacci Numbers, Şahsene Altinkaya
Bounds For A New Subclass Of Bi-Univalent Functions Subordinate To The Fibonacci Numbers, Şahsene Altinkaya
Turkish Journal of Mathematics
In this investigation, by using a relation of subordination, we define a new subclass of analytic bi-univalent functions associated with the Fibonacci numbers. Moreover, we survey the bounds of the coefficients for functions in this class.
Nonnull Curves With Constant Weighted Curvature In Lorentz-Minkowski Plane With Density, Mustafa Altin, Ahmet Kazan, Haci Bayram Karadağ
Nonnull Curves With Constant Weighted Curvature In Lorentz-Minkowski Plane With Density, Mustafa Altin, Ahmet Kazan, Haci Bayram Karadağ
Turkish Journal of Mathematics
In this paper, the parametric expressions of spacelike and timelike curves with constant weighted curvature for some cases of $a$ and $b$ in Lorentz-Minkowski plane with density $e^{ax+by}$ are obtained.
On Solvability Of Inverse Problem For One Equation Of Fourth Order, Aysel Ramazanova Telman Qizi, Yashar Mehreliyev Topush Oglu
On Solvability Of Inverse Problem For One Equation Of Fourth Order, Aysel Ramazanova Telman Qizi, Yashar Mehreliyev Topush Oglu
Turkish Journal of Mathematics
The work is devoted to study the existence and uniqueness of the classical solution of the inverse boundary value problem of determining the lowest coefficient in one fourth order equation. The original problem is reduced to an equivalent problem. The existence and uniqueness of the integral equation are proved by means of the contraction mappings principle, and we obtained that this solution is unique for a boundary value problem. Further, using these facts, we prove the existence and uniqueness of the classical solution for this problem.
Nonlinear Variants Of The Generalized Filbert And Lilbert Matrices, Emrah Kiliç, Si̇bel Koparal, Neşe Ömür
Nonlinear Variants Of The Generalized Filbert And Lilbert Matrices, Emrah Kiliç, Si̇bel Koparal, Neşe Ömür
Turkish Journal of Mathematics
In this paper, we present variants of the generalized Filbert and Lilbert matrices by products of the general Fibonacci and Lucas numbers whose indices are in certain nonlinear forms of the indices with certain integer parameters. We derive explicit formulæ for inverse matrix, LU -decomposition and inverse matrices $L^{-1}$ and $U^{-1}$ for all matrices. Generally, we present $q$-versions of these matrices and their related results.
A Class Of Fredholm Equations And Systems Of Equations Related To The Kontorovich-Lebedev And The Fourier Integral Transforms, Trinh Tuan, Nguyen Thanh Hong
A Class Of Fredholm Equations And Systems Of Equations Related To The Kontorovich-Lebedev And The Fourier Integral Transforms, Trinh Tuan, Nguyen Thanh Hong
Turkish Journal of Mathematics
In this article, we solve in closed form a class of Fredholm integral equations and systems of Fredholm integral equations with nondegenerate kernels by using techniques of convolutions and generalized convolutions related to the Kontorovich-Lebedev, Fourier sine, and Fourier cosine integral transforms.
Representations And Properties Of A New Family Of $\Omega$-Caputofractional Derivatives, Abdullah Akkurt, Joel Esteban Restrepo, Hüseyi̇n Yildirim
Representations And Properties Of A New Family Of $\Omega$-Caputofractional Derivatives, Abdullah Akkurt, Joel Esteban Restrepo, Hüseyi̇n Yildirim
Turkish Journal of Mathematics
In the most general case of $\omega$-weights, some normed functional spaces $% X_{\omega}^{p}(a,b)( 1\leq p\leq\infty)$, $AC_{\gamma,\omega}^n[a,b]$ and a generalization of the fractional integro-differentiation operator are introduced and analyzed. The boundedness of the $\omega$-weighted fractional operator over $X_{\omega}^{p}(a,b)$ is proved. Some theorems and lemmas on the properties of the invertions of the mentioned operator and several representations of functions from $AC_{\gamma,\omega}^n[a,b]$ are established. A general $\omega$-weighted Caputo fractional derivative of order $\alpha$ is studied over $AC_{\gamma,\omega}^n[a,b]$. Some representations and other properties of this fractional derivative are proved. Some conclusions are presented.
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.
