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Articles 1111 - 1140 of 2494
Full-Text Articles in Physical Sciences and Mathematics
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Turkish Journal of Mathematics
The aim of this paper is to estimate the shape of an unknown part of the boundary of a geometrical domain. The identification technique used to estimate this part is the observation of the solution of a diffusion problem on the known part of this boundary. This technique is based on the sentinels theory.
Combinatorial Enumeration Of Cyclic Covers Of $\Mathbb{P}^{1}$, Alberto Besana, Cristina Martinez Ramirez
Combinatorial Enumeration Of Cyclic Covers Of $\Mathbb{P}^{1}$, Alberto Besana, Cristina Martinez Ramirez
Turkish Journal of Mathematics
We study plane algebraic curves defined over a field $k$ of arbitrary characteristic that are ramified coverings of the projective line $\mathbb{P}^{1}(k)$ branched over a given configuration of distinct points by their ramification type specified by a partition of $d$ the degree of the covering. We enumerate them by using the combinatorics of partitions and its connection to the representation theory of the symmetric group.
On The Summability Methods Of Logarithmic Type And The Berezin Symbol, Ulaş Yamanci
On The Summability Methods Of Logarithmic Type And The Berezin Symbol, Ulaş Yamanci
Turkish Journal of Mathematics
We prove by means of the Berezin symbols some theorems for the $\left( L\right) $-summability method for sequences and series. Also, we prove a new Tauberian type theorem for $\left( L\right) $-summability.
Spectral Expansion For The Singular Dirac System With Impulsive Conditions, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Spectral Expansion For The Singular Dirac System With Impulsive Conditions, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.
A New Proof Of A Harnack Inequality For The Curve Shortening Flow, Mihai Bailesteanu
A New Proof Of A Harnack Inequality For The Curve Shortening Flow, Mihai Bailesteanu
Turkish Journal of Mathematics
We offer a new approach for determining Harnack quantities for the curve shortening flow and we show how, following this procedure, one can obtain Hamilton's Harnack inequality for this flow $\kappa_t+\frac{1}{2t}\kappa\geq\frac{\kappa_s^2}{\kappa}$, where $\kappa$ is the curvature of the curve being deformed by the flow.
Relative Stable (Co)Homology, Chaoling Huang, Li Yuan
Relative Stable (Co)Homology, Chaoling Huang, Li Yuan
Turkish Journal of Mathematics
For a fixed precovering class $\mathcal{X}$ and a fixed preenveloping class $\mathcal{Y}$, we first introduce the notions of relative stable cohomology $\widetilde{Ext}_{\mathcal{X}}(-,\ -)$ and relative stable homology $\widetilde{Tor}_{\mathcal{X}\mathcal{Y}}(-,\ -)$. Then we consider their properties and, more importantly, we study the stable (co)homology under the case of $\mathcal{P}(R)$, $\mathcal{F}(R)$, and $\mathcal{I}(R)$ and the case of $\mathcal{P}_C(R)$, $\mathcal{F}_C(R)$, and $\mathcal{I}_C(R)$. Finally, we generalize relative stable (co)homology from the case of $R$-modules to the case of $R$-complexes.
Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$, Ahmet Hamdi̇ Avşar, Hüseyi̇n Koç
Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$, Ahmet Hamdi̇ Avşar, Hüseyi̇n Koç
Turkish Journal of Mathematics
In this paper, we study Jackson and Stechkin type theorems of trigonometric polynomial approximation in the space $A_{w,\vartheta }^{p,q(\cdot )}$ by considering a modulus of smoothness defined by virtue of the Steklov operator.
On Spanning Sets And Generators Of Near-Vector Spaces, Karin-Therese Howell, Sogo Pierre Sanon
On Spanning Sets And Generators Of Near-Vector Spaces, Karin-Therese Howell, Sogo Pierre Sanon
Turkish Journal of Mathematics
In this paper we study the quasi-kernel of certain constructions of near-vector spaces and the span of a vector. We characterize those vectors whose span is one-dimensional and those that generate the whole space.
