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Articles 181 - 210 of 2595
Full-Text Articles in Physical Sciences and Mathematics
On The Weak And Strong Solutions Of The Velocity-Vorticity Model Of The $G$-Navier-Stokes Equations, Özge Kazar, Meryem Kaya
On The Weak And Strong Solutions Of The Velocity-Vorticity Model Of The $G$-Navier-Stokes Equations, Özge Kazar, Meryem Kaya
Turkish Journal of Mathematics
In this work, we consider a velocity-vorticity formulation for the $g$-Navier-Stokes equations. The system is constructed by combining the velocity-pressure system which is included by using the rotational formulation of the nonlinearity and the vorticity equation for the $g$ -Navier-Stokes equations. We prove the existence and uniqueness of weak and strong solutions of this system with the periodic boundary conditions.
Existence Results For Impulsive Dynamic Singular Nonlinear Sturm-Liouville Equations On Infinite Intervals, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna, Hamlet Abdullaoğlu Isayev
Existence Results For Impulsive Dynamic Singular Nonlinear Sturm-Liouville Equations On Infinite Intervals, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna, Hamlet Abdullaoğlu Isayev
Turkish Journal of Mathematics
The purpose of this study is to investigate an impulsive dynamic singular nonlinear Sturm-Liouville problem on infinite intervals. The existence and uniqueness of the solutions of such problem will be investigated by considering Weyl's limit-circle case.
Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, Şuayi̇p Yüzbaşi, Gamze Yildirim
Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, Şuayi̇p Yüzbaşi, Gamze Yildirim
Turkish Journal of Mathematics
In this study, the approximate solution of the nonlinear differential equation with variable delays is investigated by means of a collocation method based on the truncated Pell-Lucas series. In the first stage of the method, the assumed solution form (the truncated Pell-Lucas polynomial solution) is expressed in the matrix form of the standard bases. Next, the matrix forms of the necessary derivatives, the nonlinear terms, and the initial conditions are written. Then, with the help of the equally spaced collocation points and these matrix relations, the problem is reduced to a system of nonlinear algebraic equations. Finally, the obtained system …
An Invariant Of Regular Isotopy For Disoriented Links, İsmet Altintaş, Hati̇ce Parlatici
An Invariant Of Regular Isotopy For Disoriented Links, İsmet Altintaş, Hati̇ce Parlatici
Turkish Journal of Mathematics
In this paper, we define a two-variable polynomial invariant of regular isotopy, $M_{K}$ for a disoriented link diagram $K$. By normalizing the polynomial $M_{K}$ using complete writhe, we obtain a polynomial invariant of ambient isotopy, $N_{K}$, for a disoriented link diagram $K$. The polynomial $N_{K}$ is a generalization of the expanded Jones polynomial for disoriented links and is an expansion of the Kauffman polynomial $F$ to the disoriented links. Moreover, the polynomial $M_{K}$ is an expansion of the Kauffman polynomial $L$ to the disoriented links.
Bipolar Soft Ideal Rough Set With Applications In Covid-19, Heba I. Mustafa
Bipolar Soft Ideal Rough Set With Applications In Covid-19, Heba I. Mustafa
Turkish Journal of Mathematics
Bipolar soft rough set represents an important mathematical model to deal with uncertainty. This theory represents a link between bipolar soft set and rough set theories. This study introduced the concept of topological bipolar soft set by combining a bipolar soft set with topologies. Also, the topological structure of bipolar soft rough set has been discussed by defining the bipolar soft rough topology. The main objective of this paper is to present some solutions to develop and modify the approach of the bipolar soft rough sets. Two kinds of bipolar soft ideal approximation operators which represent extensions of bipolar soft …
A New Approach To Matrix Isomorphisms Of Complex Clifford Algebras Via Cantor Set, Derya Çeli̇k
A New Approach To Matrix Isomorphisms Of Complex Clifford Algebras Via Cantor Set, Derya Çeli̇k
Turkish Journal of Mathematics
We give a new way to obtain the standard isomorphisms of complex Clifford algebras, known as the tensor product of Pauli matrices, by representing the complex Clifford algebras on the space of complex valued functions defined over a finite subset of the Cantor set.
