# Showing papers in "Turkish journal of mathematics & computer science in 2022"

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TL;DR: In this article , the Berezin transform and the radius of an operator on the reproducing kernel Hilbert space are defined, and several sharp inequalities are studied. But they do not consider the case where the operator is a sum of two operators.

Abstract: The Berezin transform $\widetilde{T}$ and the Berezin radius of an operator $T$ on the reproducing kernel Hilbert space $\mathcal{H}\left( Q\right) $ over some set $Q$ with the reproducing kernel $K_{\eta}$ are defined, respectively, by
\[
\widetilde{T}(\eta)=\left\langle {T\frac{K_{\eta}}{{\left\Vert K_{\eta
}\right\Vert }},\frac{K_{\eta}}{{\left\Vert K_{\eta}\right\Vert }}%
}\right\rangle ,\ \eta\in Q\text{ and }\mathrm{ber}(T):=\sup_{\eta\in
Q}\left\vert \widetilde{T}{(\eta)}\right\vert .
\]
We study several sharp inequalities by using this bounded function $\widetilde{T},$ involving powers of the Berezin radius and the Berezin norms of reproducing kernel Hilbert space operators. We also give some inequalities regarding the Berezin transforms of sum of two operators.

6 citations

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TL;DR: In this article , a modification of classical Finite Difference Method (FDM) was proposed for the solution of boundary value problems which are defined on two disjoint intervals and involved additional transition conditions at an common end of these intervals.

Abstract: In this study, we have proposed a new modification of classical Finite Difference Method (FDM) for the solution of boundary value problems which are defined on two disjoint intervals and involved additional transition conditions at an common end of these intervals. The proposed modification of FDM differs from the classical FDM in calculating the iterative terms of numerical solutions. To illustrate the efficiency and reliability of the proposed modification of FDM some examples are solved. The obtained results are compared with those obtained by the standart FDM and by the analytical method. Corresponding graphical illustration are also presented.

2 citations

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TL;DR: In this paper , the authors studied the geodesics on the tangent bundle with respect to the vertical rescaled Berger deformation metric over an anti-paraK{a}hler manifold.

Abstract: In this paper, we study the geodesics on the tangent bundle $TM$ with respect to the vertical rescaled Berger deformation metric over an anti-paraK\"{a}hler manifold $(M, \varphi, g)$. In this case, we establish the necessary and sufficient conditions under which a curve be geodesic with respect to this. Finally, we also present certain examples of geodesic.

2 citations

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TL;DR: In this article , some properties of hyperbolic numbers are presented and compared with real, dual, and complex matrices, and it is revealed that there are similarities in additive properties and differences in multiplicative properties.

Abstract: In this study, firstly, we will present some properties of hyperbolic numbers. Then, we will introduce hyperbolic matrices, which are matrices with hyperbolic number entries. Additionally, we will examine the algebraic properties of these matrices and reveal its difference from other matrix structures such as real, dual, and complex matrices. As a result of comparing the results found in this work with real, dual, and complex matrices, it will be revealed that there are similarities in additive properties and differences in some multiplicative properties. Finally, we will define some special hyperbolic matrices and give their properties and relations with real matrices.

1 citations

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TL;DR: In this paper , the authors studied the following three-dimensional system of difference equations, and investigated the solutions in three different cases depending on whether the parameters are zero or non-zero.

Abstract: In this paper, we study the following three-dimensional system of
difference equations
\begin{equation*}
x_{n}=\frac{ax_{n-3}z_{n-2}+b}{cy_{n-1}z_{n-2}x_{n-3}}, \ y_{n}=\frac{ay_{n-3}x_{n-2}+b}{cz_{n-1}x_{n-2}y_{n-3}}, \ z_{n}=\frac{az_{n-3}y_{n-2}+b}{cx_{n-1}y_{n-2}z_{n-3}}, \ n\in \mathbb{N}_{0},
\end{equation*}%
where the parameters $a, b, c$ and the
initial values $x_{-j},y_{-j},z_{-j}$, $j \in \{1,2,3\}$, are real numbers. We solve aforementioned system in explicit form. Then we investigated the solutions in 3 different cases depending on whether the parameters are zero or non-zero. In addition, numerical examples are given to demonstrate the theoretical results. Finally, an application is given for solutions are related to Fibonacci numbers when $a=b=c=1$.