The Bochner-Convolution Integral For Generalized Functional-Valued Functions Of Discrete-Time Normal Martingales, Chen Jinshu
The Bochner-Convolution Integral For Generalized Functional-Valued Functions Of Discrete-Time Normal Martingales, Chen Jinshu
Turkish Journal of Mathematics
Let $M$ be a discrete-time normal martingale satisfying some mild conditions, $\mathcal{S}(M)\subset L^2(M)\subset\mathcal{S}^*(M)$ be the Gel'fand triple constructed from the functionals of $M$. As is known, there is no usual multiplication in $\mathcal{S}^*(M)$ since its elements are continuous linear functionals on $\mathcal{S}(M)$. However, by using the Fock transform, one can introduce convolution in $\mathcal{S}^*(M)$, which suggests that one can try to introduce a type of integral of an $\mathcal{S}^*(M)$-valued function with respect to an $\mathcal{S}^*(M)$-valued measure in the sense of convolution. In this paper, we just define such type of an integral. First, we introduce a class of $\mathcal{S}^*(M)$-valued measures …
Some Uncertainty Inequalities Related To The Multivariate Laguerre Function, Lotfi Kamoun, Rim Selmi
Some Uncertainty Inequalities Related To The Multivariate Laguerre Function, Lotfi Kamoun, Rim Selmi
Turkish Journal of Mathematics
In this paper, an analogous of the Heisenberg's inequality is established and three inequalities that constitute local uncertainty principle for the generalized Fourier-Laguerre transform in several variables are developed.
Oscillation Criteria For Higher-Order Neutral Type Difference Equations, Turhan Köprübaşi, Zafer Ünal, Yaşar Bolat
Oscillation Criteria For Higher-Order Neutral Type Difference Equations, Turhan Köprübaşi, Zafer Ünal, Yaşar Bolat
Turkish Journal of Mathematics
In this paper, oscillation criteria are obtained for higher-order neutral-type nonlinear delay difference equations of the form% \begin{equation} \Delta (r_{n}(\Delta ^{k-1}(y_{n}+p_{n}y_{\tau _{n}}))+q_{n}f(y_{\sigma _{n}})=0\text{, }n\geq n_{0}\text{,} \tag{0.1} \end{equation}% where $r_{n},p_{n},q_{n}\in \lbrack n_{0},\infty ),$ $r_{n}>0$, $q_{n}>0$; $% 0\leq p_{n}\leq p_{0}0$; $\tau _{\sigma }=\sigma _{\tau }$; $\frac{f(u)}{u}\geq m>0$ for $u\neq 0$. Moreover, we provide some examples to illustrate our main results.
A Class Of Warped Product Submanifolds Of Kenmotsu Manifolds, Shyamal Kumar Hui, Mica S. Stankovic, Joydeb Roy, Tanumoy Pal
A Class Of Warped Product Submanifolds Of Kenmotsu Manifolds, Shyamal Kumar Hui, Mica S. Stankovic, Joydeb Roy, Tanumoy Pal
Turkish Journal of Mathematics
In 2018 Naghi et al.studied warped product skew CR-submanifold of the form $M=M_1\times_f M_\perp$ of a Kenmotsu manifold $\bar{M}$ (throughout the paper), where $M_1=M_T\times M_\theta$ and $M_T, M_\perp, M_\theta$ represents invariant, antiinvariant, proper slant submanifold of $\bar{M}$. Next, in 2019 Hui et al. studied another class of warped product skew CR-submanifold of the form $M=M_2\times_fM_T$ of $\bar{M}$, where $M_2=M_\perp\times M_\theta$. The present paper deals with the study of a class of warped product submanifold of the form $M=M_3\times_fM_\theta$ of $\bar{M}$, where $M_3=M_T\times M_\perp$ and $M_T, M_\perp, M_\theta$ represents invariant, antiinvariant and proper pointwise slant submanifold of $\bar{M}$ . A characterization …
Stability In Commutative Rings, Başak Ay Saylam
Stability In Commutative Rings, Başak Ay Saylam
Turkish Journal of Mathematics
Let $R$ be a commutative ring with zero-divisors and $I$ an ideal of $R$. $I$ is said to be ES-stable if $JI=I^2$ for some invertible ideal $J \subseteq I$, and $I$ is said to be a weakly ES-stable ideal if there is an invertible fractional ideal $J$ and an idempotent fractional ideal $E$ of $R$ such that $I=JE$. We prove useful facts for weakly ES-stability and investigate this stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?