Forming Coupled Dispersionless Equations Of Families Of Bertrand Curves, Kemal Eren
Forming Coupled Dispersionless Equations Of Families Of Bertrand Curves, Kemal Eren
Turkish Journal of Mathematics
In this study, we establish a link of the coupled dispersionless (CD) equations system with the motion of Bertrand curve pairs. Moreover, we find the Lax equations that provide the integrability of these equations. By taking an appropriate choice of variables we show the link of the short pulse (SP) equation with the motion of Bertrand curve pairs via the reciprocal (hodograph) transformation. Finally, we prove that the conserved quantity of the corresponding coupled dispersionless equations obtained from each of these curve pairs is constant.
On The Distribution Of Adjacent Zeros Of Solutions To First-Order Neutral Differential Equations, Emad R. Attia, Ohoud N. Al-Masarer, Irena Jadlovska
On The Distribution Of Adjacent Zeros Of Solutions To First-Order Neutral Differential Equations, Emad R. Attia, Ohoud N. Al-Masarer, Irena Jadlovska
Turkish Journal of Mathematics
The purpose of this paper is to study the distribution of zeros of solutions to a first-order neutral differential equation of the form \begin{equation*} \left[x(t) + p(t) x(t-\tau)\right]' + q(t) x(t-\sigma) = 0, \quad t \geq t_0, \end{equation*} where $p\in C([t_0,\infty),[0,\infty))$, $q \in C([t_0,\infty),(0,\infty))$, $\tau,\sigma>0$, and $\sigma>\tau$. We obtain new upper bound estimates for the distance between consecutive zeros of solutions, which improve upon many of the previously known ones. The results are formulated so that they can be generalized without much effort to equations for which the distribution of zeros problem is related to the study of …
Novel Correlation Coefficients For Interval-Valued Fermatean Hesitant Fuzzy Sets With Pattern Recognition Application, İbrahi̇m Demi̇r
Novel Correlation Coefficients For Interval-Valued Fermatean Hesitant Fuzzy Sets With Pattern Recognition Application, İbrahi̇m Demi̇r
Turkish Journal of Mathematics
A combination of interval-valued Fermatean fuzzy sets with Fermatean hesitant fuzzy elements in the form of interval values is known as an interval-valued Fermatean hesitant fuzzy set. Since Fermatean hesitant fuzzy sets are effective instruments for representing more complex, ambiguous, and hazy information, interval-valued Fermatean hesitant fuzzy sets are expansions of these sets. This investigation will concentrate on four different types of correlation coefficients for Fermatean hesitant fuzzy sets and expand them to include correlation coefficients and weighted correlation coefficients for interval-valued Fermatean hesitant fuzzy sets. Finally, the numerical examples demonstrate the viability and usefulness of the suggested methodologies in …
Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş
Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş
Turkish Journal of Mathematics
Let $(H_{3},g_{1})$ and $(H_{3},g_{2})$ be the Lorentzian-Heisenberg spaces with nonflat metrics $g_{1}$ and $g_{2},\ $and $(TH_{3},g_{1}^{s}),\ (TH_{3},g_{2}^{s})$ be their tangent bundles with the Sasaki metric, respectively. In the present paper, we find nontotally geodesic distributions in tangent bundles by using lifts of contact forms from the base manifold $H_{3}.$We give examples for totally geodesic but not isocline distributions. We study the geodesics of tangent bundles by considering horizontal and natural lifts of geodesics of the base manifold $H_{3}$. We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics.
On The Band Functions And Bloch Functions, Oktay Veli̇ev
On The Band Functions And Bloch Functions, Oktay Veli̇ev
Turkish Journal of Mathematics
In this paper, we consider the continuity of the band functions and Bloch functions of the differential operators generated by the differential expressions with periodic matrix coefficients.
