A Class Of Finite Difference Schemes For Singularly Perturbed Delay Differential Equations Of Second Order,
2019
TÜBİTAK
A Class Of Finite Difference Schemes For Singularly Perturbed Delay Differential Equations Of Second Order, Pramod Chakravarthy Podila, Kamalesh Kumar
Turkish Journal of Mathematics
In this paper, we proposed a new class of finite difference schemes for solving singularly perturbed delay differential equation of second order. The proposed schemes are oscillation-free and more accurate than conventional schemes on a uniform mesh. These schemes are easily adaptable on special meshes like Shishkin mesh or Bakhvalov mesh and are uniformly convergent with respect to the perturbation parameter. The error analysis has been carried out and numerical examples are presented to show the accuracy and efficiency of the proposed schemes.
Quantum Integral Equations Of Volterra Type In Terms Of Discrete-Time Normal Martingale,
2019
TÜBİTAK
Quantum Integral Equations Of Volterra Type In Terms Of Discrete-Time Normal Martingale, Jinshu Chen, Yuling Tang
Turkish Journal of Mathematics
In this paper, we aim to introduce a quantum linear stochastic Volterra integral equation of convolution type with operator-valued kernels in a nuclear topological algebra. We first establish the existence and uniqueness of the solutions and give the explicit expression of the solutions. Then we prove the continuity, continuous dependence on free terms and other properties of the solution.
Numerical Solutions Of Black-Scholesintegro-Differential Equations With Convergenceanalysis,
2019
TÜBİTAK
Numerical Solutions Of Black-Scholesintegro-Differential Equations With Convergenceanalysis, Azim Rivaz, Mahmoud Mohseni Moghadam, Samaneh Baniasadi
Turkish Journal of Mathematics
Stochastic integro-differential equations are obtained when we consider prices jump in financial modelling. In this paper, these equations are solved numerically by applying the two-dimensional Tau method with ordinary bases. Next, the numerical solutions of the equations above are investigated by the ordinary bases to the Hermitian one. Moreover, we provide an error analysis for the Tau method with ordinary bases. Also, we will prove that the errors of the approximate solutions decay exponentially in weighted ${L^{2}}$-norm. At the end, we will provide some numerical examples which show the efficiency and accuracy of the method.
Some Unpublished Reclaw Theorems And Their Applications To Baire-Star-One Functions,
2019
TÜBİTAK
Some Unpublished Reclaw Theorems And Their Applications To Baire-Star-One Functions, Tomasz Natkaniec, Waldemar Sieg
Turkish Journal of Mathematics
Lunina's 7-tuples $\langle E^1,\ldots, E^7\rangle$ of sets of pointwise convergence, divergence to $\infty$, divergence to $-\infty$, etc. for sequences of Baire-star-one functions are cha\-racterized. Generalization on ideal convergence of such sequences is discussed. Limits and ideal limits of sequences of Baire-star-one functions are considered in the last part of the article.
$\Alpha$-Associated Metrics On Rigged Null Hypersurfaces,
2019
TÜBİTAK
$\Alpha$-Associated Metrics On Rigged Null Hypersurfaces, Ferdinand Ngakeu, Hans Fotsing Tetsing
Turkish Journal of Mathematics
Let $x:(M,g)\to(\Bm,\bg)$ be a null hypersurface isometrically immersed into a proper semi-Riemannian manifold $(\overline{M},\bar g)$. A rigging for $M$ is a vector field $\zeta$ defined on some open subset of $\overline{M}$ containing $M$ such that $\zeta_p\notin T_pM$ for every $p\in M$. Such a vector field induces an everywhere transversal null vector field $N$ defined over $M$ and which induces on $M$ the same geometrical objects as $\zeta$. Let $\bar \eta$ be the 1-form that is $\bar g$-metrically equivalent to $N$ and let $\eta=x^\star\bar\eta$ be its pullback on $M$. For a given nowhere vanishing smooth function $\alpha$ on $M$, we have …
On Isotropic Projective Ricci Curvature Of C-Reducible Finsler Metrics,
2019
TÜBİTAK
On Isotropic Projective Ricci Curvature Of C-Reducible Finsler Metrics, Laya Ghaemnezhad, Bahman Rezaei, Mehran Gabrani
Turkish Journal of Mathematics
Projective Ricci curvature is a projective invariant quantity in Finsler geometry which is introduced by Z. Shen. In this paper, we study special projective Ricci curvature of C-reducible Finsler metrics. The necessary and sufficient conditions of these metrics, which cause these metrics to be weak or isotropic projective Ricci curvature, are found and it is proved that C-reducible Douglas metric of isotropic PRic-curvature must be PRic flat. The same theorem for C-reducible metrics of scalar flag curvature is also investigated.
