Bertrand And Mannheim Curves Of Framed Curves In The 3-Dimensional Euclidean Space,
2020
TÜBİTAK
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
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,
2020
TÜBİTAK
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,
2020
TÜBİTAK
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,
2020
TÜBİTAK
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",
2020
TÜBİTAK
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,
2020
TÜBİTAK
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,
2020
TÜBİTAK
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.
Degree Of Approximation By Means Of Hexagonal Fourier Series,
2020
TÜBİTAK
Degree Of Approximation By Means Of Hexagonal Fourier Series, Ali̇ Güven
Turkish Journal of Mathematics
Let $f$ be a continuous function which is periodic with respect to the hexagon lattice, and let $A$ be a lower triangular infinite matrix of nonnegative real numbers with nonincreasing rows. The degree of approximation of the function $f$ by matrix means $T_{n}^{\left( A\right) }\left( f\right) $ of its hexagonal Fourier series is estimated in terms of the modulus of continuity of $f.$
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces,
2020
TÜBİTAK
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces, Yusuf Zeren, Miqdad Ismailov, Cemi̇l Karaçam
Turkish Journal of Mathematics
The analogs of Korovkin theorems in grand-Lebesgue spaces are proved. The subspace $G^{p)} (-\pi ;\pi )$ of grand Lebesgue space is defined using shift operator. It is shown that the space of infinitely differentiable finite functions is dense in $G^{p)}(-\pi ;\pi )$. The analogs of Korovkin theorems are proved in $G^{p)} (-\pi ;\pi )$. These results are established in $G^{p)} (-\pi ;\pi )$ in the sense of statistical convergence. The obtained results are applied to a sequence of operators generated by the Kantorovich polynomials, to Fejer and Abel-Poisson convolution operators.
The Fekete-Szegö Inequality For Subclasses Of Analytic Functions Related To Modified Sigmoid Functions,
2020
TÜBİTAK
The Fekete-Szegö Inequality For Subclasses Of Analytic Functions Related To Modified Sigmoid Functions, Muhammet Kamali̇, Hali̇t Orhan, Murat Çağlar
Turkish Journal of Mathematics
In this paper, the authors investigate the initial coefficient bounds for a new generalized subclass of analytic functions related to Sigmoid functions. Also, the relevant connections with the famous classical Fekete?Szegö inequality for these classes are discussed.
The Homogenization Of Diffusion-Convection Equations In Non-Periodic Structures,
2020
TÜBİTAK
The Homogenization Of Diffusion-Convection Equations In Non-Periodic Structures, Anvarbek Meirmanov, Oleg Galtsev
Turkish Journal of Mathematics
We consider the homogenization of diffusion-convective problems with given divergence-free velocities in nonperiodic structures defined by sequences of characteristic functions(the first sequence). These quence of concentration (the second sequence)is uniformly bounded in the space of square-summable functions with square-summable derivatives with respect to spatial variables. At the same time, the sequence of time-derivative of product of these concentrations on the characteristic functions, that define a nonperiodic structure, is bounded in the space of square-summable functions from time interval into the conjugated space of functions depending on spatial variables, withsquare-summable derivatives. We prove the strong compactness of the second sequences in …
An Improved Trudinger--Moser Inequality And Its Extremal Functions Involving $L^P$-Norm In $\Mathbb{R}^2$,
2020
TÜBİTAK
An Improved Trudinger--Moser Inequality And Its Extremal Functions Involving $L^P$-Norm In $\Mathbb{R}^2$, Xiaomeng Li
Turkish Journal of Mathematics
Let $W^{1,2}(\mathbb{R}^2)$ be the standard Sobolev space. Denote for any real number $p>2$ \begin{align*}\lambda_{p}=\inf\limits_{u\in W^{1,2}(\mathbb{R}^2),u\not\equiv0}\frac{\int_{\mathbb{R}^{2}}( \nabla u ^2+ u ^2)dx}{(\int_{\mathbb{R}^{2}} u ^pdx)^{2/p}}. \end{align*} Define a norm in $W^{1,2}(\mathbb{R}^2)$ by \begin{align*}\ u\ _{\alpha,p}=\left(\int_{\mathbb{R}^{2}}( \nabla u ^2+ u ^2)dx-\alpha(\int_{\mathbb{R}^{2}} u ^pdx)^{2/p}\right)^{1/2}\end{align*} where $0\leq\alpha2$ and $0\leq\alpha
Gradient Weyl-Ricci Soliton,
2020
TÜBİTAK
Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç
Turkish Journal of Mathematics
The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric. We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.
