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Articles 1 - 30 of 169
Full-Text Articles in Physical Sciences and Mathematics
The $2$-Adic And $3$-Adic Valuation Of The Tripell Sequence And An Application, Jhon Jairo Bravo, Maribel Díaz, José Luis Ramírez
The $2$-Adic And $3$-Adic Valuation Of The Tripell Sequence And An Application, Jhon Jairo Bravo, Maribel Díaz, José Luis Ramírez
Turkish Journal of Mathematics
Let $(T_n)_{n\geq 0}$ denote the Tripell sequence, defined by the linear recurrence $T_n=2T_{n-1} + T_{n-2}+T_{n-3}$ for $n\geq 3$ with $T_0=0$, $T_{1}=1$ and $T_2=2$ as initial conditions. In this paper, we study the $2$-adic and $3$-adic valuation of the Tripell sequence and, as an application, we determine all Tripell numbers which are factorials.
Geometric Properties Of Partial Sums Of Generalized Koebe Function, Erhan Deni̇z, Erkan Yalçin
Geometric Properties Of Partial Sums Of Generalized Koebe Function, Erhan Deni̇z, Erkan Yalçin
Turkish Journal of Mathematics
The aim of the present paper is to investigate the starlikeness, convexity, and close-to-convexity of some partial sums of the generalized Koebe function. Furthermore, we give some special results related with special cases of $c$ constant. The results, which are presented in this paper, would generalize those in related works of several earlier authors.
Conformally Flat Willmore Spacelike Hypersurfaces In $\Mathbb{R}^{N+1}_1$, Zonggang Deng, Tongzhu Li
Conformally Flat Willmore Spacelike Hypersurfaces In $\Mathbb{R}^{N+1}_1$, Zonggang Deng, Tongzhu Li
Turkish Journal of Mathematics
In this paper, we give the equation satisfied by umbilics-free Willmore spacelike hypersurfaces using the conformal invariants in Lorentzian space forms. At the same time, we give the equation satisfied by hyperelastic spacelike curves in $2$-dimensional Lorentzian space forms and classify the closed hyperelastic spacelike curves. Finally conformally flat Willmore spacelike hypersurfaces are classified in terms of the hyperelastic spacelike curves in $2$-dimensional Lorentzian space forms.
Coefficient Estimates For The Class Of Quasi Q-Convex Functions, Osman Altintaş, Seher Meli̇ke Aydoğan
Coefficient Estimates For The Class Of Quasi Q-Convex Functions, Osman Altintaş, Seher Meli̇ke Aydoğan
Turkish Journal of Mathematics
In this paper we introduce and investigate the class of $ P_{q}(\lambda,\beta, A, B)$, which is called quasi q-starlike and quasi q-convex with respect to the values of the parameter $\lambda$. We give coefficient bounds estimates and the results for the main theorem.
On Orthomorphism Elements In Ordered Algebra, Bahri̇ Turan, Hüma Gürkök
On Orthomorphism Elements In Ordered Algebra, Bahri̇ Turan, Hüma Gürkök
Turkish Journal of Mathematics
Let C be an ordered algebra with a unit e. The class of orthomorphism elements Orthe(C) of C was introduced and studied by Alekhno in "The order continuity in ordered algebras". If C = L(G), where G is a Dedekind complete Riesz space, this class coincides with the band Orth(G) of all orthomorphism operators on G. In this study, the properties of orthomorphism elements similar to properties of orthomorphism operators are obtained. Firstly, it is shown that if C is an ordered algebra such that $C_r$, the set of all regular elements of C, is a Riesz space with the …
Regular Sequences In The Subrings Of C(X), Fariborz Azarpanah, Delavar Esmaeilvandi
Regular Sequences In The Subrings Of C(X), Fariborz Azarpanah, Delavar Esmaeilvandi
Turkish Journal of Mathematics
We show that the intermediate subalgebras between $C^*(X)$ and C(X) do not contain regular sequences with length $\geq$ 2. This shows that depth(A(X)) $\leq$ 1 for each intermediate subalgebra A(X) between $C^*(X)$ and C(X). Whenever an intermediate subalgebra A(X) is proper, i.e. A(X) $\neq$ C(X), we observe that the depth of A(X) is exactly 1. Using this, it turns out that depth($C^*(X)$) = 0 if and only if $X$ is a pseuodocompact almost $P$ -space. The regular sequences in the subrings of the form $I + \mathbb{R}$ of C(X), where $I$ is a $z$-ideal of C(X), are also investigated and …
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 …
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy
Turkish Journal of Mathematics
In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its applications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when the order m is odd.
Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü
Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü
Turkish Journal of Mathematics
In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additionally, we prove some fixed point …
Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay, Abdelaziz Mebarki, Selma Baghli Bendimerad
Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay, Abdelaziz Mebarki, Selma Baghli Bendimerad
Turkish Journal of Mathematics
Our problem through this work is to give the existence of mild solutions for the first order class of neutral functional multivalued integro-differential evolution equations with infinite state-dependent delay using the nonlinear alternative of Frigon for multivalued contraction maps in Fréchet spaces combined with the semi-group theory.