Some Ergodic Properties Of Multipliers On Commutative Banach Algebras,
2019
TÜBİTAK
Some Ergodic Properties Of Multipliers On Commutative Banach Algebras, Heybetkulu Mustafayev, Hayri̇ Topal
Turkish Journal of Mathematics
A commutative semisimple regular Banach algebra $A$ with the Gelfand space $ \Sigma _{A}$ is called a Ditkin algebra if each point of $\Sigma _{A}\cup \left\{ \infty \right\} $ is a set of synthesis for $A$. Generalizing the Choquet-Deny theorem, it is shown that if $T$ is a multiplier of a Ditkin algebra $A,$ then $\left\{ \varphi \in A^{\ast }:T^{\ast }\varphi =\varphi \right\} $ is finite dimensional if and only if \textnormal{card}$\mathcal{F}_{T}$ is finite, where $\mathcal{F}_{T}=\left\{ \gamma \in \Sigma _{A}:\widehat{T}\left( \gamma \right) =1\right\} $ and $ \widehat{T}$ is the Helgason-Wang representation of $T.$
Perfect Numerical Semigroups,
2019
TÜBİTAK
Perfect Numerical Semigroups, María Ángeles Moreno Frías, Jose Carlos Rosales
Turkish Journal of Mathematics
A numerical semigroup is perfect if it does not have isolated gaps. In this paper we will order the perfect numerical semigroups with a fixed multiplicity. This ordering allows us to give an algorithm procedure to obtain them. We also study the perfect monoid, which is a subset of $\N$ that can be expressed as an intersection of perfect numerical semigroups, and we present the perfect monoid generated by a subset of $\N$. We give an algorithm to calculate it. We study the perfect closure of a numerical semigroup, as well as the perfect numerical semigroup with maximal embedding dimension, …
On Positive Periodic Solutions Of Second-Order Semipositonedifferential Equations,
2019
TÜBİTAK
On Positive Periodic Solutions Of Second-Order Semipositonedifferential Equations, Fanglei Wang, Nannan Yang
Turkish Journal of Mathematics
Using the Krasnosel'skii's fixed point theorem, we establish the existence and multiplicity of positive $\mathrm{T}$-periodic solutions of second-order semipositone system $ \left \{\begin{array}{lcr} x''(t)+a(t)x(t)=\lambda f(t,x(t)),\\ x(0)=x(\mathrm{T}),x'(0)=x'(\mathrm{T}), \end{array}\right. $ where $x=(x_1,x_2,\cdots,x_n)$, $f(t,x)=(f_1(t,x),f_2(t,x),\cdots,f_n(t,x))$ is bounded below.
A Blow-Up Result For Nonlocal Thin-Film Equation With Positive Initial Energy,
2019
TÜBİTAK
A Blow-Up Result For Nonlocal Thin-Film Equation With Positive Initial Energy, Mustafa Polat
Turkish Journal of Mathematics
In this note, we consider a thin-film equation including a diffusion term, a fourth order term and a nonlocal source term under the periodic boundary conditions. In particular, a finite time blow-up result is established for the case of positive initial energy provided that \[ \frac{\pi^2}{a^2}\leq \frac{2}{p-1},\] where $a$ is the length of the interval and $p>1$ is the power of nonlinear force term. Also upper and lower blow-up times are estimated.