On The Density And Transitivity Of Sets Of Operators, Mohammad Ansari, Bahram Khani Robati, Karim Hedayatian
On The Density And Transitivity Of Sets Of Operators, Mohammad Ansari, Bahram Khani Robati, Karim Hedayatian
Turkish Journal of Mathematics
By the well-known result of Yood, every strictly transitive algebra of operators on a Banach space is WOT-dense. This motivated us to investigate the relationships between SOT and WOT largeness of sets of operators and the transitivity behavior of them. We show that, to obtain Yood's result, strict transitivity may not be replaced by the weaker condition of hypertransitivity. We prove that, for a wide class of topological vector spaces, every SOT-dense set of operators is hypertransitive. The general form of SOT-dense sets that are not strictly transitive is presented. We also describe the form of WOT-dense sets that are …
Variational Multiscale Method For The Optimal Control Problems Of Convectio--Diffusion-Reaction Equations, Ayteki̇n Bayram Çibik, Fi̇kri̇ye Nuray Yilmaz
Variational Multiscale Method For The Optimal Control Problems Of Convectio--Diffusion-Reaction Equations, Ayteki̇n Bayram Çibik, Fi̇kri̇ye Nuray Yilmaz
Turkish Journal of Mathematics
In this paper, we analyze a projection-based variational multiscale (VMS) method for the optimal control problems governed by the convection-diffusion-reaction equations. We derive the first-order optimality conditions by the \emph{optimize-then-discretize} method. After expressing the discrete optimal control problem, we obtain the stability properties of state and adjoint variables. We also prove that the error in each variable is optimal. Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables.
The Cauchy-Kowalevski Theorem Applied For Counting Connections With A Prescribed Ricci Tensor, Barbara Opozda, Wlodzimierz M. Mikulski
The Cauchy-Kowalevski Theorem Applied For Counting Connections With A Prescribed Ricci Tensor, Barbara Opozda, Wlodzimierz M. Mikulski
Turkish Journal of Mathematics
How many linear connections are there with a prescribed Ricci tensor? The question is answered in the analytic case by using the Cauchy-Kowalevski theorem
An Application Of $Q$-Sumudu Transform For Fractional $Q$-Kinetic Equation, Sunil Dutt Purohit, Faruk Uçar
An Application Of $Q$-Sumudu Transform For Fractional $Q$-Kinetic Equation, Sunil Dutt Purohit, Faruk Uçar
Turkish Journal of Mathematics
The aim of this paper is to give an alternative solution for the $q$-kinetic equation involving the Riemann--Liouville fractional $q$-integral operator. The solution is obtained in terms of the $q$-Mittag--Leffler functions using inverse $q$-Sumudu transform. As applications, some corollaries are presented to illustrate the main results.
Higher Order Generalized Geometric Polynomials, Levent Kargin, Bayram Çeki̇m
Higher Order Generalized Geometric Polynomials, Levent Kargin, Bayram Çeki̇m
Turkish Journal of Mathematics
According to the generalized Mellin derivative, we introduce a new family of polynomials called higher order generalized geometric polynomials and obtain some arithmetical properties of them. Then we investigate the relationship of these polynomials with degenerate Bernoulli, degenerate Euler, and Bernoulli polynomials. Finally, we evaluate several series and integrals in closed forms.
The Rank Of Apparition Of Powers Of Lucas Sequence, Prasanta Kumar Ray, Nuretti̇n Irmak, Bijan Kumar Patel
The Rank Of Apparition Of Powers Of Lucas Sequence, Prasanta Kumar Ray, Nuretti̇n Irmak, Bijan Kumar Patel
Turkish Journal of Mathematics
This note is devoted to studying the divisibility relation $u_{n}^{k+1} u_{m}$ for a least positive integer $m$, where $\{u_{n}\}_{n \geq 0}$ is a nondegenerate Lucas sequence with characteristic polynomial $x^{2}-ax - b,$ for some relatively prime integers $a$ and $b$.
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Turkish Journal of Mathematics
In this paper, the authors study some subordination and superordination properties for classes of $p$-valent meromorphic, analytic, and univalent functions associated with a linear operator $\mathfrak{L}_{p,\lambda}^{m,\ell}(a,c,\mu)$ of the Erdélyi-Kober type. Connections with several earlier results are also pointed out.