Fourth Order Differential Operators With Distributional Potentials, Eki̇n Uğurlu, Elgi̇z Bairamov
Fourth Order Differential Operators With Distributional Potentials, Eki̇n Uğurlu, Elgi̇z Bairamov
Turkish Journal of Mathematics
In this paper, regular and singular fourth order differential operators with distributional potentials are investigated. In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied. These symmetric operators are considered as acting on the single and direct sum Hilbert spaces. The latter one consists of three Hilbert spaces such that a squarely integrable space and two spaces of complex numbers. Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single …
Existence And Uniqueness Of Solutions For Nonlinear Caputo Fractional Difference Equations, Churong Chen, Martin Bohner, Baoguo Jia
Existence And Uniqueness Of Solutions For Nonlinear Caputo Fractional Difference Equations, Churong Chen, Martin Bohner, Baoguo Jia
Turkish Journal of Mathematics
We study two cases of nabla fractional Caputo difference equations. Our main tool used is a Banach fixed pointtheorem, which allows us to give some existence and uniqueness theorems of solutions for discrete fractional Caputo equations. In addition, we develop the existence results for delta fractional Caputo difference equations, which correct ones obtained in Chen and Zhou. We present two examples to illustrate our main results.
On Bishop Frame Of A Pseudo Null Curve In Minkowski Space-Time, Jelena Djordjevic, Emilija Nesovic
On Bishop Frame Of A Pseudo Null Curve In Minkowski Space-Time, Jelena Djordjevic, Emilija Nesovic
Turkish Journal of Mathematics
In this paper, we introduce the Bishop frame of a pseudo null curve $\alpha$ in Minkowski space-time. We obtain the Bishop frame's equations and the relation between the Frenet frame and the Bishop frame. We find the third order nonlinear differential equation whose particular solutions determine the form of the Bishop curvatures. By using space-time geometric algebra, we derive the Darboux bivectors $D$ and $\tilde{D}$ of the Frenet and the Bishop frame of $\alpha$, respectively. We give geometric interpretations of the Frenet and the Bishop curvatures of $\alpha$ in terms of areas of the projections of the corresponding Darboux bivectors …
Bertrand And Mannheim Curves Of Framed Curves In The 3-Dimensional Euclidean Space, Shun'ichi Honda, Masatomo Takahashi
Bertrand And Mannheim Curves Of Framed Curves In The 3-Dimensional Euclidean Space, Shun'ichi Honda, Masatomo Takahashi
Turkish Journal of Mathematics
A Bertrand curve is a space curve whose principal normal line is the same as the principal normal line of another curve. On the other hand, a Mannheim curve is a space curve whose principal normal line is the same as the binormal line of another curve. By definitions, another curve is a parallel curve with respect to the direction of the principal normal vector. Even if that is the regular case, the existence conditions of the Bertrand and Mannheim curves seem to be wrong in some previous research. Moreover, parallel curves may have singular points. As smooth curves with …
Inverse Problems For Differential Operators With Two Delays Larger Than Half The Length Of The Interval And Dirichlet Conditions, Biljana Vojvodic, Milenko Pikula, Vladimir Vladicic, Fatma Ayça Çeti̇nkaya
Inverse Problems For Differential Operators With Two Delays Larger Than Half The Length Of The Interval And Dirichlet Conditions, Biljana Vojvodic, Milenko Pikula, Vladimir Vladicic, Fatma Ayça Çeti̇nkaya
Turkish Journal of Mathematics
This paper deals with nonself-adjoint second-order differential operators with two constant delays from $\left[\frac{\pi}{2}, \pi\right)$ and two real-valued potentials from $L_{2} [0,\pi]$. An inverse spectral problem of recovering operators from the spectra of four boundary value problems is studied.
