On Geometric Applications Of Quaternions,
2020
TÜBİTAK
On Geometric Applications Of Quaternions, Burcu Bektaş Demi̇rci̇, Nazim Aghayev
Turkish Journal of Mathematics
Quaternions have become a popular and powerful tool in various engineering fields, such as robotics, image and signal processing, and computer graphics. However, classical quaternions are mostly used as a representation of rotation of a vector in $3$-dimensions, and connection between its geometric interpretation and algebraic structures is still not well-developed and needs more improvements. In this study, we develop an approach to understand quaternions multiplication defining subspaces of quaternion $\mathbb{H}$, called as $\mbox{Plane}(N)$ and $\mbox{Line}(N)$, and then, we observe the effects of sandwiching maps on the elements of these subspaces. Finally, we give representations of some transformations in geometry …
Solvability And Maximal Regularity Results For A Differential Equation With Diffusion Coefficient,
2020
TÜBİTAK
Solvability And Maximal Regularity Results For A Differential Equation With Diffusion Coefficient, Kordan Ospanov, Adilet Yesbayev
Turkish Journal of Mathematics
We consider a second-order differential equation with rapidly growing intermediate coefficients. We obtain a solvability result in the cases that the diffusion coefficient of equation is unbounded or it tends to zero at the infinity. Under additional conditions, we prove the $L_p - $ maximal regularity estimate for the solution of this equation.
Bilateral-Type Solutions To The Fixed-Circle Problem With Rectified Linear Units Application,
2020
TÜBİTAK
Bilateral-Type Solutions To The Fixed-Circle Problem With Rectified Linear Units Application, Ni̇hal Taş
Turkish Journal of Mathematics
In this paper, we prove new fixed-circle (resp. fixed-disc) results using the bilateral type contractions on a metric space. To do this, we modify some known contractive conditions called the Jaggi-type bilateral contraction and the Dass-Gupta type bilateral contraction. We give some examples to show the validity of our obtained results. Also, we construct an application to rectified linear units activation functions used in the neural networks. This application shows the importance of studying "fixed-circle problem".
Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions,
2020
TÜBİTAK
Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the $n$th$~(n\geq 3)$ Taylor-Maclaurin coefficients $\left\vert a_{n}\right\vert $ of functions belong to these new subclasses with $a_{k}=0$ for $2\leq k\leq n-1$, also we find non-sharp estimates on the first two coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $. The results, which are presented in this paper, would generalize those in related earlier works of several authors.
On Lyapunov-Type Inequalities For Boundary Value Problems Of Fractional Caputo-Fabrizio Derivative,
2020
TÜBİTAK
On Lyapunov-Type Inequalities For Boundary Value Problems Of Fractional Caputo-Fabrizio Derivative, Şuayi̇p Toprakseven
Turkish Journal of Mathematics
In this study, Lyapunov-type inequalities for fractional boundary value problems involving the fractional Caputo Fabrizio differential equation with mixed boundary conditions when the fractional order of $\beta \in (1,2]$ and Dirichlet-type boundary condition when the fractional order of $\sigma \in (2,3]$ have been derived. Some consequences of the results related to the fractional Sturm?Liouville eigenvalue problems have also been given. Additionally, we examine the nonexistence of the solution of the fractional boundary value problem.
Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator,
2020
TÜBİTAK
Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator, Wei-Chuan Chen, Yanhsiou Cheng
Turkish Journal of Mathematics
In this paper, we study the inverse nodal problem and the eigenvalue gap for the one-dimensional sloshing problem with the $p$-Laplacian operator. By applying the Prüfer substitution, we first derive the reconstruction formula of the depth function by using the information of the nodal data. Furthermore, we employ the Tikhonov regularization method to consider how to reconstruct the depth function using only zeros of one eigenfunction. Finally, we investigate the eigenvalue gap under the restriction of symmetric single-well depth functions. We show the gap attains its minimum when the depth function is constant.