A Note On "Some Properties Of Second-Order Weak Subdifferentials" [Turkish Journal Of Mathematics (2021)45: 955-960], Qilin Wang, Min Liu
A Note On "Some Properties Of Second-Order Weak Subdifferentials" [Turkish Journal Of Mathematics (2021)45: 955-960], Qilin Wang, Min Liu
Turkish Journal of Mathematics
In this note, we provide an example to illustrate that Proposition 2.4 in [Turkish Journal of Mathematics (2021)45: 955-960)] is incorrect, and give a modification of the proposition. Two examples are provided to illustrate the modified result. Meanwhile, we establish a convex function, and correct the proof of Theorem 2.3 in [Turkish Journal of Mathematics (2021)45: 955-960)] by the function.
Geometric Singularities And Regularity Of Solution Of The Stokes System In Nonsmooth Domains, Yasir Nadeem Anjam
Geometric Singularities And Regularity Of Solution Of The Stokes System In Nonsmooth Domains, Yasir Nadeem Anjam
Turkish Journal of Mathematics
This paper deals with the geometrical singularities of the weak solution of the mixed boundary value problem governed by the stationary Stokes system in two-dimensional nonsmooth domains with corner points and points at which the type of boundary conditions changes. The presence of these points on the boundary generally generates local singularities in the solution. We will see the impact of the geometrical singularities of the boundary or the mixed boundary conditions on the qualitative properties of the solution including its regularity. Moreover, the asymptotic singular representations for the solution which inherently depend on the zeros of certain transcendental functions …
Separation, Connectedness, And Disconnectedness, Mehmet Baran
Separation, Connectedness, And Disconnectedness, Mehmet Baran
Turkish Journal of Mathematics
The aim of this paper is to introduce the notions of hereditarily disconnected and totally disconnected objects in a topological category and examine the relationship as well as interrelationships between them. Moreover, we characterize each of $T_{2}$, connected, hereditarily disconnected, and totally disconnected objects in some topological categories and compare our results with the ones in the category of topological spaces.
The Class Of Demi Kb-Operators On Banach Lattices, Hedi Benkhaled, Aref Jeribi
The Class Of Demi Kb-Operators On Banach Lattices, Hedi Benkhaled, Aref Jeribi
Turkish Journal of Mathematics
In this paper, we introduce and study the new concept of demi KB-operators. Let $E$ be a Banach lattice. An operator $T: E\longrightarrow E$ is said to be a demi KB-operator if, for every positive increasing sequence $\{x_{n}\}$ in the closed unit ball $\mathcal{B}_{E}$ of $E$ such that $\{x_{n}-Tx_{n}\}$ is norm convergent to $x\in E$, there is a norm convergent subsequence of $\{x_{n}\}$. If the latter sequence has a weakly convergent subsequence then $T$ is called a weak demi KB-operator. We also investigate the relationship of these classes of operators with classical notions of operators, such as b-weakly demicompact operators …
Approximation Results For The Moments Of Random Walk With Normally Distributed Interference Of Chance, Zülfi̇ye Hanali̇oğlu, Aynura Poladova, Tahi̇r Khani̇yev
Approximation Results For The Moments Of Random Walk With Normally Distributed Interference Of Chance, Zülfi̇ye Hanali̇oğlu, Aynura Poladova, Tahi̇r Khani̇yev
Turkish Journal of Mathematics
In this study, a random walk process $\left(X\left(t\right)\right)$ with normally distributed interference of chance is considered. In the literature, this process has been shown to be ergodic and the limit form of the ergodic distribution has been found. Here, unlike previous studies, the moments of the $X\left(t\right)$ process are investigated. Although studies investigating the moment problem for various stochastic processes (such as renewal-reward processes) exist in the literature, it has not been considered for random walk processes, as it requires the use of new mathematical tools. Therefore, in this study, firstly, the exact formulas for the first four moments of …
Inverse Nodal Problem For The Quadratic Pencil Of The Sturm$-$Liouville Equations With Parameter-Dependent Nonlocal Boundary Condition, Yaşar Çakmak, Baki̇ Keski̇n
Inverse Nodal Problem For The Quadratic Pencil Of The Sturm$-$Liouville Equations With Parameter-Dependent Nonlocal Boundary Condition, Yaşar Çakmak, Baki̇ Keski̇n
Turkish Journal of Mathematics
In this paper, we consider the inverse nodal problem for a quadratic pencil of the Sturm$-$Liouville equations with parameter-dependent Bitsadze$-$Samarskii type nonlocal boundary condition and we give an algorithm for the reconstruction of the potential functions by obtaining the asymptotics of the nodal points.