A New Solution To The Discontinuity Problem On Metric Spaces,
2020
TÜBİTAK
A New Solution To The Discontinuity Problem On Metric Spaces, Ufuk Çeli̇k, Ni̇hal Özgür
Turkish Journal of Mathematics
We study on the Rhoades' question concerning the discontinuity problem at fixed point for a self-mapping T of a metric space. We obtain a new solution to this question. Our result generalizes some recent theorems existing in the literature and implies the uniqueness of the fixed point. However, there are also cases where the fixed point set of a self-mapping contains more than 1 element. Therefore, by a geometric point of view, we extend the Rhoades' question to the case where the fixed point set is a circle. We also give a solution to this extended version.
An Extragradient Algorithm For Split Generalized Equilibrium Problem And The Set Of Fixed Points Ofquasi-$\Phi $-Nonexpansive Mappings In Banach Spaces, Olawale Oyewole, Oluwatosin Mewomo, Lateef Jolaoso, Safeer Hussain Khan
Turkish Journal of Mathematics
In this paper, we study the problem of finding a common solution to split generalized mixed equilibrium problem and fixed point problem for quasi-$% \phi $-nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach space $E_1$ and a smooth, strictly convex, and reflexive Banach space $% E_2$. An iterative algorithm with Armijo linesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergence result is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally, numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our …
A Study On Horadam Hybrid Numbers,
2020
TÜBİTAK
A Study On Horadam Hybrid Numbers, Tuncay Deni̇z Şentürk, Göksal Bi̇lgi̇ci̇, Ahmet Daşdemi̇r, Zafer Ünal
Turkish Journal of Mathematics
In this paper, we study Horadam hybrid numbers. For these numbers, we give the exponential generating function, Poisson generating function, generating matrix, Vajda's, Catalan's, Cassini's, and d'Ocagne's identities. In addition, we offer Honsberger formula, general bilinear formula, and some summation formulas for these numbers.
Abstract Korovkin-Type Theorems In The Filter Setting With Respect To Relative Uniform Convergence,
2020
TÜBİTAK
Abstract Korovkin-Type Theorems In The Filter Setting With Respect To Relative Uniform Convergence, Antonio Boccuto, Kami̇l Demi̇rci̇, Sevda Yildiz
Turkish Journal of Mathematics
We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of a net of functions with respect to another fixed filter, a particular case of which is that of all neighborhoods of a point, belonging to the domain of the involved functions. We give some examples, in which we show that our results are strict generalizations of the classical ones.
A Semi-Markovian Renewal Reward Process With $\Gamma(G)$ Distributed Demand,
2020
TÜBİTAK
A Semi-Markovian Renewal Reward Process With $\Gamma(G)$ Distributed Demand, Asli Bektaş Kamişlik, Büşra Alakoç, Tülay Kesemen, Tahi̇r Khani̇yev
Turkish Journal of Mathematics
We consider a classical semi-Markovian stochastic model of type $(s,S)$ with Logistic distributed demand random variables. Logistic distribution is a member of special distribution class known as $\Gamma(g)$ that encounters in many real-life applications involving extreme value theory. The objective of this study is to observe some major characteristics of a stochastic process $X(t)$ which represents semi-Markovian renewal reward process of type $(s,S)$. We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion for ergodic distribution function and for $n^{th}$ order moments of ergodic distribution of the process $X(t)$.
On A Three-Dimensional Solvable System Of Difference Equations,
2020
TÜBİTAK
On A Three-Dimensional Solvable System Of Difference Equations, Yacine Halim, Massaoud Berkal, Amira Khelifa
Turkish Journal of Mathematics
In this paper we solve the following system of difference equations \begin{equation*} x_{n+1}=\dfrac{z_{n-1}}{a+by_nz_{n-1}},\quad y_{n+1}=\dfrac{x_{n-1}}{a+bz_nx_{n-1}},\quad z_{n+1}=\dfrac{y_{n-1}}{a+bx_ny_{n-1}},\quad n\in \mathbb{N}_{0} \end{equation*} where parameters $a, b$ and initial values $x_{-1},x_{0},y_{-1},y_{0},z_{-1},z_{0}$ are nonzero real numbers, and give a representation of its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constant coefficients associated to the system.
