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Full-Text Articles in Physical Sciences and Mathematics
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.
Biharmonic Pnmcv Submanifolds In Euclidean 5-Space, Rüya Şen, Nuretti̇n Cenk Turgay
Biharmonic Pnmcv Submanifolds In Euclidean 5-Space, Rüya Şen, Nuretti̇n Cenk Turgay
Turkish Journal of Mathematics
In this article, we study 3-dimensional biconservative and biharmonic submanifolds of $\mathbb{E}^5$ with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into $\mathbb{E}^5$ can be determined intrinsically. Then, we complete the proof of Chen's biharmonic conjecture for PNMCV submanifolds of $\mathbb{E}^5$.
Hahn-Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Hahn-Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this paper, we study the basic theory of regular Hahn-Hamiltonian systems. In this context, we establish an existence and uniqueness result. We introduce the corresponding maximal and minimal operators for this system and some properties of these operators are investigated. Moreover, we give a criterion under which these operators are self-adjoint. Finally, an expansion theorem is proved.
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 …
Duality Approach To The Regularity Problems For The Navier-Stokes Equations, Grigory Seregin
Duality Approach To The Regularity Problems For The Navier-Stokes Equations, Grigory Seregin
Turkish Journal of Mathematics
In this note, we describe a way to study local regularity of a weak solution to the Navier-Stokes equations, satisfying the simplest scale-invariant restriction, with the help of zooming and duality approach to the corresponding mild bounded ancient solution.
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.
Convergence Of A Linearly Regularized Nonlinear Wave Equation To The P-System, Hüsnü Ata Erbay, Saadet Erbay, Albert Kohen Erki̇p
Convergence Of A Linearly Regularized Nonlinear Wave Equation To The P-System, Hüsnü Ata Erbay, Saadet Erbay, Albert Kohen Erki̇p
Turkish Journal of Mathematics
We consider a second-order nonlinear wave equation with a linear convolution term. When the convolution operator is taken as the identity operator, our equation reduces to the classical elasticity equation which can be written as a $p$-system of first-order differential equations. We first establish the local well-posedness of the Cauchy problem. We then investigate the behavior of solutions to the Cauchy problem in the limit as the kernel function of the convolution integral approaches to the Dirac delta function, that is, in the vanishing dispersion limit. We consider two different types of the vanishing dispersion limit behaviors for the convolution …
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.
Three-Dimensional Homogeneous Contact Metric Manifold With Weakly $\Eta$-Einstein Structures, Sun Hyang Chun, Yunhee Euh
Three-Dimensional Homogeneous Contact Metric Manifold With Weakly $\Eta$-Einstein Structures, Sun Hyang Chun, Yunhee Euh
Turkish Journal of Mathematics
In this paper, we determine the geometric structures of 3-dimensional weakly $\eta$-Einstein almost contact metric manifolds and classify 3-dimensional weakly $\eta$-Einstein simply connected homogeneous contact metric manifolds based on Perrone's classification.
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.
Energy Decay And Blow-Up Of Solutions For A Class Of System Of Generalized Nonlinear Klein-Gordon Equations With Source And Damping Terms, Zeynep Sümeyye Çeli̇k, Şevket Gür, Erhan Pi̇şki̇n
Energy Decay And Blow-Up Of Solutions For A Class Of System Of Generalized Nonlinear Klein-Gordon Equations With Source And Damping Terms, Zeynep Sümeyye Çeli̇k, Şevket Gür, Erhan Pi̇şki̇n
Turkish Journal of Mathematics
In this work, we investigate generalized coupled nonlinear Klein-Gordon equations with nonlinear damping and source terms and initial-boundary value conditions, in a bounded domain. We obtain decay of solutions by use of Nakao inequality. The blow up of solutions with negative initial energy is also established.
A Study On Conformable Fractional Version Of Bullen-Type Inequalities, Fati̇h Hezenci̇, Hüseyi̇n Budak, Hasan Kara
A Study On Conformable Fractional Version Of Bullen-Type Inequalities, Fati̇h Hezenci̇, Hüseyi̇n Budak, Hasan Kara
Turkish Journal of Mathematics
In this paper, we give an equality for the case of differentiable convex functions involving conformable fractional integrals. Bullen-type inequalities for the conformable fractional integrals are established by using this equality. Some important inequalities are obtained by taking advantage of the convexity, the Hölder inequality and the power mean inequality. By using special choices, we present some known results in the literature. Furthermore, we give an example using a graph in order to show that our main results are correct.
The Inequalities On Dual Numbers And Their Topological Structures, Buşra Aktaş, Olgun Durmaz, Hali̇t Gündoğan
The Inequalities On Dual Numbers And Their Topological Structures, Buşra Aktaş, Olgun Durmaz, Hali̇t Gündoğan
Turkish Journal of Mathematics
Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings.
Atomic Systems In Krein Spaces, Osmin Ferrer Villar, Edilberto Arroyo Ortiz, José Naranjo Martínez
Atomic Systems In Krein Spaces, Osmin Ferrer Villar, Edilberto Arroyo Ortiz, José Naranjo Martínez
Turkish Journal of Mathematics
In the present article, we establish a definition of atomic systems in the Krein spaces, specifically, we establish the fundamental tools of the theory of atomic systems in the formalism of the Krein spaces and give a complete characterization of them. We also show that the atomic systems do not depend on the decomposition of the Krein space.
Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic
Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic
Turkish Journal of Mathematics
This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph, and the last is the graph-associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to $\mathcal{H}$-polytopes.
Global Existence, Asymptotic Behavior And Blow Up Of Solutions For A Kirchhoff-Type Equation With Nonlinear Boundary Delay And Source Terms, Houria Kamache, Nouri Boumaza, Billel Gheraibia
Global Existence, Asymptotic Behavior And Blow Up Of Solutions For A Kirchhoff-Type Equation With Nonlinear Boundary Delay And Source Terms, Houria Kamache, Nouri Boumaza, Billel Gheraibia
Turkish Journal of Mathematics
The main goal of this work is to study an initial boundary value problem for a Kirchhoff-type equation with nonlinear boundary delay and source terms. This paper is devoted to prove the global existence, decay, and the blow up of solutions. To the best of our knowledge, there are not results on the Kirchhoff type-equation with nonlinear boundary delay and source terms.