On Holomorphic Poly-Norden Manifolds,
2020
TÜBİTAK
On Holomorphic Poly-Norden Manifolds, Çağri Karaman, Zühre Topuz
Turkish Journal of Mathematics
In this paper, we investigated a new manifold with a poly-Norden structure, which is inspired by the positive root of the equation $x^{2}-mx-1=0$. We call this new manifold as holomorphic poly-Norden manifolds. We examine some properties of the Riemann curvature tensor and give an example of this manifold. Then, we define a different connection on this manifold which is named the semisymmetric metric poly F-connection and study some properties of the curvature and torsion tensor field according to this connection.
Some Results On Prime Rings With Multiplicative Derivations,
2020
TÜBİTAK
Some Results On Prime Rings With Multiplicative Derivations, Gurninder Singh Sandhu, Di̇dem Karalarlioğlu Camci
Turkish Journal of Mathematics
Let $R$ be a prime ring with center $Z(R)$ and an automorphism $\alpha.$ A mapping $\delta:R\to R$ is called multiplicative skew derivation if $\delta(xy)=\delta(x)y+ \alpha(x)\delta(y)$ for all $x,y\in R$ and a mapping $F:R\to R$ is said to be multiplicative (generalized)-skew derivation if there exists a unique multiplicative skew derivation $\delta$ such that $F(xy)=F(x)y+\alpha(x)\delta(y)$ for all $x,y\in R.$ In this paper, our intent is to examine the commutativity of $R$ involving multiplicative (generalized)-skew derivations that satisfy the following conditions: (i) $F(x^{2})+x\delta(x)=\delta(x^{2})+xF(x)$, (ii) $F(x\circ y)=\delta(x\circ y)\pm x\circ y$, (iii) $F([x,y])=\delta([x,y])\pm [x,y]$, (iv) $F(x^{2})=\delta(x^{2})$, (v) $F([x,y])=\pm x^{k}[x,\delta(y)]x^{m}$, (vi) $F(x\circ y)=\pm x^{k}(x\circ\delta(y))x^{m}$, (vii) $F([x,y])=\pm …
On The Variational Curves Due To The Ed-Frame Field In Euclidean 4-Space,
2020
TÜBİTAK
On The Variational Curves Due To The Ed-Frame Field In Euclidean 4-Space, Muradi̇ye Çi̇mdi̇ker, Yasi̇n Ünlütürk
Turkish Journal of Mathematics
In this study, we define a variational field for constructing a family of Frenet curvesof the length l lying on a connected oriented hypersurface and calculate the length of the variational curves due to the ED-frame field in Euclidean 4-space. And then, we derive the intrinsic equations for the variational curves and also obtain boundary conditions for this type of curves due to the ED-frame field in Euclidean 4-space.
An Analytical Investigatıon On Starlikeness And Convexity Properties For Hypergeometric Functions,
2020
TÜBİTAK
An Analytical Investigatıon On Starlikeness And Convexity Properties For Hypergeometric Functions, İsmet Yildiz, Alaatti̇n Akyar
Turkish Journal of Mathematics
In this study, we analytically investigate hypergeometric functions having some properties such as convexity and starlike. We fundamentally focus on obtaining desired conditions on the parameters \(a,b\), and $c$ in order that a hypergeometric function to be in various subclasses of starlike and convex functions of order \(\alpha=2^{-r}\) and order \(\alpha=2^{-r}\) type $\beta=2^{-1}$, with $r$ is a positive integer.
Units And 2-Class Field Towers Of Some Multiquadratic Number Fields,
2020
TÜBİTAK
Units And 2-Class Field Towers Of Some Multiquadratic Number Fields, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi
Turkish Journal of Mathematics
In this paper, we investigate the unit groups, the 2-class groups, the 2-class field towers and the structures of the second 2-class groups of some multiquadratic number fields of degree 8 and 16.
On 3-Dimensional Almost Einstein Manifolds With Circulant Structures,
2020
TÜBİTAK
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 …
On Ulam's Type Stability Criteria For Fractional Integral Equations Including Hadamard Type Singular Kernel,
2020
TÜBİTAK
On Ulam's Type Stability Criteria For Fractional Integral Equations Including Hadamard Type Singular Kernel, Yasemi̇n Başci, Süleyman Öğrekçi̇, Adi̇l Misir
Turkish Journal of Mathematics
In this paper, we deal with the Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU) stability of Hadamard type fractional integral equations on compact intervals. The stability conditions are developed using a new generalized metric (GM) definition and the fixed point technique by motivating Wang and Lin Ulam's type stability of Hadamard type fractional integral equations. Filomat 2014; 28(7): 1323-1331. Moreover, our approach is efficient and ease in use than to the previously studied approaches. Finally, we give two examples to explain our main results.
