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Articles 211 - 240 of 2595
Full-Text Articles in Physical Sciences and Mathematics
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.
On A New Subclass Of Biunivalent Functions Associated With The $(P,Q)$-Lucas Polynomials And Bi-Bazilevic Type Functions Of Order $\Rho+I\Xi$, Hali̇t Orhan, İbrahi̇m Aktaş, Hava Arikan
On A New Subclass Of Biunivalent Functions Associated With The $(P,Q)$-Lucas Polynomials And Bi-Bazilevic Type Functions Of Order $\Rho+I\Xi$, Hali̇t Orhan, İbrahi̇m Aktaş, Hava Arikan
Turkish Journal of Mathematics
Using $ (p, q) $-Lucas polynomials and bi-Bazilevic type functions of order $\rho +i\xi,$ we defined a new subclass of biunivalent functions. We obtained coefficient inequalities for functions belonging to the new subclass. In addition to these results, the upper bound for the Fekete-Szegö functional was obtained. Finally, for some special values of parameters, several corollaries were presented.
Global Bifurcation Of Positive Solutions For A Class Of Superlinear First-Order Differential Systems, Lijuan Yang, Ruyun Ma
Global Bifurcation Of Positive Solutions For A Class Of Superlinear First-Order Differential Systems, Lijuan Yang, Ruyun Ma
Turkish Journal of Mathematics
We are concerned with the first-order differential system of the form $$\left\{ \begin{array}{ll} u'(t)+a(t)u(t)=\lambda b(t) f(v(t-\tau(t))), &t\in\mathbb{R},\\ v'(t)+a(t)v(t)=\lambda b(t)g(u(t-\tau(t))), &t\in\mathbb{R},\\ \end{array} \right. $$ where $\lambda\in\mathbb{R}$~is a parameter. $a,b\in C(\mathbb{R},[0,+\infty))$ are two $\omega$-periodic functions such that $\int_0^\omega a(t)\text{d}t>0$,~$\int_0^\omega b(t)\text{d}t>0$,~$\tau\in C(\mathbb{R},\mathbb{R})$ is an $\omega$-periodic function. The nonlinearities~$f,g\in C(\mathbb{R},(0,+\infty))$~are two nondecreasing continuous functions and satisfy superlinear conditions at infinity.~By using the bifurcation theory,~we will show the existence of an unbounded component of positive solutions, which is bounded in positive $\lambda$-direction.
On The Properties Of Solutions For Nonautonomous Third-Order Stochastic Differential Equation With A Constant Delay, Ayman Mohammed Mahmoud, Doaa Ali Mohamed Bakhit
On The Properties Of Solutions For Nonautonomous Third-Order Stochastic Differential Equation With A Constant Delay, Ayman Mohammed Mahmoud, Doaa Ali Mohamed Bakhit
Turkish Journal of Mathematics
In this work, complete Lyapunov functionals (LFs) are constructed and used for the established conditions on the nonlinear functions appearing in the main equation, to guarantee stochastically asymptotically stable (SAS), uniformly stochastically bounded (USB) and uniformly exponentially asymptotically stable (UEAS) in probability of solutions to the nonautonomous third-order stochastic differential equation (SDE) with a constant delay as \begin{align*} \begin{split} \dddot{x}(t)&+a(t)f(x(t),\dot{x}(t))\ddot{x}(t)+b(t)\phi(x(t))\dot{x}(t) +c(t)\psi(x(t-r))\\&+g(t,x)\dot{\omega}(t)=p(t,x(t),\dot{x}(t),\ddot{x}(t)). \end{split} \end{align*} In Section 4, we give two numerical examples as an application to illustrate the results.
Jackson-Type Theorem In The Weak $L_{1}$-Space, Rashid Aliev, Eldost Ismayilov
Jackson-Type Theorem In The Weak $L_{1}$-Space, Rashid Aliev, Eldost Ismayilov
Turkish Journal of Mathematics
The weak $L_{1}$-space meets in many areas of mathematics. For example, the conjugate functions of Lebesgue integrable functions belong to the weak $L_{1}$-space. The difficulty of working with the weak $L_{1}$-space is that the weak $L_{1}$-space is not a normed space. Moreover, infinitely differentiable (even continuous) functions are not dense in this space. Due to this, the theory of approximation was not produced in this space. In the present paper, we introduced the concept of the modulus of continuity of the functions from the weak $L_{1}$-space, studied its properties, found a criterion for convergence to zero of the modulus of …
On The Measure Of Noncompactness In $L_P(\Mathbb{R}^+)$ And Applications To A Product Of $N$-Integral Equations, Mohamed M. A. Metwali, Vishnu Narayan Mishra
On The Measure Of Noncompactness In $L_P(\Mathbb{R}^+)$ And Applications To A Product Of $N$-Integral Equations, Mohamed M. A. Metwali, Vishnu Narayan Mishra
Turkish Journal of Mathematics
In this article, we prove a new compactness criterion in the Lebesgue spaces $L_p({\mathbb{R}}^+), 1 \leq p < \infty$ and use such criteria to construct a measure of noncompactness in the mentioned spaces. The conjunction of that measure with the Hausdroff measure of noncompactness is proved on sets that are compact in finite measure. We apply such measure with a modified version of Darbo fixed point theorem in proving the existence of monotonic integrable solutions for a product of $n$-Hammerstein integral equations $n\geq 2$.