1 citations

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TL;DR: In this article , the notion of commutativity for covariant and contravariant mappings in bipolar metric spaces was introduced and some common fixed point theorems were proved.

Abstract: In this article, we introduce the notion of commutativity for covariant and contravariant mappings in bipolar metric spaces. Afterwards, by using this notion, we prove some common fixed point theorems which show the existence and uniqueness of common fixed point for covariant and contravariant mappings satisfying contractive type conditions.

1 citations

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TL;DR: In this paper , the authors introduce new adjoint curves which are associated curves in Euclidean space of three dimensions, which are generated with the help of integral curves of special Smarandache curves.

Abstract: In this paper, we introduce new adjoint curves which are associated curves in Euclidean space of three
dimension. They are generated with the help of integral curves of special Smarandache curves. We attain some
connections between Frenet apparatus of these new adjoint curves and main curve. We characterize these curves in
which conditions they are general helix and slant helix. Finally, we exemplify them with figures

1 citations

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TL;DR: In this paper , the authors derived a realistic and close confidence interval for the parameter which denotes the underlying number of simultaneous reactions in the system by satifying the leap condition, which is the condition that the propensity function during the time interval $ t $ to $[ t+\tau ]$ should not be altered for the chosen time step.

Abstract: In the biological systems, Monte Carlo approaches are used to provide the stochastic simulation of the chemical reactions. The major stochastic simulation algorithms (SSAs) are the direct method, also known as the Gillespie algorithm, the first reaction method and the next reaction method. While these methods give accurate generation of the results, they are computationally demanding for large complex systems. To increase the computational efficiency of SSAs, approximate SSAs can be option. The approximate methods rely on the leap condition. This condition means that the propensity function during the time interval $ t $ to $[ t+\tau ]$ should not be altered for the chosen time step $\tau$. Here, to proceed with the system's history axis from one time step to the next, we compute how many times each reaction can be realized in each small time interval $\tau$ so that we can observe plausible simultaneous reactions. Hence, this study aims to generate a realistic and close confidence interval for the parameter which denotes the underlying numbers of simultaneous reactions in the system by satifying the leap condition. For this purpose, the poisson $\tau$-leap algorithm and the approximate Gillespie algorithm, as the extension of the Gillespie algorithm, are handled. In the estimation for the associated parameters in both algorithms, we derive their maximum likelihood estimators, moment estimatora and bayesian estimators. From the derivations, we theoretically show that our novel confidence intervals are narrower than the current confidence intervals under the leap condition.

1 citations

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TL;DR: In this paper , the B-lift curve is defined in Lorentzian 3-space and the relationship between the Frenet vectors of the Bertrand curve and the natural lift curve is examined.

Abstract: In this article, based on Thorpe’s definition, we define a new curve called the B-lift curve in Lorentzian
3-space and examine the Frenet vectors of the B-lift curve. Furthermore, we examine the relationship between the
Frenet vectors of the Bertrand curve and the Frenet vectors of the natural lift curve. Finally, we give an example on
these results.

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TL;DR: In this paper , the 3D Euclidean space of spatial quaternionic Bertrand curve pairs is examined and some characterizations of the Bertrand curves are obtained in a 3D space.

Abstract: In this article, spatial quaternionic Bertrand curve pairs in the 3-dimensional Euclidean space are examined. Algebraic properties of quaternions, basic definitions and theorems are given. Later, some characterizations of spatial quaternionic Bertrand curve pairs are obtained in the 3-dimensional Euclidean space.

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TL;DR: The MBA-ABC algorithm has a superior performance when compared with the A- ABC algorithm when finding the minimum distance of Bose, Chaudhuri, and Hocquenghem codes (a special type of linear codes).

