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Articles 451 - 480 of 10317
Full-Text Articles in Physical Sciences and Mathematics
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.
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.
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.
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 $\mathcal{I}$.
H2(G) Production From Dimethylamine Borane By Cu0/Wo3 Nps Catalyst, Doaa Al-Hameedawi̇, Seda Karaboğa, İzzet Morkan
H2(G) Production From Dimethylamine Borane By Cu0/Wo3 Nps Catalyst, Doaa Al-Hameedawi̇, Seda Karaboğa, İzzet Morkan
Turkish Journal of Chemistry
Cu0 NPs supported on tungsten (VI) oxide (WO3) were in situ generated from the reduction of Cu2+ ions during dehydrogenation of dimethylamine borane (DMAB). The Cu0/WO3 NPs displayed tangible catalytic activity in H2 (g) releasing reaction and they were identified by using advanced techniques. Cu0/WO3 NPs were found as active catalyst providing one equiv. H2(g) per mole of DMAB. The results from TEM images display the formation of Cu0 NPs with an average particle size of 4.6 ± 1.0 nm on the surface of WO3. Moreover, Cu0/WO3 NPs with various metal loadings were prepared and tested as catalyst in dehydrogenation …
Twisted Dirac Operators And The Kastler-Kalau-Walze Type Theorem For Five Dimensional Manifolds With Boundary, Tong Wu, Sining Wei, Yong Wang
Twisted Dirac Operators And The Kastler-Kalau-Walze Type Theorem For Five Dimensional Manifolds With Boundary, Tong Wu, Sining Wei, Yong Wang
Turkish Journal of Mathematics
In this paper, we prove the Kastler-Kalau-Walze type theorems for twisted Dirac operators on 5-dimensional manifolds with boundary.
On The Relation Between Oscillation Of Solutions Of Differential Equations And Corresponding Equations On Time Scales, Olexandr Stanzhytskyi, Roza Uteshova, Victoriia Tsan, Zoia Khaletska
On The Relation Between Oscillation Of Solutions Of Differential Equations And Corresponding Equations On Time Scales, Olexandr Stanzhytskyi, Roza Uteshova, Victoriia Tsan, Zoia Khaletska
Turkish Journal of Mathematics
This paper studies oscillatory properties of solutions of a dynamic equation on the set of time scales $\mathbf{T}_\lambda$ provided that the graininess function $\mu_\lambda$ approaches zero as $\lambda\to 0$. We derived the conditions under which oscillation of solutions of differential equations implies that of solutions of the corresponding equations defined on time scales with the same initial data, and vice versa.
Qualitative Study Of A Second Order Difference Equation, Messaoud Berkal, Juan Francisco Navarro
Qualitative Study Of A Second Order Difference Equation, Messaoud Berkal, Juan Francisco Navarro
Turkish Journal of Mathematics
In this paper, we study a second order rational difference equation. We analyze the stability of the unique positive equilibrium of the equation and prove the existence of a Neimark-Sacker bifurcation, validating our theoretical analysis via a numerical exploration of the system.
On Max-Min Solutions Of Fuzzy Games With Nonlinear Memberships Functions, Adem Cengi̇z Çevi̇kel
On Max-Min Solutions Of Fuzzy Games With Nonlinear Memberships Functions, Adem Cengi̇z Çevi̇kel
Turkish Journal of Mathematics
In this paper, we deal with two-person zero-sum games with fuzzy goals. We investigated the cases where the membership functions of the players are nonlinear. We examined how the solutions should be if the membership functions of players were exponential functions. In case players' membership functions are exponential, we developed a new method for the maximin solution according to a degree of attainment of the fuzzy goals. An application was made to show the effectiveness of the method.
On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova
On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova
Turkish Journal of Mathematics
In this paper, we study two classes of operator-differential equations of the third order with a multiple characteristic, considered on the whole axis. We introduce the concept of a smooth regular solution of order 1 and obtain sufficient conditions for the "smoothly" regular solvability of these equations.
Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri
Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri
Turkish Journal of Mathematics
In this paper, we investigate geodesics of the tangent bundle $TM$ of a Riemannian manifold $(M,g)$ endowed with an arbitrary pseudo-Riemannian $g$-natural metric of Kaluza-Klein type. Then considering a class of naturally defined almost complex structures on $TM$, constructed by V. Oproiu, we construct a class of magnetic fields and we characterize the corresponding magnetic curves on $TM$, when $(M,g)$ is a space form.
Curves And Stick Figures Not Contained In A Hypersurface Of A Given Degree, Edoardo Ballico
Curves And Stick Figures Not Contained In A Hypersurface Of A Given Degree, Edoardo Ballico
Turkish Journal of Mathematics
A stick figure $X\subset \mathbb{P}^r$ is a nodal curve whose irreducible components are lines. For fixed integers $r\ge 3$, $s\ge 2$ and $d$ we study the maximal arithmetic genus of a connected stick figure (or any reduced and connected curve) $X\subset \mathbb{P}^r$ such that $\deg (X)=d$ and $h^0(\mathcal{I}_X(s-1))=0$. We consider Halphen's problem of obtaining all arithmetic genera below the maximal one.