On Some Properties Of Hyperstonean Spaces, Banu Güntürk, Bahaetti̇n Cengi̇z
On Some Properties Of Hyperstonean Spaces, Banu Güntürk, Bahaetti̇n Cengi̇z
Turkish Journal of Mathematics
This paper is devoted to hyperstonean spaces that are precisely the Stone spaces of measure algebras, or the Stone spaces of the Boolean algebras of $% L^{p}$-projections of Banach spaces for $1$ $\leq p
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and necessary and sufficient, conditions for the functions belonging to these classes, respectively, are also given. Furthermore, various properties like order of starlikeness and radius of convexity of the subclasses of these classes and radii of starlikeness and convexity of these subclasses are examined.
On The Hilbert Formulas And Of Change Of Integration Order For Some Singular Integrals In The Unit Circle, Juan Bory Reyes, Ricardo Abreu Blaya, Marco Antonio Perez De La Rosa, Baruch Schneider
On The Hilbert Formulas And Of Change Of Integration Order For Some Singular Integrals In The Unit Circle, Juan Bory Reyes, Ricardo Abreu Blaya, Marco Antonio Perez De La Rosa, Baruch Schneider
Turkish Journal of Mathematics
We obtain some analogues of the Hilbert formulas on the unit circle for $\alpha$-hy\-per\-ho\-lo\-mor\-phic function theory when $\alpha$ is a complex number. Such formulas relate a pair of components of the boundary value of an $\alpha$-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincaré-Bertrand formula for the $\alpha$-hyperholomorphic singular integrals in the unit circle is presented.
Hyperplanes, Parallelism, And Related Problems In Veronese Spaces, Krzysztof Petelczyc, Krzysztof Prazmowski, Malgorzata Prazmowska, Mariusz Zynel
Hyperplanes, Parallelism, And Related Problems In Veronese Spaces, Krzysztof Petelczyc, Krzysztof Prazmowski, Malgorzata Prazmowska, Mariusz Zynel
Turkish Journal of Mathematics
We determine hyperplanes in Veronese spaces associated with projective spaces and polar spaces, and we analyze the geometry of parallelisms induced by these hyperplanes. We also discuss whether or not parallelisms on Veronese spaces associated with affine spaces can be imposed.
Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu
Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu
Turkish Journal of Mathematics
In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.
Unconditional Wavelet Bases In Lebesgue Spaces, Yan Zhang, Yun Zhang Li
Unconditional Wavelet Bases In Lebesgue Spaces, Yan Zhang, Yun Zhang Li
Turkish Journal of Mathematics
In this paper, we prove that an orthonormal wavelet basis associated with a general isotropic expansive matrix must be an unconditional basis for all $L^{p}$(ℝ${}^{d})$ with $1$<$p$<$\infty$, provided the wavelet functions satisfy some usual conditions.
Bounds For Radii Of Starlikeness And Convexity Of Some Special Functions, İbrahi̇m Aktaş, Arpad Baricz, Hali̇t Orhan
Bounds For Radii Of Starlikeness And Convexity Of Some Special Functions, İbrahi̇m Aktaş, Arpad Baricz, Hali̇t Orhan
Turkish Journal of Mathematics
In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler--Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In …
Reducing Subspaces Of Toeplitz Operators On Dirichlet Type Spaces Of The Bidisk, Hongzhao Lin
Reducing Subspaces Of Toeplitz Operators On Dirichlet Type Spaces Of The Bidisk, Hongzhao Lin
Turkish Journal of Mathematics
The reducing subspaces of Toeplitz operators $T_{z_1^N}$(or $T_{z_2^N}$), $T_{z_1^Nz_2^N}$, and $T_{z_1^Nz_2^M}$ on Dirichlet type spaces of the bidisk ${\mathcal{D}}_\alpha({{{\mathbb{D}}}^{2}})$ are described, which extends the results for the corresponding operators on the Bergman space of the bidisk.
