On Hom-F-Manifold Algebras And Quantization,
2022
TÜBİTAK
On Hom-F-Manifold Algebras And Quantization, Abdelkader Benhassine, Taoufik Chtioui, Mohamed Ali Maalaoui, Sami Mabrouk
Turkish Journal of Mathematics
The notion of a $F$-manifold algebras is an algebraic description of a $F$-manifold. In this paper, we introduce the notion of Hom-$F$-manifold algebras which is generalisation of $F$-manifold algebras and Hom-Poisson algebras. We develop the representation theory of Hom-$F$-manifold algebras and generalize the notion of Hom-pre-Poisson algebras by introducing the Hom-pre-$F$-manifold algebras which give rise to a Hom-$F$-manifold algebra through the subadjacent commutative Hom-associative algebra and the subadjacent Hom-Lie algebra. Using Ο-operators on a Hom-$F$-manifold algebras we construct a Hom-pre-$F$-manifold algebras on a module. Then, we study Hom-pre-Lie formal deformations of commutative Hom-associative algebra and we prove that Hom-$F$-manifold algebras …
Rough Approximations Based On Different Topologies Via Ideals,
2022
TÜBİTAK
Rough Approximations Based On Different Topologies Via Ideals, Ayşegül Çaksu Güler, Esra Dalan Yildirim, Oya Özbakir
Turkish Journal of Mathematics
In this paper, we generalize the notations of rough sets based on the topological space. Firstly, we produce various topologies by using the concept of ideal, $C_j$-neighbourhoods and $P_j$-neighbourhoods. When we compare these topologies with previous topologies, we see that these topologies are more general. Then we introduce new methods to find the approximations by using these generated topologies. When we compare these methods with the previous methods, we see that these methods are more accurate.
Clairaut Semi-Invariant Riemannian Maps From Almost Hermitian Manifolds,
2022
TÜBİTAK
Clairaut Semi-Invariant Riemannian Maps From Almost Hermitian Manifolds, Sushil Kumar, Rajendra Prasad, Sumeet Kumar
Turkish Journal of Mathematics
In this article, we define Clairaut semi-invariant Riemannian maps (CSIR Maps, In short) from almost Hermitian manifolds onto Riemannian manifolds and investigate fundamental results on such maps. We also obtain conditions for totally geodesicness on distributions defined in the introduced notion. Moreover, we provide an explicit example of CSIR map.
Product-Type Operators On Weak Vector Valued $\Alpha$-Besov Spaces,
2022
TÜBİTAK
Product-Type Operators On Weak Vector Valued $\Alpha$-Besov Spaces, Sepideh Nasresfahani, Ebrahim Abbasi
Turkish Journal of Mathematics
Let $\psi_1$ and $\psi_2$ be analytic functions on the open unit disk $\mathbb{D}$ and $\phi$ an analytic self map on $\mathbb{D}$. Let $M_\psi$, $C_\phi$ and $D$ denote the multiplication, composition and differentiation operators. We consider operators $M_{\psi_1} C_\phi$, $M_{\psi_2} C_\phi D$ and the Stevi\'c-Sharma operator $T_{\psi_1,\psi_2,\phi}(f)=M_{\psi_1}C_\phi (f)+M_{\psi_2}C_\phi D(f)$ on $\alpha$-Besov space $\mathcal{B}_{p,\alpha}$ and weak vector valued $\alpha$-Besov space $ w\mathcal{B}_{p,\alpha}(X)$ for complex Banach space $X$ and find some equivalent statements for boundedness of these operators. Also, boundedness and compactness of composition operator $C_\phi$ on $\mathcal{B}_{p,\alpha}(\mathbb{D})$ and $w\mathcal{B}_{p,\alpha}(\mathbb{D})$ are given.
On Elastic Graph Spines Associated To Quadratic Thurston Maps,
2022
TÜBİTAK
On Elastic Graph Spines Associated To Quadratic Thurston Maps, Meli̇ke Yeti̇şer, Ali̇ Berkay Yeti̇şer
Turkish Journal of Mathematics
For a quadratic Thurston map having two distinct critical points and $n$ postcritical points, we count the number of possible dynamical portraits. We associate elastic graph spines to several hyperbolic quadratic Thurston rational functions. These functions have four postcritical points, real coefficients, and invariant real intervals. The elastic graph spines are constructed such that each has embedding energy less than one. These are supporting examples to Dylan Thurston's recent positive characterization of rational maps. Using the same characterization, we prove that with a combinatorial restriction on the branched covering and a cycle condition on the dynamical portrait, a quadratic Thurston …
Hyperelastic Curves Along Riemannian Maps,
2022
TÜBİTAK
Hyperelastic Curves Along Riemannian Maps, Tunahan Turhan, Gözde Özkan Tükel, Bayram Şahi̇n
Turkish Journal of Mathematics
The main purpose of this paper is to examine what kind of information the smooth Riemannian map defined between two Riemannian manifolds provides about the character of the Riemannian map when a horizontal hyperelastic curve on the total manifold is carried to a hyperelastic curve on the base manifold. For the solution of the mentioned problem, firstly, the behavior of an arbitrary horizontal curve on the total manifold under a Riemannian map is investigated and the equations related to pullback connection are obtained. The necessary conditions are given for the Riemannian map to be h-isotropic or totally umbilical when a …
Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds,
2022
TÜBİTAK
Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds, Tüli̇n Altunöz
Turkish Journal of Mathematics
We consider simply connected $4$-manifolds admitting Lefschetz fibrations over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are exotic symplectic $4$-manifolds in the homeomorphism classes of $\mathbb{C} P^{2}\#8\overline{\mathbb{C} P^{2}}$ and $\mathbb{C} P^{2}\#9\overline{\mathbb{C} P^{2}}$, respectively. From these, we provide upper bounds for the minimal number of singular fibers of such fibrations. In addition, we prove that this number is equal to $18$ for $g=3$ when such fibrations are hyperelliptic. Moreover, we discuss these numbers for higher genera.