Solvability Of A System Of Nonlinear Difference Equations Of Higher Order,
2019
TÜBİTAK
Solvability Of A System Of Nonlinear Difference Equations Of Higher Order, Merve Kara, Yasi̇n Yazlik
Turkish Journal of Mathematics
In this paper, we show that the following higher-order system of nonlinear difference equations, $ x_{n}=\frac{x_{n-k}y_{n-k-l}}{y_{n-l}\left( a_{n}+b_{n}x_{n-k}y_{n-k-l}\right)}, \ y_{n}=\frac{y_{n-k}x_{n-k-l}}{x_{n-l}\left( \alpha_{n}+\beta_{n}y_{n-k}x_{n-k-l}\right)}, \ n\in \mathbb{N}_{0}, $ where $k,l\in \mathbb{N}$, $\left(a_{n} \right)_{n\in \mathbb{N}_{0}}, \left(b_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\alpha_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\beta_{n} \right)_{n\in \mathbb{N}_{0}}$ and the initial values $x_{-i}, \ y_{-i}$, $i=\overline {1,k+l}$, are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case $k=2, l=k$.
Existence Resultsfor Some Neutral Functional Integrodifferential Equations With Bounded Delay,
2019
TÜBİTAK
Existence Resultsfor Some Neutral Functional Integrodifferential Equations With Bounded Delay, Sylvain Koumla, Radu Precup, Abdou Sene
Turkish Journal of Mathematics
In this paper, we study a class of neutral functional integrodifferential equations with finite delay in Banach spaces. We are interested in the global existence, uniqueness of mild solutions with values in the Banach space and in its subspace $D(A).$ The results are based on Banach's and Schauder's fixed point theorems and on the technique of equivalent norms. As an application, we consider a diffusion neutral functional integrodifferential equation.
Trigonometric Expressions For Gaussian $_2f_1$-Series,
2019
TÜBİTAK
Trigonometric Expressions For Gaussian $_2f_1$-Series, Wenchang Chu
Turkish Journal of Mathematics
The classical Gaussian $_2F_1$-series containing two free variables $\{x,y\}$ and two integer parameters $\{m,n\}$ are investigated by the linearization method. Several closed formulae are derived in terms of trigonometric functions. Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating $_3F_2$-series.
Cremona Transformations Of Plane Configurations Of 6 Points,
2019
TÜBİTAK
Cremona Transformations Of Plane Configurations Of 6 Points, Remzi̇ye Arzu Zabun
Turkish Journal of Mathematics
We analyze how a set of 6 points of $\Rp 2$ in general position changes under quadratic Cremona transformations based at triples of points of the given six. As an application, we give an alternative approach to determining the deformation types (i.e. icosahedral, bipartite, tripartite and hexagonal) of 36 real Schlafli double sixes on any nonsingular real cubic surface performed by Segre.
On Surfaces Endowed With A Canonical Principal Direction In Euclidean 4-Spaces,
2019
TÜBİTAK
On Surfaces Endowed With A Canonical Principal Direction In Euclidean 4-Spaces, Alev Kelleci̇, Nuretti̇n Cenk Turgay, Mahmut Ergüt
Turkish Journal of Mathematics
In this paper, we introduce canonical principal direction (CPD) submanifolds with higher codimension in Euclidean spaces. Then we obtain a classification of surfaces endowed with CPD relative to a fixed direction in Euclidean 4-space.