Abstract: Finding the minimum distance of linear codes is a non-deterministic polynomial-time-hard problem and different approaches are used in the literature to solve this problem.
Although, some of the methods focus on finding the true distances by using exact algorithms, some of them focus on optimization algorithms to find the lower or upper bounds of the distance. In this study,
we focus on the latter approach. We first give the swarm intelligence background of artificial bee colony algorithm, we explain the algebraic approach of such algorithm and call it the algebraic artificial bee colony algorithm (A-ABC). Moreover, we develop the A-ABC algorithm by integrating it with the algebraic differential mutation operator. We call the developed algorithm the mutation-based algebraic artificial bee colony algorithm (MBA-ABC). We apply both; the A-ABC and MBA-ABC algorithms to the problem of finding the minimum distance of linear codes. The achieved results indicate that the MBA-ABC algorithm has a superior performance when compared with the A-ABC algorithm when finding the minimum distance of Bose, Chaudhuri, and Hocquenghem (BCH) codes (a special type of linear codes).

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TL;DR: In this article , a collocation method based on Fibonacci polynomials is used for approximately solving a class of nonlinear differential equations with initial conditions, where the problem is firstly reduced into a nonlinear algebraic system via collocation points, and then the unknown coefficients of the approximate solution function are calculated.

Abstract: In this study, a collocation method based on Fibonacci polynomials is used for approximately solving a class of nonlinear differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature.

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TL;DR: In this article , a numerical solution for singularly perturbed problem with nonlocal boundary conditions is obtained using the finite difference method on the Bakhvalov-Shishkin mesh and the error is obtained first-order in the discrete maximum norm.

Abstract: In this paper, numerical solution for singularly perturbed problem with nonlocal boundary conditions is obtained. Finite difference method is used to discretize this problem on the Bakhvalov-Shishkin mesh. The some properties of exact solution are analyzed. The error is obtained first-order in the discrete maximum norm. Finally, an example is solved to show the advantages of the finite difference method.

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TL;DR: In this paper , the existence of solutions for hybrid stochastic differential equations with the -Hilfer fractional derivative was discussed and the main tool used in this study was associated with the technique of fixed point theorems due to Dhage.

Abstract: In this paper, we discuss the existence of solutions for hybrid stochastic differential equations (HSDEs) with the -Hilfer fractional derivative. The main tool used in our study is associated with the technique of fixed point theorems due to Dhage.

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TL;DR: In this article , the authors presented two efficient computational methods based on Legendre wavelets to solve the Korteweg-de Vries equation, which is utilized to formulate the propagation of water waves and occurs in different fields such as hydrodynamics waves in cold plasma acoustic waves in harmonic crystals.

Abstract: In this research work, we examine the Korteweg-de Vries equation (KdV), which is utilized to formulate the propagation of water waves and occurs in different fields such as hydrodynamics waves in cold plasma acoustic waves in harmonic crystals. This research work presents two efficient computational methods based on Legendre wavelets to solve the Korteweg-de Vries. The three-step Taylor method is first applied to the Korteweg-de Vries equation for time discretization. Then, the Galerkin method and the collocation method are used for spatial discretization. With these approaches, bringing the approximate solutions of the Korteweg-de Vries equation turns into getting the solution of the algebraic equation system. The solution of this system gives the Legendre wavelet coefficients. Substituting the obtained coefficients into the Legendre wavelet series expansion, the approximate solution can be obtained. The presented wavelet methods are tested by studying different problems at the end of this study.

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TL;DR: The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type of solution that is suitable for the application of physical applications as mentioned in this paper , and it is shown that the $\theta$-operator method can be used as a symbolic computational approach to obtain the indicial equation and the recurrence relation.

Abstract: The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type of solution. It is shown that the $\theta$-operator method can be used as a symbolic computational approach to obtain the indicial equation and the recurrence relation. Consequently, the singularity structure leads to the transformations that yield a solution in terms of a special function, if the equation is suitable. Hypergeometric and Heun-type equations are mostly employed in physical applications. Thus, only these equations and their confluent types are considered with SageMath routines which are assembled in the open-source package symODE2.