Generalized Elliptical Quaternions With Some Applications, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r
Generalized Elliptical Quaternions With Some Applications, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r
Turkish Journal of Mathematics
In this article, quaternions, which is a preferred and elegant method for expressing spherical rotations, are generalized with the help of generalized scalar product spaces, and elliptical rotations on any given ellipsoid are examined by them. To this end, firstly, we define the generalized elliptical scalar product space which accepts the given ellipsoid as a sphere and determines skew symmetric matrices, and the generalized vector product related to this scalar product space. Then we define the generalized elliptical quaternions by using these notions. Finally, elliptical rotations on any ellipsoid in the space are examined by using the unit generalized elliptical …
Studying A Doubly Nonlinear Model Of Slightly Compressible Forchheimer Flows In Rotating Porous Media, Emi̇ne Çeli̇k, Luan Hoang, Thinh Kieu
Studying A Doubly Nonlinear Model Of Slightly Compressible Forchheimer Flows In Rotating Porous Media, Emi̇ne Çeli̇k, Luan Hoang, Thinh Kieu
Turkish Journal of Mathematics
We study the generalized Forchheimer flows of slightly compressible fluids in rotating porous media. In the problem's model, the varying density in the Coriolis force is fully accounted for without any simplifications. It results in a doubly nonlinear parabolic equation for the density. We derive a priori estimates for the solutions in terms of the initial, boundary data and physical parameters, emphasizing on the case of unbounded data. Weighted Poincare-Sobolev inequalities suitable to the equation's nonlinearity, adapted Moser's iteration, and maximum principle are used and combined to obtain different types of estimates.
Attractors For Semigroups With Multi-Dimensional Time And Pdes In Unbounded Domains, Anna Kostianko, Sergey Zelik
Attractors For Semigroups With Multi-Dimensional Time And Pdes In Unbounded Domains, Anna Kostianko, Sergey Zelik
Turkish Journal of Mathematics
We develop the attractors theory for the semigroups with multidimensional time belonging to some closed cone in an Euclidean space and apply the obtained general results to partial differential equations (PDEs) in unbounded domains. The main attention is payed to elliptic boundary problems in general unbounded domains. In contrast to the previous works in this direction our theory does not require the underlying domain to be cylindrical or cone-like or to be shift semiinvariant with respect to some direction. In particular, the theory is applicable to the exterior domains.
Discontinuous Galerkin Method For Blow-Up Solutions Of Nonlinear Wave Equations, Asma Azaiez, Mondher Benjemaa, Aida Jrajria, Hatem Zaag
Discontinuous Galerkin Method For Blow-Up Solutions Of Nonlinear Wave Equations, Asma Azaiez, Mondher Benjemaa, Aida Jrajria, Hatem Zaag
Turkish Journal of Mathematics
e develop and study an explicit time-space discrete discontinuous Galerkin finite element method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is considered. We also investigate the blow-up phenomena and we prove that under weak convergence assumptions, the numerical blow-up time tends toward the theoretical one. The validity of our results is confirmed throughout several examples and benchmarks.