A Simple And Constructive Proof To A Generalization Of Lüroth's Theorem,
2022
TÜBİTAK
A Simple And Constructive Proof To A Generalization Of Lüroth's Theorem, Francois Ollivier, Brahim Sadik
Turkish Journal of Mathematics
A generalization of Lüroth's theorem expresses that every transcendence degree $1$ subfield of the rational function field is a simple extension. In this note we show that a classical proof of this theorem also holds to prove this generalization.
Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds,
2022
TÜBİTAK
Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds, Deng Yihua
Turkish Journal of Mathematics
In this paper, we consider gradient estimates for positive solutions to the following equation $$\triangle_V u+au^p\log u=0$$ on complete noncompact Riemannian manifold with $k$-dimensional Bakry-Emery Ricci curvature bounded from below. Using the Bochner formula and the Cauchy inequality, we obtain upper bounds of $ \nabla u $ with respect to the lower bound of the Bakry-Emery Ricci curvature.
On The Convergence Of The Abel-Poisson Means Of Multiple Fourier Series,
2022
TÜBİTAK
On The Convergence Of The Abel-Poisson Means Of Multiple Fourier Series, Si̇nem Sezer, Meli̇h Eryi̇ği̇t, Si̇mten Bayrakçi
Turkish Journal of Mathematics
Let $ A_\varepsilon (x,f)$ be the Abel-Poisson means of an integrable function $f(x)$ on $n$-dimensional torus $ \mathbf{T}^n, \; \;\; i= 1,\ldots,n \; (n\geq 2) $ in the Euclidean $n$-space. The famous Bochner's theorem asserts that for any function $ f\in L^1(\mathbf{T}^n)$ the Abel-Poisson means $A_\varepsilon (x,f)$ are pointwise converge to $f(x)$ a.e., that is, $$ \underset{\varepsilon \rightarrow0^+}{\lim}\, A_\varepsilon (x,f)= f(x), \;\; a.e.\; x\in \mathbf{T}^n. $$ In this paper we investigate the rate of convergence of Abel-Poisson means at the so-called $\mu$-smoothness point of $f$ .
The Integer-Antimagic Spectra Of A Disjoint Union Of Hamiltonian Graphs,
2022
TÜBİTAK
The Integer-Antimagic Spectra Of A Disjoint Union Of Hamiltonian Graphs, Uğur Odabaşi, Dan Roberts, Richard M. Low
Turkish Journal of Mathematics
Let $A$ be a nontrivial abelian group. A simple graph $G = (V, E)$ is $A$-antimagic, if there exists an edge labeling $f: E(G) \to A \backslash \{0\}$ such that the induced vertex labeling $f^+(v)=\sum_{uv\in E(G)} f(uv)$ is a one-to-one map. The {integer-antimagic spectrum} of a graph $G$ is the set IAM$(G) = \{k: G {is} \mathbb{Z}_k{-antimagic and } k \geq 2\}$. In this paper, we determine the integer-antimagic spectra for a disjoint union of Hamiltonian graphs.