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TL;DR: In this paper , the authors concentrate on hyper generalized and quasi-generalized φ-varphi-recurrent π-cosymplectic manifolds and obtain some significant characterizations which classify such manifolds.

Abstract: In this paper, we concentrate on hyper generalized $\varphi-$recurrent $\alpha-$cosymplectic manifolds and quasi generalized $\varphi-$recurrent $\alpha-$cosymplectic manifolds and obtain some significant characterizations which classify such manifolds.

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TL;DR: In this article , a third order convergent finite-difference method for the approximate solution of the boundary value problems is proposed, which employs Taylor series expansion and method of undetermined coefficients.

Abstract: We propose a third order convergent finite-difference method for the approximate solution of the boundary value problems. We developed our numerical technique by employing Taylor series expansion and method of undetermined coefficients. The convergence property of the proposed finite difference method discussed. To demonstrate the computational accuracy and effectiveness of the proposed method numerical results presented.

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TL;DR: In this paper , an integrability condition and curvature properties for the Tachibana operator for the Riemannian structure on manifold and bundle are investigated. But the authors only focused on tangent and cotangent bundles.

Abstract: Our aim in this paper is to study of silver Riemannian structures on manifold and bundle. An integrability condition and curvature properties for silver Riemannian structure are investigated via the Tachibana operator . After twin silver Riemannian metric is studied. Examples of silver structures are given on tangent and cotangent bundles

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TL;DR: In this article , the properties of projective, concircular and conharmonic curvature tensor fields on a complex Sasakian manifold are investigated, and the authors show that the curvatures of the tensor field can be modelled as a tensor tensor.

Abstract: In this article, the properties of projective, concircular and conharmonic curvature tensor fields on a complex Sasakian manifold are investigated.

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TL;DR: In this paper , a new integral representation of the Jost solution of Sturm-Liouville equation with impuls in the semi axis was constructed and the uniqueness of the determination of the potential by the scattering data was proved.

Abstract: In this paper, we construct the new integral representation of the Jost solution of Sturm-Liouville equation with impuls in the semi axis $[0,+\infty )$ and we give this type of relation, examine the properties of the Kernel function and their partial derivatives with $x$ and $\ t$, constructed integral representation and obtain the partial differential equation provided by this Kernel function. Finally, in the paper we prove uniqueness of the determination of the potential by the scattering data.

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TL;DR: In this article , the authors define two new double sequence spaces by using the 4D Jordan totient matrix and show that these newly described double-sequence spaces are Banach spaces with their norm.

Abstract: The 4 dimensional (4d) Jordan totient matrix which is described by the aid of the famous Jordan's function and some new Jordan totient double sequence spaces described as the domain of this aforementioned matrix have been examined by Erdem and Demiriz . In the present paper, first of all we define two new double sequence spaces by using the 4d Jordan totient matrix and we show that this newly described double sequence spaces are Banach spaces with their norm. Then, we give some inclusion relations including this spaces. Moreover, we compute the $\alpha$-, $\beta(bp)$- and $\gamma$-duals and finally, we characterize some new 4d matrix transformation classes and complete this work with some significant results.

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TL;DR: In this article , singularly perturbed quasilinear boundary value problems are taken into account, and a finite finite factor derived based on Shishkin-type mesh (S-mesh) is proposed.

Abstract: A bstract . In this paper, singularly perturbed quasilinear boundary value problems are taken into account. With this purpose, a finite di ff erence scheme is proposed on Shishkin-type mesh (S-mesh). Quasilinearization technique and interpolating quadrature rules are used to establish the numerical scheme. Then, an error estimate is derived. A numerical experiment is demonstrated to verify the theory.

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TL;DR: The notion of Ti (i = 0; 1; 2; 3; 4) separation axioms in intuitionistic fuzzy hypersoft topological spaces are introduced and some of its properties are discussed.

Abstract: In the present paper, we introduce the notion of Ti (i = 0; 1; 2; 3; 4) separation axioms in intuitionistic fuzzy hypersoft topological spaces and discuss some of its properties. By using this notions, we also give some basic theorems of separation axioms in intuitionistic fuzzy hypersoft topological spaces. Finally, we present hereditary property of intuitionistic fuzzy hypersoft topological spaces.