Inverse Problem For Sturm-Liouville Differential Operators With Finite Number Of Constant Delays, Mohammad Shahriari
Inverse Problem For Sturm-Liouville Differential Operators With Finite Number Of Constant Delays, Mohammad Shahriari
Turkish Journal of Mathematics
In this manuscript,we study nonself-adjoint second-order differential operators with finite number of constant delays. We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from their spectra. An inverse spectral problem is studied for recovering differential operator from the potential from spectra of two boundary value problems with one common boundary condition.The uniqueness theorem is proved for this inverse problem.
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 …
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 …
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces, Yusuf Zeren, Miqdad Ismailov, Cemi̇l Karaçam
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.
An Improved Trudinger--Moser Inequality And Its Extremal Functions Involving $L^P$-Norm In $\Mathbb{R}^2$, Xiaomeng Li
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
Analytic Functions Associated With Cardioid Domain, Sarfraz Nawaz Malik, Mohsan Raza, Janusz Sokol, Saira Zainab
Analytic Functions Associated With Cardioid Domain, Sarfraz Nawaz Malik, Mohsan Raza, Janusz Sokol, Saira Zainab
Turkish Journal of Mathematics
In this article, we define and study new domain for analytic functions which is named as cardioid domain for being of cardioid structure. Analytic functions producing cardioid domain are defined and studied to some extent. The Fekete-Szegö inequality is also investigated for such analytic functions.
Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak
Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak
Turkish Journal of Mathematics
This scientific investigation deals with introducing certain basic information relating to the error functions in z-plane, establishing extensive relations between various series expansions of the complex error functions and presenting a number of their implications.
On The Chromatic Polynomial And The Domination Number Of $K$-Fibonacci Cubes, Ömer Eğeci̇oğlu, Eli̇f Saygi, Zülfükar Saygi
On The Chromatic Polynomial And The Domination Number Of $K$-Fibonacci Cubes, Ömer Eğeci̇oğlu, Eli̇f Saygi, Zülfükar Saygi
Turkish Journal of Mathematics
Fibonacci cubes are defined as subgraphs of hypercubes, where the vertices are those without two consecutive 1's in their binary string representation. $k$-Fibonacci cubes are in turn special subgraphs of Fibonacci cubes obtained by eliminating certain edges. This elimination is carried out at the step analogous to where the fundamental recursion is used to construct Fibonacci cubes themselves from the two previous cubes by link edges. In this work, we calculate the vertex chromatic polynomial of $k$-Fibonacci cubes for $k=1,2$. We also determine the domination number and the total domination number of $k$-Fibonacci cubes for $n,k \leq 12$ by using …
New Criteria For The Oscillation And Asymptotic Behavior Of Second-Order Neutral Differential Equations With Several Delays, Başak Karpuz, Shyam Sundar Santra
New Criteria For The Oscillation And Asymptotic Behavior Of Second-Order Neutral Differential Equations With Several Delays, Başak Karpuz, Shyam Sundar Santra
Turkish Journal of Mathematics
In this paper, necessary and sufficient conditions for asymptotic behavior are established of the solutions to second-order neutral delay differential equations of the form \begin{equation} \frac{d}{d{}t}\Biggl(r(t)\biggl(\frac{d}{d{}t}[x(t)-p(t)x(\tau(t))]\biggr)^{\gamma}\Biggr)+\sum_{i=1}^{m}q_{i}(t)f_{i}\bigl(x(\sigma_{i}(t))\bigr)=0 \quad\text{for}\ t\geq{}t_{0}.\nonumber \end{equation} We consider two cases when $f_{i}(u)/u^{\beta}$ is nonincreasing for $\gamma>\beta$, and nondecreasing for $\beta>\gamma$, where $\beta$ and $\gamma$ are quotients of two positive odd integers. Our main tool is Lebesgue's dominated convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.
Locally $D_\Delta$-Connected And Locally $D_\Delta$-Compact Spaces, Harshit Mathur, Davinder Singh
Locally $D_\Delta$-Connected And Locally $D_\Delta$-Compact Spaces, Harshit Mathur, Davinder Singh
Turkish Journal of Mathematics
The local analogues of the notions of $d_\delta$-connectedness and $D_\delta$-compactness of a topological space are introduced, and are named respectively, locally $d_\delta$-connectedness and locally $D_\delta$-compactness. Several properties including characterization of the concepts are discussed.
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 …
On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova
On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova
Turkish Journal of Mathematics
A 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e. these structures are circulant. An associated manifold, whose metric is expressed by both structures, is studied. Three classes of such manifolds are considered. Two of them are determined by special properties of the curvature tensor of the manifold. The third class is composed by manifolds whose structure is parallel with respect to the Levi-Civitaconnection of the metric. Some geometric characteristics of these manifolds are obtained. Examples …
Existence Of Self-Similar Solutions To Smoluchowski's Coagulation Equation With Product Kernel, Tanfer Tanriverdi̇
Existence Of Self-Similar Solutions To Smoluchowski's Coagulation Equation With Product Kernel, Tanfer Tanriverdi̇
Turkish Journal of Mathematics
We explore, by using formal analysis, the existence of mass conserving self-similar solutions for Smoluchowski's coagulation equation when kernel $K(x,y)=x^{\lambda} y^{\mu}+x^{\mu} y^{\lambda}$ with $0
On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker
On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker
Turkish Journal of Mathematics
In this article, we introduced a new power series whose coefficients are probabilities of the Pascal distribution. We investigated new approaches between the Pascal distribution series and some subclasses of normalized analytic functions. Also, we defined some mappings containing these functions the Alexander type integral operator. Moreover, we obtained sufficient conditions such that these mappings belong to some subclass of univalent functions.