Blow-Up Of Solutions For Wave Equation With Multiple ?(X)-Laplacian And Variable Exponent Nonlinearities, Aya Khaldi, Amar Ouaoua, Messaoud Maouni
Blow-Up Of Solutions For Wave Equation With Multiple ?(X)-Laplacian And Variable Exponent Nonlinearities, Aya Khaldi, Amar Ouaoua, Messaoud Maouni
Turkish Journal of Mathematics
We consider an initial value problem related to the equation \begin{equation*} u_{tt}-{div}\left( \left\vert \nabla u\right\vert ^{m\left( x\right) -2}\nabla u\right) -{div}\left( \left\vert \nabla u_{t}\right\vert ^{r\left( x\right) -2}\nabla u_{t}\right) -\gamma \Delta u_{t}=\left\vert u\right\vert ^{p\left( x\right) -2}u, \end{equation*} with homogeneous Dirichlet boundary condition in a bounded domain $\Omega $. Under suitable conditions on variable-exponent $m\left( .\right) ,$ $r\left( .\right), $ and $p\left( .\right) ,$ we prove a blow-up of solutions with negative initial energy.
On The Rank Of Generalized Order-Preserving Transformation Semigroups, Haytham Darweesh Mustafa Abusarri̇s, Gonca Ayik
On The Rank Of Generalized Order-Preserving Transformation Semigroups, Haytham Darweesh Mustafa Abusarri̇s, Gonca Ayik
Turkish Journal of Mathematics
For any two non-empty (disjoint) chains $X$ and $Y$, and for a fixed order-preserving transformation $\theta : Y \rightarrow X$, let $\mathcal{GO} (X,Y; \theta )$ be the generalized order-preserving transformation semigroup. Let $\mathcal{O}(Z)$ be the order-preserving transformation semigroup on the set $Z=X\cup Y$ with a defined order. In this paper, we show that $\mathcal{GO}(X,Y;\theta)$ can be embedded in $O(Z,Y)=\{\, \alpha\in \mathcal{O}(Z)\, :\, Z\alpha \subseteq Y\,\}$, the semigroup of order-preserving transformations with restricted range. If $\theta \in \mathcal{GO}(Y,X)$ is one-to-one, then we show that $\mathcal{GO}(X,Y; \theta)$ and $O(X, im (\theta))$ are isomorphic semigroups. If we suppose that $\left X \right =m$,\, …
Szabos Algorithm And Applications, Michel Bertrand Djiadeu Ngaha, Salomon Joseph Mbatakou, Romain Nimpa Pefoukeu
Szabos Algorithm And Applications, Michel Bertrand Djiadeu Ngaha, Salomon Joseph Mbatakou, Romain Nimpa Pefoukeu
Turkish Journal of Mathematics
In this paper, Szabos algorithm is used as the main tool to find locally symmetric left invariant Riemannian metrics on some $4$-dimensional Lie groups. Locally symmetric left invariant Riemannian Lie groups constitute an important subclass of Riemannian Lie groups with zero-divergence Weyl-tensor the so-called C-manifolds. Some properties of the curvature operator of these 4-dimensional C-manifolds are studied.
Perfect Fluid Spacetimes And $K$-Almost Yamabe Solitons, Krishnendu De, Uday Chand De, Aydin Gezer
Perfect Fluid Spacetimes And $K$-Almost Yamabe Solitons, Krishnendu De, Uday Chand De, Aydin Gezer
Turkish Journal of Mathematics
In this article, we presumed that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and creative approach, here we study $k$-almost Yamabe solitons and gradient $k$-almost Yamabe solitons. First, two examples are constructed to ensure the existence of gradient $k$-almost Yamabe solitons. Then we show that if a perfect fluid spacetime admits a $k$-almost Yamabe soliton, then its potential vector field is Killing if and only if the divergence of the potential vector field vanishes. Besides, we prove that if a perfect fluid spacetime permits a …
Spin Structures On Generalized Real Bott Manifolds, Asli Güçlükan İlhan, Sabri̇ Kaan Gürbüzer, Semra Pamuk
Spin Structures On Generalized Real Bott Manifolds, Asli Güçlükan İlhan, Sabri̇ Kaan Gürbüzer, Semra Pamuk
Turkish Journal of Mathematics
In this paper, we give a necessary and sufficient condition for a generalized real Bott manifold to have a spin structure in terms of column vectors of the associated matrix. We also give an interpretation of this result to the associated acyclic $\omega$-weighted digraphs. Using this, we obtain a family of real Bott manifolds that does not admit spin structure.