Global Regularity For The 3d Axisymmetric Incompressible Hall-Mhd System With Partial Dissipation And Diffusion, Meilin Jin, Quansen Jiu, Huan Yu
Global Regularity For The 3d Axisymmetric Incompressible Hall-Mhd System With Partial Dissipation And Diffusion, Meilin Jin, Quansen Jiu, Huan Yu
Turkish Journal of Mathematics
In this paper, we study the Cauchy problem for the 3D incompressible axisymmetric Hall-MHD system with horizontal velocity dissipation and vertical magnetic diffusion.We obtain a unique global smooth solution of which in the cylindrical coordinate system the swirl velocity fields, the radial and the vertical components of the magnetic fields are trivial. This type of solution has been studied for the MHD system in [17][16] and [15] and for the Hall-MHD system with total dissipation and diffusion in [11]. Some new and fine estimates are obtained in this paper to overcome the difficulties raised from the Hall term and the …
Einstein's Model Of "The Movement Of Small Particles In A Stationary Liquid" Revisited: Finite Propagation Speed, Akif Ibragimov, Zeev Sobol, Isanka Hevage
Einstein's Model Of "The Movement Of Small Particles In A Stationary Liquid" Revisited: Finite Propagation Speed, Akif Ibragimov, Zeev Sobol, Isanka Hevage
Turkish Journal of Mathematics
The aforementioned celebrated model, though a breakthrough in Stochastic processes and a great step toward the construction of the Brownian motion, leads to a paradox: infinite propagation speed and violation of the 2nd law of thermodynamics. We adapt the model by assuming the diffusion matrix is dependent on the concentration of particles, rather than constant it was up to Einstein, and prove a finite propagation speed under the assumption of a qualified decrease of the diffusion for small concentrations. The method involves a nonlinear degenerated parabolic PDE in divergent form, a parabolic Sobolev-type inequality, and the Ladyzhenskaya-Ural'tseva iteration lemma.
On $\Gamma$-Hypersemigroups, Niovi Kehayopulu
On $\Gamma$-Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
The results on $\Gamma$-hypersemigroups are obtained either as corollaries of corresponding results on $\vee e$ or $poe$-semigroups or on the line of the corresponding results on $le$-semigroups. It has come to our attention that Theorem 3.22 in [4] cannot be obtained as corollary to Theorem 2.2 of the same paper as for a $\Gamma$-hypersemigroup, $({\cal P}^*(M),\Gamma,\subseteq)$ is a $\vee e$-semigroup and not an $le$-semigroup. Also on p. 1850, l. 12 in [4], the "$le$-semigroup" should be changed to "$\vee e$-semigroup". In the present paper we prove Theorems 3.26 and 3.28 stated without proof in [4]. On this occasion, some further …
On Bell Based Appell Polynomials, Zeynep Özat, Mehmet Ali̇ Özarslan, Bayram Çeki̇m
On Bell Based Appell Polynomials, Zeynep Özat, Mehmet Ali̇ Özarslan, Bayram Çeki̇m
Turkish Journal of Mathematics
Recently, several Bell based polynomials such as Bernoulli, Euler, Genocchi and Apostol versions were defined and investigated. The main aim of this paper is to introduce the general family of Bell based Appell polynomials, which includes many new members in addition to the existing ones, and to investigate their properties including determinantal representation, recurrence relation, derivative formula, addition formula, shift operators and differential equation. Furthermore, we introduce 2-iterated Bell-Appell polynomials and investigate their similar properties. With the help of this 2-iterated family, we also obtain the closed form summation formulae between the usual and the generalized versions of the Bell …
On $K$-Generalized Lucas Sequence With Its Triangle, Abdullah Açikel, Amrouche Said, Hacene Belbachir, Nuretti̇n Irmak
On $K$-Generalized Lucas Sequence With Its Triangle, Abdullah Açikel, Amrouche Said, Hacene Belbachir, Nuretti̇n Irmak
Turkish Journal of Mathematics
In this paper, we investigate several identities of $k$-generalized Lucas numbers with $k$-generalized Fibonacci numbers. We also establish a link between generalized $s$-Lucas triangle and bi$^{s}$nomial coefficients given by the coefficients of the development of a power of $(1+x+x^{2}+\cdots+x^{s}),$ with $s \in \mathbb{N}.$