Novel Fano Type Lower Bounds On The Minimum Error Probability Of List $M$-Ary Hypothesis Testing, Berkan Dülek
Novel Fano Type Lower Bounds On The Minimum Error Probability Of List $M$-Ary Hypothesis Testing, Berkan Dülek
Turkish Journal of Mathematics
he problem of list $M$-ary hypothesis testing with fixed list size $L< M$ is considered. Based on some random observation, the test outputs a list of $L$ candidates out of $M$ possible hypotheses. The probability of list error is defined as the probability of the event that the list output by the test does not contain the true hypothesis that has generated the observation. An identity is derived that relates the minimum average probability of error of the optimal list hypothesis test to the minimum average probability of error of an optimal maximum a posteriori probability decision rule. The latter decides among an alternative set of hypotheses corresponding to all possible $L$-component mixtures of the distributions that characterize the observation under the original $M$ candidate hypotheses. As an application, the proposed identity is employed to obtain novel Fano type lower bounds on the minimum error probability of list $M$-ary hypothesis testing.
On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n
On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n
Turkish Journal of Mathematics
In this article, we study Hilbert series of non-Cohen-Maculay tangent cones for some 4-generated pseudosymmetric monomial curves. We show that the Hilbert function is nondecreasing by explicitly computing it. We also compute standard bases of these toric ideals.
Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram
Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram
Turkish Journal of Mathematics
In this work, we are interested in a boundary value problem (BVP) generated by a Klein -Gordon equation (KG) with Jump conditions and a boundary condition. First, we introduce scattering solutions and Jost solution of the problem. Then, we give the scattering function and we prove some properties of it. Lastly, we conclude the paper by a special example.
Metrical Almost Periodicity, Metrical Approximations Of Functions And Applications, Belkacem Chaouchi, Marko Kostic, Daniel Velinov
Metrical Almost Periodicity, Metrical Approximations Of Functions And Applications, Belkacem Chaouchi, Marko Kostic, Daniel Velinov
Turkish Journal of Mathematics
In this paper, we analyze Levitan and Bebutov metrical approximations of functions $F :\Lambda \times X \rightarrow Y$ by trigonometric polynomials and $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n}$, $X$ and $Y$ are complex Banach spaces, and $\rho$ is a general binary relation on $Y$. We also analyze various classes of multidimensional Levitan almost periodic functions in general metric and multidimensional Bebutov uniformly recurrent functions in general metric. We provide several applications of our theoretical results to the abstract Volterra integro-differential equations and the partial differential equations.
Clairaut Riemannian Maps, Kiran Meena, Akhilesh Yadav
Clairaut Riemannian Maps, Kiran Meena, Akhilesh Yadav
Turkish Journal of Mathematics
In this paper, first we define Clairaut Riemannian map between Riemannian manifolds by using a geodesic curve on the base space and find necessary and sufficient conditions for a Riemannian map to be Clairaut with a nontrivial example. We also obtain necessary and sufficient condition for a Clairaut Riemannian map to be harmonic. Thereafter, we study Clairaut Riemannian map from Riemannian manifold to Ricci soliton with a nontrivial example. We obtain scalar curvatures of $rangeF_\ast$ and $(rangeF_\ast)^\bot$ by using Ricci soliton. Further, we obtain necessary conditions for the leaves of $rangeF_\ast$ to be almost Ricci soliton and Einstein. We also …
Closure Operators, Irreducibility, Urysohn's Lemma, And Tietze Extension Theorem For Proximity Spaces, Samed Özkan, Muammer Kula, Sümeyye Kula, Tesni̇m Meryem Baran
Closure Operators, Irreducibility, Urysohn's Lemma, And Tietze Extension Theorem For Proximity Spaces, Samed Özkan, Muammer Kula, Sümeyye Kula, Tesni̇m Meryem Baran
Turkish Journal of Mathematics
In this paper, we introduce two notions of closure in the category of proximity spaces which satisfy (weak) hereditariness, productivity, and idempotency, and we characterize each of $T_{i}, i=0,1,2$, proximity spaces by using these closure operators and show how these subcategories are related. Furthermore, we characterize the irreducible proximity spaces and investigate the relationship among each of irreducible, connected and $T_{i}, i=1,2$, proximity spaces. Finally, we present Tietze extension theorem and Urysohn's lemma for proximity spaces.
The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales
The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales
Turkish Journal of Mathematics
A covariety is a nonempty family $C$ of numerical semigroups that satisfies a certain conditions. In this work we will show that if $F$ is a positive integer, then the set of Arf numerical semigroup with Frobenius number $F$, denoted by $(F)$, is a covatiety. The previous results will be used to give an algorithm which calculates the set $(F).$ Also we will see that if $X\subseteq S\backslash \Delta(F)$ for some $S\in (F),$ then there is the smallest element of $(F)$ containing $X.$
An Adaptive Image Restoration Algorithm Based On Hybrid Total Variation Regularization, Cong Thang Pham, Thi Thu Thao Tran, Hung Vi Dang, Hoai Phuong Dang
An Adaptive Image Restoration Algorithm Based On Hybrid Total Variation Regularization, Cong Thang Pham, Thi Thu Thao Tran, Hung Vi Dang, Hoai Phuong Dang
Turkish Journal of Electrical Engineering and Computer Sciences
In imaging systems, the mixed Poisson-Gaussian noise (MPGN) model can accurately describe the noise present. Total variation (TV) regularization-based methods have been widely utilized for Poisson-Gaussian removal with edge-preserving. However, TV regularization sometimes causes staircase artifacts with piecewise constants. To overcome this issue, we propose a new model in which the regularization term is represented by a combination of total variation and high-order total variation. We study the existence and uniqueness of the minimizer for the considered model. Numerically, the minimization problem can be efficiently solved by the alternating minimization method. Furthermore, we give rigorous convergence analyses of our algorithm. …