Struwe Compactness Results For A Critical $P-$Laplacian Equation Involving Critical And Subcritical Hardy Potential On Compact Riemannian Manifolds, Tewfik Ghomari, Youssef Maliki
Struwe Compactness Results For A Critical $P-$Laplacian Equation Involving Critical And Subcritical Hardy Potential On Compact Riemannian Manifolds, Tewfik Ghomari, Youssef Maliki
Turkish Journal of Mathematics
Let $(M,g)$ be a compact Riemannian manifold. In this paper, we prove Struwe-type decomposition formulas for Palais-Smale sequences of functional energies corresponding to the equation: \begin{equation*} \Delta_{g,p}u-\frac{h(x)}{(\rho_{x_{o}}(x))^{s}}\left u\right ^{p-2}u =f(x)\left u\right ^{p^{\ast}-2}u, \end{equation*} where $\Delta_{g,p} $ is the $p-$Laplacian operator, $p^*=\frac{np}{n-p}$, $0
On Orthogonally Additive Band Operators And Orthogonally Additive Disjointness Preserving Operators, Bahri̇ Turan, Demet Tülü
On Orthogonally Additive Band Operators And Orthogonally Additive Disjointness Preserving Operators, Bahri̇ Turan, Demet Tülü
Turkish Journal of Mathematics
Let $M$ and $N$ be Archimedean vector lattices. We introduce orthogonally additive band operators and orthogonally additive inverse band operators from $M$ to $N$ and examine their properties. We investigate the relationship between orthogonally additive band operators and orthogonally additive disjointness preserving operators and show that under some assumptions on vector lattices $M$ or $N$, these two classes are the same. By using this relation, we show that if ${\mu }$ is a bijective orthogonally additive band operator (resp. orthogonally additive disjointness preserving operator) from $M$ into $N$ then ${\mu }^{-1}$:$N$${\rightarrow}$$M$ is an orthogonally additive band operator (resp. orthogonally additive …
Spectral And Topological Properties Of Linear Operators On A Hilbert Space, Salah Mecheri, Aissa Nasli Bakir
Spectral And Topological Properties Of Linear Operators On A Hilbert Space, Salah Mecheri, Aissa Nasli Bakir
Turkish Journal of Mathematics
We introduce the class of $(M, k)$-quasi-$*$-paranormal operators on a Hilbert space $H$. This class extends the classes of $*$-paranormal and $k$-quasi-$*$-paranormal operators. An operator $T$ on a complex Hilbert space is called $(M, k)$-quasi-$*$-paranormal if there exists $M>0$ such that \begin{equation*} \sqrt{M}\left\Vert T^{k+2}x\right\Vert \left\Vert T^{k}x\right\Vert \geq \left\Vert T^{\ast }T^{k}x\right\Vert ^{2} \end{equation*} for all $x\in H.$ In the present article, we give operator matrix representation of a $(M, k)$-quasi-$*$-paranormal operator. The compactness, the invariant subspace, and some topological properties of this class of operators are studied. Several properties of this class of operators are also presented.
Left-Definite Hamiltonian Systems And Corresponding Nested Circles, Eki̇n Uğurlu
Left-Definite Hamiltonian Systems And Corresponding Nested Circles, Eki̇n Uğurlu
Turkish Journal of Mathematics
This work aims to construct the Titchmarsh-Weyl $M(\lambda )-$theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter $\lambda $. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.