On The Geometry Of Nearly Trans-Sasakian Manifolds, Aligadzhi R. Rustanov, Tatiana L. Melekhina, Svetlana V. Kharitonova
On The Geometry Of Nearly Trans-Sasakian Manifolds, Aligadzhi R. Rustanov, Tatiana L. Melekhina, Svetlana V. Kharitonova
Turkish Journal of Mathematics
The geometry of nearly trans-Sasakian manifolds is researched in this paper. The complete group of structural equations and the components of the Lee vector on the space of the associated $G$-structure are obtained for such manifolds. Conditions are found under which a nearly trans-Sasakian structure is a trans-Sasakian, a cosymplectic, a closely cosymplectic, a Sasakian structure or a Kenmotsu structure. The conditions are obtained when the nearly trans-Sasakian structure is a special generalized Kenmotsu structure of the second kind. A complete classification of nearly trans-Sasakian manifolds is obtained, i.e. it is proved that a nearly trans-Sasakian manifold is either a …
A Generalization Of The Notion Of Helix, Pascual Lucas, Jose Antonio Ortega-Yagues
A Generalization Of The Notion Of Helix, Pascual Lucas, Jose Antonio Ortega-Yagues
Turkish Journal of Mathematics
In this paper we generalize the notion of helix in the three-dimensional Euclidean space, which we define as that curve $\alpha$ for which there is an $F$-constant vector field $W$ along $\alpha$ that forms a constant angle with a fixed direction $V$ (called an axis of the helix). We find the natural equation and the geometric integration of helices $\alpha$ where the $F$-constant vector field $W$ is orthogonal to its axis.
Polynomials Taking Integer Values On Primes In A Function Field, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa, Boonrod Yuttanan
Polynomials Taking Integer Values On Primes In A Function Field, Tuangrat Chaichana, Vichian Laohakosol, Rattiya Meesa, Boonrod Yuttanan
Turkish Journal of Mathematics
Let $\mathbb{F}_q[x]$ be the ring of polynomials over a finite field $\mathbb{F}_q$ and $\mathbb{F}_q(x)$ its quotient field. Let $\mathbb{P}$ be the set of primes in $\mathbb{F}_q[x]$, and let $\mathcal{I}$ be the set of all polynomials $f$ over $\mathbb{F}_q(x)$ for which $f(\mathbb{P})\subseteq\mathbb{F}_q[x]$. The existence of a basis for $\mathcal{I}$ is established using the notion of characteristic ideal; this shows that $\mathcal{I}$ is a free $\mathbb{F}_q[x]$-module. Through localization, explicit shapes of certain bases for the localization of $\mathcal{I}$ are derived, and a well-known procedure is described as to how to obtain explicit forms of some bases of $\mathcal{I}$.
Nilary Group Rings And Algebras, Omar Al-Mallah, Gary Birkenmeier, Hafedh Alnogashi
Nilary Group Rings And Algebras, Omar Al-Mallah, Gary Birkenmeier, Hafedh Alnogashi
Turkish Journal of Mathematics
A ring $A$ is (principally) nilary, denoted (pr-)nilary, if whenever $XY=0,$ then there exists a positive integer $n$ such that either $X^n=0$ or $Y^n=0$ for all (principal) ideals $X$, $Y$ of $A$. We determine necessary and/or sufficient conditions for the group ring $A[G]$ to be (principally) nilary in terms of conditions on the ring $A$ or the group $G$. For example, we show that: (1) If $A[G]$ is (pr-)nilary, then $A$ is (pr-)nilary and either $G$ is prime or the order of each finite nontrivial normal subgroup of $G$ is nilpotent in $A$. (2) Assume that $G$ is finite. Then …
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 …
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.
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.
Some Fractional Dirac Systems, Yüksel Yalçinkaya
Some Fractional Dirac Systems, Yüksel Yalçinkaya
Turkish Journal of Mathematics
In this work, including $\alpha\epsilon(0,1)$; we examined the Dirac system in the frame which includes$\ \alpha$ order right and left Reimann-Liouville fractional integrals and derivatives with exponential kernels, and the Dirac system which includes $\alpha$ order right and left Caputo fractional integrals and derivatives with exponential kernels. Furthermore, we have given some definitions and properties for discrete exponential kernels and their associated fractional sums and fractional differences, and we have studied discrete fractional Dirac systems.