On Uniformly $Pr$-Ideals In Commutative Rings,
2019
TÜBİTAK
On Uniformly $Pr$-Ideals In Commutative Rings, Rabi̇a Nagehan Üregen
Turkish Journal of Mathematics
Let $R\ $be a commutative ring with nonzero identity and $I\ $a proper ideal of $R.\ $Then $I\ $is called a uniformly $pr$-ideal if there exists $N\in% \mathbb{N} $ such that $ab\in I\ $with $ann(a)=0\ $then $b^{N}\in I.\ $We say that the smallest $N\in% \mathbb{N} $ is called order of $I\ $and denoted by $ord_{R}(I)=N.\ $In this paper, we give some examples and characterizations of this new class of ideals.
Riemannian Manifolds Admitting A New Type Of Semisymmetric Nonmetric Connection,
2019
TÜBİTAK
Riemannian Manifolds Admitting A New Type Of Semisymmetric Nonmetric Connection, Sudhakar K. Chaubey, Ahmet Yildiz
Turkish Journal of Mathematics
We define a new type of semisymmetric nonmetric connection on a Riemannian manifold and establish its existence. It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions. We also find many basic results of the Riemannian manifolds and study the properties of group manifolds and submanifolds of the Riemannian manifolds with respect to the semisymmetric nonmetric connection. To validate our findings, we construct a nontrivial example of a $3$-dimensional Riemannian manifold equipped with a semisymmetric nonmetric connection.
Fixed Point Properties For A Degenerate Lorentz-Marcinkiewicz Space,
2019
TÜBİTAK
Fixed Point Properties For A Degenerate Lorentz-Marcinkiewicz Space, Veysel Nezi̇r
Turkish Journal of Mathematics
We construct an equivalent renorming of $\ell^1$, which turns out to produce a degenerate $\ell^1$-analog Lorentz-Marcinkiewicz space $\ell_{\delta,1}$, where the weight sequence $\delta={(\delta_n)}_{n\in\N}=(2,1,1,1,\cdots)$ is a decreasing positive sequence in $\ell^\infty\backslash c_0$, rather than in $c_0\backslash\ell^1$ (the usual Lorentz situation). Then we obtain its isometrically isomorphic predual $\ell^0_{\delta,\infty}$ and dual $\ell_{\delta,\infty}$, corresponding degenerate $c_0$-analog and $\ell^\infty$-analog Lorentz-Marcinkiewicz spaces, respectively. We prove that both spaces $\ell_{\delta,1}$ and $\ell^0_{\delta,\infty}$ enjoy the weak fixed point property (w-fpp) for nonexpansive mappings yet they fail to have the fixed point property (fpp) for nonexpansive mappings since they contain an asymptotically isometric copy of $\ell^1$ and $c_0$, …
Basicity Of A System Of Exponents With A Piecewise Linear Phase In Morrey-Type Spaces,
2019
TÜBİTAK
Basicity Of A System Of Exponents With A Piecewise Linear Phase In Morrey-Type Spaces, Bilal Bilalov, Fidan Seyidova
Turkish Journal of Mathematics
In this paper a perturbed system of exponents with a piecewise linear phase depending on two real parameters is considered. The sufficient conditions for these parameters are found, under which the considered system of exponents is complete, minimal, or it forms a basis for a Morrey-type space.
Weak-Stability And Saddle Point Theorems For A Multiobjective Optimization Problem With An Infinite Number Of Constraints,
2019
TÜBİTAK
Weak-Stability And Saddle Point Theorems For A Multiobjective Optimization Problem With An Infinite Number Of Constraints, Ta Quang Son, Ching Feng Wen
Turkish Journal of Mathematics
In this paper, we focus on weak-stability and saddle point theorems of multiobjective optimization problems that have an infinite number of constraints. The obtained results are based on the notion of weak-subdifferentials for vector functions. Some properties of weak stability for the problems are introduced. Relationships between strong duality and saddle points of the augmented Lagrange vector functions associated to the problems are investigated. Connections between weak-stability and saddle point theorems of the problems are established. An example is given.