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TL;DR: Performance evaluation shows that proposed vehicle detection method increases F1 and recall values significantly compared to the motion and object detection methods alone, and outperforms SCBU and MCD methods which are widely used for performance comparison in motion detection studies in the literature.

Abstract: Moving vehicle detection is one of important issues in surveillance and traffic monitoring applications for aerial images. In this study, a vehicle detection method is proposed by combining motion and object detection. A method based on background modeling and subtraction is applied for motion detection, while Faster-RCNN architecture is used for object detection. Motion detection result is enhanced with the proposed superpixel based refinement method. Experimental study shows that performance of motion detection increases about 8\% for $F_1$ metric with the proposed post processing method. Object detection, motion detection and superpixel segmentation methods interact with each other in parallel processes with the proposed software architecture, which significantly increases the working speed of the method. In last step of the proposed method, each vehicle is tracked with the kalman filter. The performance of proposed method is evaluated on the VIVID dataset. The performance evaluation shows that proposed method increases F1 and recall values significantly compared to the motion and object detection methods alone. It also outperforms SCBU and MCD methods which are widely used for performance comparison in motion detection studies in the literature.

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TL;DR: In this paper , the authors defined third order bronze Fibonacci quaternions and obtained the generating functions, the Binet's formula and some properties of these Quaternions, including d'Ocagne's and Cassini's identities.

Abstract: In this study, we define third order bronze Fibonacci quaternions. We obtain the generating functions, the Binet's formula and some properties of these quaternions. We give d'Ocagne's-like and Cassini's-like identity and we use q-determinants for quaternionic matrices to give the Cassini's identity for third order bronze Fibonacci quaternions.

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TL;DR: In this paper , by using weight g-statistical density, the authors introduced weight gstatistical supremum-infimum for real valued sequences, which is defined as the limit of the maximum density of a real valued sequence.

Abstract: In this paper, by using weight g-statistical density we introduce weight g-statistical supremum-infimum
for real valued sequences. We also define weight g-statistical limit supremum-infimum with the help of above new
concepts. In addition, we shall establish some results about weight g-statistical core.

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TL;DR: In this article , a new generalization of Gaussian Pell-Lucas polynomials, called $d-$Gaussian PLC, was defined, and the generating function and Binet formula were presented.

Abstract: We define a new generalization of Gaussian Pell-Lucas polynomials. We call it $d-$Gaussian Pell-Lucas polynomials. Then we present the generating function and Binet formula for the polynomials. We give a matrix representation of $d-$Gaussian Pell-Lucas polynomials. Using the Riordan method, we obtain the factorizations of Pascal matrix involving the polynomials.

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TL;DR: In this article , the integrability of almost paracomplex structures on the manifolds with torsion was studied and a new class of anti-paraHermitian manifolds associated with these manifold connections was introduced.

Abstract: In the present paper firstly, we introduce classes of anti-paraK\"{a}hler-Codazzi manifolds and we discuss the problem of integrability for almost paracomplex structures on thes manifolds. Secondly, we introduce a new classes of anti-paraHermitian manifolds associated with these anti-paraHermitian metric connections with torsion, we look for the conditions in which it becomes are anti-paraK\"{a}hler manifolds or anti-paraK\"{a}hler-Codazzi manifolds.

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TL;DR: In this paper , the authors investigated the independent transversal domination number for the transformation graph of the path graph, cycle graph, star graph, wheel graph, complete graph and cycle graph.

Abstract: A dominating set of a graph $G$ which intersects every independent set of a maximum cardinality in $G$ is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of $G$ and is denoted by $\gamma_{it}(G)$. In this paper we investigate the independent transversal domination number for the transformation graph of the path graph $P_{n}^{+-+}$, the cycle graph $C_{n}^{+-+}$, the star graph $S_{1,n}^{+-+}$, the wheel graph $W_{1,n}^{+-+}$ and the complete graph $K_{n}^{+-+}$.