Existence And Multiplicity Of Solutions For P(.)-Kirchhoff-Type Equations,
2022
TÜBİTAK
Existence And Multiplicity Of Solutions For P(.)-Kirchhoff-Type Equations, Rabi̇l Ayazoğlu, Sezgi̇n Akbulut, Ebubeki̇r Akkoyunlu
Turkish Journal of Mathematics
his paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for $p(.)$-Kirchhoff-type equation% \begin{equation*} \left\{ \begin{array}{c} M\left( \int_{\Omega }\frac{\left\vert \nabla u\right\vert ^{p(x)}}{p(x)}% dx\right) \left( -\Delta _{p(x)}u\right) =f(x,u),\text{ in }\Omega , \\ u=0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{on }\partial \Omega .% \end{array}% \right. \end{equation*}% Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of …
Li-Yorke Chaos And Topological Distributional Chaos In A Sequence,
2022
TÜBİTAK
Li-Yorke Chaos And Topological Distributional Chaos In A Sequence, Naveenkumar Yadav, Sejal Shah
Turkish Journal of Mathematics
We study here the topological notion of Li-Yorke chaos defined for uniformly continuous self-maps defined on uniform Hausdorff spaces, which are not necessarily compact metrizable. We prove that a weakly mixing uniformly continuous self-map defined on a second countable Baire uniform Hausdorff space without isolated points is Li-Yorke chaotic. Further, we define and study the notion of topological distributional chaos in a sequence for uniformly continuous self-maps defined on uniform Hausdorff spaces. We prove that Li-Yorke chaos is equivalent to topological distributional chaos in a sequence for uniformly continuous self-maps defined on second countable Baire uniform Hausdorff space without isolated …
An Alternative Method For Spp With Full Rank (2,1)-Block Matrix And Nonzero Right-Hand Side Vector,
2022
TÜBİTAK
An Alternative Method For Spp With Full Rank (2,1)-Block Matrix And Nonzero Right-Hand Side Vector, Gül Karaduman, Mei Yang
Turkish Journal of Mathematics
We propose an alternative method to solve large linear saddle point problems arising from computational sciences and engineering such as finite element approximations to Stokes problems, image reconstructions, tomography, genetics, statistics, and model order reductions for dynamical systems. Such problems have large sparse 2-by-2 block structure coefficient matrices with zero (2,2)-block matrix. A new technique is presented to solve saddle point problems with full row rank (2,1)-block matrix and nonzero right-hand side vector. By constructing a projection matrix and transforming the original problem into a least squares problem, a new reduced least squares problem is solved via the well-known iterative …
Quasilinear Systems With Unpredictable Relay Perturbations,
2022
TÜBİTAK
Quasilinear Systems With Unpredictable Relay Perturbations, Mehmet Onur Fen, Fatma Fen
Turkish Journal of Mathematics
It is rigorously proven under certain assumptions that a quasilinear system with discontinuous right-hand side possesses a unique unpredictable solution. The discontinuous perturbation function on the right-hand side is defined by means of an unpredictable sequence. A Gronwall-Coppel type inequality is utilized to achieve the main result, and the stability of the unpredictable solution is discussed. Examples with exponentially asymptotically stable and unstable unpredictable solutions are provided.
On Nonhomogeneous Geometric Quadratic Stochastic Operators,
2022
TÜBİTAK
On Nonhomogeneous Geometric Quadratic Stochastic Operators, Siti Nurlaili Karim, Nur Zatul Akmar Hamzah, Nasir Ganikhodjaev
Turkish Journal of Mathematics
n this paper, we construct a nonhomogeneous geometric quadratic stochastic operator generated by 2-partition $\xi$ on countable state space $X=\mathbb{Z}^{*}$. The limiting behavior of such operator is studied. We have proved that such operator possesses the regular property.
Numerical Simulations Of Traveling Waves In A Counterflow Filtration Combustion Model,
2022
TÜBİTAK
Numerical Simulations Of Traveling Waves In A Counterflow Filtration Combustion Model, Fati̇h Özbağ
Turkish Journal of Mathematics
We focused on traveling combustion waves that appear in a simplified, one-dimensional combustion model in porous media. The system we consider is a reaction-convection-diffusion system that can be reduced into two-dimension in order to prove traveling waves by phase plane analysis. In previous studies combustion wave velocity was assumed positive and their existence was proven. Also, all possible wave sequences that solve boundary value problems on infinite intervals with constant boundary data were identified. In this study, we generalize the previous work by including the case of negative combustion wave speed and taking the assumption that oxygen is carried faster …
Study Of The $\Phi$-Generalized Type $K$-Fractional Integrals Or Derivatives And Some Of Their Properties,
2022
TÜBİTAK
Study Of The $\Phi$-Generalized Type $K$-Fractional Integrals Or Derivatives And Some Of Their Properties, Mustafa Aydin, Nazim I. Mahmudov
Turkish Journal of Mathematics
A novel fractional integral in the sense of Riemann-Liouville integral and two new fractional derivatives in the sense of Riemann-Liouville derivative and Caputo derivative with respect to another function and two parameters are introduced. Some significant properties of them are presented like semigroup property, inverse property, etc. The solution of the Cauchy-type problem for the nonhomogenous linear differential equation with the $\phi$-generalized Caputo $k$-fractional derivative is given by using the method of successive approximation.
On Sharpening And Generalization Of Rivlin's Inequality,
2022
TÜBİTAK
On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic
Turkish Journal of Mathematics
n inequality due to T. J. Rivlin from 1960 states that if $P(z)$ is a polynomial of degree $n$ having no zeros in $ z
Univalence Criteria For Analytic Functions Obtained Using Fuzzydifferential Subordinations,
2022
TÜBİTAK
Univalence Criteria For Analytic Functions Obtained Using Fuzzydifferential Subordinations, Georgia Irina Oros
Turkish Journal of Mathematics
Ever since Lotfi A. Zadeh published the paper "Fuzzy Sets" in 1965 setting the basis of a new theory named fuzzy sets theory, many scientists have developed this theory and its applications. Mathematicians were especially interested in extending classical mathematical results in the fuzzy context. Such an extension was also done relating fuzzy sets theory and geometric theory of analytic functions. The study begun in 2011 has many interesting published outcomes and the present paper follows the line of the previous research in the field. The aim of the paper is to give some references related to the connections already …