Solution Of Nonlinear Ordinary Differential Equations With Quadratic And Cubic Terms By Morgan-Voyce Matrix-Collocation Method, Mehmet Tarakçi, Mustafa Özel, Mehmet Sezer
Solution Of Nonlinear Ordinary Differential Equations With Quadratic And Cubic Terms By Morgan-Voyce Matrix-Collocation Method, Mehmet Tarakçi, Mustafa Özel, Mehmet Sezer
Turkish Journal of Mathematics
Nonlinear differential equations have many applications in different science and engineering disciplines. However, a nonlinear differential equation cannot be solved analytically and so must be solved numerically. Thus, we aim to develop a novel numerical algorithm based on Morgan-Voyce polynomials with collocation points and operational matrix method to solve nonlinear differential equations. In the our proposed method, the nonlinear differential equations including quadratic and cubic terms having the initial conditions are converted to a matrix equation. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB. The solution of this method for …
A Simple Derivation Of The Refined Sphere Packing Bound Under Certain Symmetry Hypotheses, Bariş Naki̇boğlu
A Simple Derivation Of The Refined Sphere Packing Bound Under Certain Symmetry Hypotheses, Bariş Naki̇boğlu
Turkish Journal of Mathematics
A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is $\mathit{\Omega}\left(n^{-0.5(1-E_{sp}'(R))}\right)$ for all codes on certain families of channels (including the Gaussian channels and the nonstationary Renyi symmetric channels) and for the constant composition codes on stationary memoryless channels. The resulting nonasymptotic bounds have definite approximation error terms. As a preliminary result that might be of interest on its own, the trade-off between type I and type II error probabilities in the hypothesis testing problem with (possibly non-stationary) independent samples is determined …
The Statistically Unbounded $\Tau$-Convergence On Locally Solid Riesz Spaces, Abdullah Aydin
The Statistically Unbounded $\Tau$-Convergence On Locally Solid Riesz Spaces, Abdullah Aydin
Turkish Journal of Mathematics
A sequence $(x_n)$ in a locally solid Riesz space $(E,\tau)$ is said to be statistically unbounded $\tau$-convergent to $x\in E$ if, for every zero neighborhood $U$, $\frac{1}{n}\big\lvert\{k\leq n:\lvert x_k-x\rvert\wedge u\notin U\}\big\rvert\to 0$ as $n\to\infty$. In this paper, we introduce the concept of the $st$-$u_\tau$-convergence and give the notions of $st$-$u_\tau$-closed subset, $st$-$u_\tau$-Cauchy sequence, $st$-$u_\tau$-continuous and $st$-$u_\tau$-complete locally solid vector lattice. Also, we give some relations between the order convergence and the $st$-$u_\tau$-convergence.
Erratum To "Study On Quasi-$\Gamma$-Hyperideals In $\Gamma$-Semihypergroups", Niovi Kehayopulu
Erratum To "Study On Quasi-$\Gamma$-Hyperideals In $\Gamma$-Semihypergroups", Niovi Kehayopulu
Turkish Journal of Mathematics
We wrote this note to show that the definition of $\Gamma$-hypersemigroups in [2] should be corrected, and that it is not enough to replace the hyperoperation $\circ$ of the hypersemigroup by $\Gamma$ to pass from a hypersemigroup to a $\Gamma$-hypersemigroup. Care should be taken about the definitions of $(m,n)$-quasi-$\Gamma$-hyperideal, the $m$-left $\Gamma$-hyperideal and the $n$-right $\Gamma$-hyperideal as well.
Global Existence And Blow-Up Of Solutions Of The Time-Fractional Space-Involution Reaction-Diffusion Equation, Rami̇z Tapdigoğlu, Berikbol Torebek
Global Existence And Blow-Up Of Solutions Of The Time-Fractional Space-Involution Reaction-Diffusion Equation, Rami̇z Tapdigoğlu, Berikbol Torebek
Turkish Journal of Mathematics
A time-fractional space-nonlocal reaction-diffusion equation in a bounded domain is considered. First, the existence of a unique local mild solution is proved. Applying Poincaré inequality it is obtained the existence and boundedness of global classical solution for small initial data. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time.
New Multiple Solutions For A Schrödinger-Poisson System Involving Concave-Convex Nonlinearities, Chun-Yu Lei, Gao-Sheng Liu, Chang-Mu Chu, Hong-Min Suo
New Multiple Solutions For A Schrödinger-Poisson System Involving Concave-Convex Nonlinearities, Chun-Yu Lei, Gao-Sheng Liu, Chang-Mu Chu, Hong-Min Suo
Turkish Journal of Mathematics
In this paper, we study the following critical growth Schrödinger-Poisson system with concave-convex nonlinearities term $\left\{\begin{array} -\Delta u + u + \eta\varphi u = \lambda f(x) u^{q-1} + u^5, in R^3, \\ -\Delta \varphi = u^2, in R^3,\end{array}\right. $ where $1 < q < 2, \eta\in \mathbb{R}, \lambda > 0$ is a real parameter and $f \in L^{\frac{6}{6-q}} (\mathbb{R}^3)$ is a nonzero nonnegative function. Using the variational method, we obtain that there exists a positive constant $\lambda_* > 0$ such that for all $\lambda \in (0,\lambda_*)$, the system has at least two positive solutions.