Application Of Spectral Mapping Method To Dirac Operator, Rauf Ami̇rov, Merve Arslantaş
Application Of Spectral Mapping Method To Dirac Operator, Rauf Ami̇rov, Merve Arslantaş
Turkish Journal of Mathematics
In the present study, theorems related to the uniqueness of the solution of inverse problems for Dirac equations system are proved by applying spectral mapping method. With the help of this method, the inverse problem is reduced to the so-called main equation, which corresponds to the problem of existence and uniqueness of the solution of the system of linear equations in the Banach space.
Lattice Ordered Semigroups And $\Gamma$-Hypersemigroups, Niovi Kehayopulu
Lattice Ordered Semigroups And $\Gamma$-Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
As we have already seen in Turkish Journal of Mathematics (2019) 43: 2592-2601 many results on hypersemigroups do not need any proof as they can be obtained from lattice ordered semigroups. The present paper goes a step further, to show that many results on $\Gamma$-hypersemigroups as well can be obtained from lattice ordered semigroups. It can be instructive to prove them directly, but even in that case the proofs go along the lines of lattice ordered semigroups (or $poe$-semigroups). In the investigation, we faced the problem to correct the definition of $\Gamma$-hypersemigroups given in the existing bibliography.
Dynamics Of A Fluid Equation With Neumann Boundary Conditions, Limin Chen, Shengjun Li, Yumei Zou
Dynamics Of A Fluid Equation With Neumann Boundary Conditions, Limin Chen, Shengjun Li, Yumei Zou
Turkish Journal of Mathematics
We study the dynamics of a Neumann boundary value problem arising in fluid dynamics. We prove the nonexistence, existence and uniqueness of positive solutions under suitable conditions. At the same time, under stricter conditions, we also obtain the dynamic properties of the Neumann boundary value problem, such as the stability and instability of positive solutions. The methods of proof mainly involve the upper and lower solutions method, eigenvalue theory and some analysis techniques.
Hypergeometric Distribution Of The Number Of Draws From An Urn With Two Types Of Items Before One Of The Counts Reaches A Threshold, J. L. Gonzalez-Santander
Hypergeometric Distribution Of The Number Of Draws From An Urn With Two Types Of Items Before One Of The Counts Reaches A Threshold, J. L. Gonzalez-Santander
Turkish Journal of Mathematics
We consider an urn with $R$ elements of one type and $B$ elements of other type. We calculate the probability distribution $P_{n_{R},n_{B}}^{R,B}\left( s\right) $ wherein the random variable $s$ is the number of draws from the urn until we reach $n_{R}$ elements of type $R$ or $n_{B}$ elements of type $B$. We calculate the mean value $\left\langle s\right\rangle $ and the standard deviation $\sigma $ of $P_{n_{R},n_{B}}^{R,B}\left( s\right) $ in terms of hypergeometric functions. For $n_{R}=n_{B}$ and $B=R$ , we reduce $\left\langle s\right\rangle $ and $\sigma $ in terms of elementary functions. Also, the normalization condition leads to a new …
Vacuum Isolating And Blow-Up Analysis For Edge Hyperbolic System On Edge Sobolev Spaces, Morteza Koozehgar Kalleji, Nematollah Kadkhoda
Vacuum Isolating And Blow-Up Analysis For Edge Hyperbolic System On Edge Sobolev Spaces, Morteza Koozehgar Kalleji, Nematollah Kadkhoda
Turkish Journal of Mathematics
This paper deals with the study of the initial-boundary value problem of edge-hyperbolic system with damping term on the manifold with edge singularity. More precisely, it is analyzed the invariance and vacuum isolating of the solution sets to the edge-hyperbolic systems on edge Sobolev spaces. Then, by using a family of modified potential wells and concavity methods, it is obtained existence and nonexistence results of global solutions with exponential decay and is shown the blow-up in finite time of solutions on the manifold with edge singularities.
Classification Of Some Subclasses Of 6-Dimensional Nilpotent Leibniz Algebras, Ismail Demir
Classification Of Some Subclasses Of 6-Dimensional Nilpotent Leibniz Algebras, Ismail Demir
Turkish Journal of Mathematics
This article is a contribution to the improvement of classification theory in Leibniz algebras. We extend the method of congruence classes of matrices of bilinear forms that was used to classify complex nilpotent Leibniz algebras with one dimensional derived algebra. In this work we focus on applying this method to the classification of 6-dimensional complex nilpotent Leibniz algebras with two dimensional derived algebra.