Existence And Multiplicity For Positive Solutions Of A System Of First Order Differential Equations With Multipoint And Integral Boundary Conditions, Le Thi Phuong Ngoc, Nguyen Thanh Long
Existence And Multiplicity For Positive Solutions Of A System Of First Order Differential Equations With Multipoint And Integral Boundary Conditions, Le Thi Phuong Ngoc, Nguyen Thanh Long
Turkish Journal of Mathematics
In this paper, we state and prove theorems related to the existence and multiplicity for positive solutions of a system of first order differential equations with multipoint and integral boundary conditions. The main tool is the fixed point theory. In order to illustrate the main results, we present some examples.
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 $\mathbb{E}^5$.
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.
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.
An Inverse Problem Of Finding A Time-Dependent Coefficient In A Fractional Diffusion Equation, Durdimurod Durdiev, Dilshod Durdiev
An Inverse Problem Of Finding A Time-Dependent Coefficient In A Fractional Diffusion Equation, Durdimurod Durdiev, Dilshod Durdiev
Turkish Journal of Mathematics
This article is concerned with the study of unique solvability of an inverse coefficient problem of determining the coefficient at the lower term of a fractional diffusion equation. The direct problem is the initial-boundary problem for this equation with usual initial and homogeneous Dirichlet conditions. To determine the unknown coefficient, an overdetermination condition is given as the Neumann condition at the left end of the spatial interval. The theorems of existence and uniqueness of inverse problem solution are obtained. Furthermore, we propose a numerical algorithm based on a finite-difference scheme to accurately compute the inverse problem of simultaneously determining a …
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.
Metallic-Like Structures And Metallic-Like Maps, Adelina Manea
Metallic-Like Structures And Metallic-Like Maps, Adelina Manea
Turkish Journal of Mathematics
The metallic-like $(a,b)$-manifold is a manifold endowed with a polynomial structure of second degree which unifies the almost product, complex structures and includes metallic structures. We introduce the metallic-like maps between metallic-like $(a,b)$-manifolds and we give a criterion for the nonconstancy of these maps. We prove that an almost contact structure on a Riemannian manifold induces a metallic-like $(a,b)$-structure and we give an example of a nonconstant metallic-like endomorphism of a particular almost contact manifold.
$\Ast$-Semiclean Rings, Shefali Gupta, Dinesh Udar
$\Ast$-Semiclean Rings, Shefali Gupta, Dinesh Udar
Turkish Journal of Mathematics
A ring $R$ is called semiclean if every element of $R$ can be expressed as sum of a periodic element and a unit. In this paper, we introduce a new class of ring, which is the $\ast$-version of the semiclean ring, i.e. the $\ast$-semiclean ring. A $\ast$-ring is $\ast$-semiclean if each element is a sum of a $\ast$-periodic element and a unit. The term $\ast$-semiclean is a stronger notion than semiclean. In this paper, many properties of $\ast$-semiclean rings are discussed. It is proved that if $p \in P(R)$ such that $pRp$ and $(1-p)R(1-p)$ are $\ast$-semiclean rings, then $R$ is …
Effect Of Fractional Analysis On Some Special Curves, Aykut Has, Beyhan Yilmaz
Effect Of Fractional Analysis On Some Special Curves, Aykut Has, Beyhan Yilmaz
Turkish Journal of Mathematics
In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curves is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Caputo fractional analysis that fits the algebraic structure of differential geometry is used. This is because the Caputo fractional derivative of the constant function is zero. This is an important advantage and allows a variety of fractional physical problems to be based on a geometric basis. This effect is examined with the help …
Unipotence In Positive Characteristic For Groups Of Finite Morley Rank, Jules Gael Tindzogho Ntsiri
Unipotence In Positive Characteristic For Groups Of Finite Morley Rank, Jules Gael Tindzogho Ntsiri
Turkish Journal of Mathematics
In this article we define a new form of unipotence in groups of finite Morley rank which extends Burdges unipotence to any characteristic. In particular, we show that every connected solvable group of finite Morley rank $G$ has a definable connected subgroup $H$ whose derived subgroup $H'$ is a good unipotent subgroup of finite Morley rank.
Characterizations And Representations Of Weak Core Inverses And $M$-Weak Group Inverses, Wende Li, Jianlong Chen, Yukun Zhou
Characterizations And Representations Of Weak Core Inverses And $M$-Weak Group Inverses, Wende Li, Jianlong Chen, Yukun Zhou
Turkish Journal of Mathematics
In a ring with an involution, we first present some necessary and sufficient conditions for the existence of the $m$-weak group inverse and expression. As an application, we prove that a regular element $a$ is $(m+1)$-weak group invertible if and only if $a^2a^{-}$ is $m$-weak group invertible, where $a^{-}$ is an inner inverse of $a$. The relevant results for weak core inverses and for pseudocore inverses are given. In addition, we present some new characterizations of weak core inverses, and also investigate maximal classes