Asymptotic Socle Behaviors For Cones Over Curves In Positive Characteristic,
2020
TÜBİTAK
Asymptotic Socle Behaviors For Cones Over Curves In Positive Characteristic, Jinjia Li
Turkish Journal of Mathematics
This paper studies the distribution of socle degrees of $R/I^{[p^e]}$ when $e$ is large, for a homogeneous ideal $I$ in a two-dimensional standard-graded normal domain $R$ in positive characteristic $p$. We prove that the distribution is very much related to the asymptotic slopes of the syzygy bundle Syz$(I)$, which have been known to determine the Hilbert-Kunz multiplicity of $I$.
Characterizations Of Dual Curves And Dual Focal Curves In Dual Lorentzian Space $ D^{3}_{1} $,
2020
TÜBİTAK
Characterizations Of Dual Curves And Dual Focal Curves In Dual Lorentzian Space $ D^{3}_{1} $, Sareh Mehdizadeh Gilani, Nemat Abazari, Yusuf Yayli
Turkish Journal of Mathematics
In this paper, we have introduced dual Lorentzian connection, bracket and curvature tensor on dual Lorentzian space $ D_{1}^{3} .$ We have studied a dual curve in different situations in dual Lorentzian space $D^{3}_{1} $ and have found Bishop Darboux vector and some relations according to this vector field, Bishop frame and focal curve of the present dual curve. It has been shown that Bishop Darboux vector has a similar amount in three different cases of a dual curve and the first dual focal curvature of the aforementioned curve is constant function.
On Some Sums At The $A$-Points Of The $K$-Th Derivatives Of The Dirichlet $L$-Functions,
2020
TÜBİTAK
On Some Sums At The $A$-Points Of The $K$-Th Derivatives Of The Dirichlet $L$-Functions, Mohammed Mekkaoui, Abdallah Derbal, Kamel Mazhouda
Turkish Journal of Mathematics
Let $L^{(k)}(s,\chi)$ be the $k$-th derivative of the Dirichlet L-function associated with a primitive character $\chi$ mod $q$ and $a$ be a complex number. The solutions of $L^{(k)}(s,\chi)=a$ are called $a$-points. In this paper, we give an asymptotic formula for the sums
On Basicity Of The System Of Eigenfunctions Of One Discontinuous Spectral Problem For Second Order Differential Equation For Grand-Lebesgue Space, Yusuf Zeren, Miqdad Ismailov, Fati̇h Şi̇ri̇n
Turkish Journal of Mathematics
Basicity of the system of eigenfunctions of some\textbf{ }discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space $L_{p)} (-1;1)$ is studied in this work. Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace $G_{p)} (-1;1)$ of $L_{p)} (-1;1)$ generated by shift operator is considered. Basicity of the system of eigenfunctions for the space $G_{p)} (-1;1)\oplus C$, $1
Existence Of Self-Similar Solutions To Smoluchowski's Coagulation Equation With Product Kernel,
2020
TÜBİTAK
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
Surface Pencil With A Common Adjoint Curve,
2020
TÜBİTAK
Surface Pencil With A Common Adjoint Curve, Ergi̇n Bayram
Turkish Journal of Mathematics
In the present paper,we construct surfaces possessing an adjoint curve of a given space curve as an asymptotic curve, geodesic or line of curvature. We obtain conditions for ruled surfaces and developable ones. Finally, we present illustrative examples to show the validity of the present method.
Some Results On Top Generalized Local Cohomology Modules With Respect To A System Of Ideals,
2020
TÜBİTAK
Some Results On Top Generalized Local Cohomology Modules With Respect To A System Of Ideals, Nguyen Minh Tri
Turkish Journal of Mathematics
Let $R$ be a commutative Noetherian ring and $\Phi$ be a system of ideals of $R.$ In this paper, we study the annihilators and the set of attached prime ideals of top generalized local cohomology modules with respect to a system of ideals.