An Operational Matrix Method For Solving Linear Fredholm‒Volterra Integro-Differential Equations, Şuayi̇p Yüzbaşi, Nurbol Ismailov
An Operational Matrix Method For Solving Linear Fredholm‒Volterra Integro-Differential Equations, Şuayi̇p Yüzbaşi, Nurbol Ismailov
Turkish Journal of Mathematics
The aim of this paper is to propose an efficient method to compute approximate solutions of linear Fredholm‒Volterra integro-differential equations (FVIDEs) using Taylor polynomials. More precisely, we present a method based on operational matrices of Taylor polynomials in order to solve linear FVIDEs. By using the operational matrices of integration and product for the Taylor polynomials, the problem for linear FVIDEs is transformed into a system of linear algebraic equations. The solution of the problem is obtained from this linear system after the incorporation of initial conditions. Numerical examples are presented to show the applicability and the efficiency of the …
Worst-Case Large Deviations Upper Bounds For I.I.D. Sequencesunder Ambiguity, Mustafa Ç. Pinar
Worst-Case Large Deviations Upper Bounds For I.I.D. Sequencesunder Ambiguity, Mustafa Ç. Pinar
Turkish Journal of Mathematics
An introductory study of large deviations upper bounds from a worst-case perspective under parameter uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging min‒max (or max‒min) problems that admit some simplifications and some explicit results, mostly in the case of the normal probability law.
Exponential Stability Of Periodic Solutions Of Recurrent Neural Networks With Functional Dependence On Piecewise Constant Argument, Marat Akhmet, Duygu Aruğaslan Çi̇nçi̇n, Nur Cengi̇z
Exponential Stability Of Periodic Solutions Of Recurrent Neural Networks With Functional Dependence On Piecewise Constant Argument, Marat Akhmet, Duygu Aruğaslan Çi̇nçi̇n, Nur Cengi̇z
Turkish Journal of Mathematics
In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.
On Product And Golden Stuctures And Harmonicity, Sadetti̇n Erdem
On Product And Golden Stuctures And Harmonicity, Sadetti̇n Erdem
Turkish Journal of Mathematics
In this work, almost product and almost golden structures are studied. Conditions for those structures being integrable and parallel are investigated. Moreover, the harmonicity of a map between almost product or almost golden manifolds with pure or hyperbolic metric is discussed under certain conditions.
On The Fekete--Szeg\"{O} Type Functionals For Starlike And Convex Functions, Pawel Zaprawa
On The Fekete--Szeg\"{O} Type Functionals For Starlike And Convex Functions, Pawel Zaprawa
Turkish Journal of Mathematics
In the paper we discuss two functionals of the Fekete--Szeg\"{o} type: $\Phi_f(\mu) = a_2 a_4-\mu a_3{}^2$ and $\Theta_f(\mu) = a_4-\mu a_2a_3$ for an analytic function $f(z) = z+a_2z^2+a_3z^3+\ldots$, $z\in\Delta$, ($\Delta = \{z\in\mathbb{C}: z
An Efficient Technique To Solve Nonlinear Equations Usingmultiplicative Calculus, Muhammad Waseem, Muhammad Aslam Noor, Farooq Ahmed Shah, Khalida Inayat Noor
An Efficient Technique To Solve Nonlinear Equations Usingmultiplicative Calculus, Muhammad Waseem, Muhammad Aslam Noor, Farooq Ahmed Shah, Khalida Inayat Noor
Turkish Journal of Mathematics
In this paper, we develop an efficient technique in the framework of multiplicative calculus and suggest a new class of numerical methods for solving multiplicative nonlinear equations \textit{g}(\textit{x}% ) = 1. We also develop the convergence criteria of the proposed methods. We solve the population growth model and minimization problem, which demonstrate the implementation and efficiency of the new techniques. We also show that these techniques perform much better as compared to the similar ordinary methods for solving ordinary nonlinear equations \textit{f}(\textit{x}) = 0.
Small Covers Over Products Of A Simple Polytope With A Simplex, Wei Dai, Yanying Wang
Small Covers Over Products Of A Simple Polytope With A Simplex, Wei Dai, Yanying Wang
Turkish Journal of Mathematics
This paper proves that the number of small covers over products of a simple polytope with a $n$-simplex, up to D-J equivalence, is a polynomial in the variable $2^n$. A similar result holds for orientable small covers. We also provide a new way of computation, namely computing the finite number of representatives and interpolating polynomially. The ratio between the number of orientable small covers and the number of small covers is given. As an application, by interpolation, we determine the polynomials related to small covers and orientable small covers over products of a prism with a simplex up to D-J …