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Articles 3721 - 3750 of 10319
Full-Text Articles in Physical Sciences and Mathematics
Fedja's Proof Of Deepti's Inequality, Sofiya Ostrovska, Mehmet Turan
Fedja's Proof Of Deepti's Inequality, Sofiya Ostrovska, Mehmet Turan
Turkish Journal of Mathematics
The paper aims to present, in a systematic way, an elegant proof of Deepti's inequality. Both the inequality and various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none have appeared in the literature thus far. In this work, suggestions pertaining to users 'Deepti' and 'fedja' are traced, whence the title. The results or the paper are new, and the proof is divided into a series of statements, many of which are of interest in themselves.
The United Stable Solution Set Of Interval Continuous-Time Algebraic Riccati Equation And Verified Numerical Computation Of Its Outer Estimation, Tayyebe Haqiri, Mahmoud Mohseni Moghadam, Azim Rivaz
The United Stable Solution Set Of Interval Continuous-Time Algebraic Riccati Equation And Verified Numerical Computation Of Its Outer Estimation, Tayyebe Haqiri, Mahmoud Mohseni Moghadam, Azim Rivaz
Turkish Journal of Mathematics
This paper introduces the interval continuous-time algebraic Riccati equation $\mathbf{A}^* X + X\mathbf{A} + \mathbf{Q} -X \mathbf{G} X=0$, where $\mathbf{A}, \mathbf{G}$, and $\mathbf{Q}$ are known $n \times n$ complex interval matrices, $\mathbf{G}$ and $\mathbf{Q}$ are Hermitian, and $X$ is an unknown matrix of the same size, and develops two approaches for enclosing the united stable solution set of this interval equation. We first discuss the united stable solution set and then derive a nonlinear programming method in order to find an enclosure for the united stable solution set. We also advance an efficient technique for enclosing the united stable solution …
Some Series Involving The Euler Zeta Function, Min-Soo Kim
Some Series Involving The Euler Zeta Function, Min-Soo Kim
Turkish Journal of Mathematics
In this paper, using the Boole summation formula, we obtain a new integral representation of $n$-th quasi-periodic Euler functions $\overline{E}_n(x)$ for $n=1,2,\ldots.$ We also prove several series involving Euler zeta functions $\zeta_{E}(s),$ which are analogues of the corresponding results by Apostol on some series involving the Riemann zeta function $\zeta(s).$
Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal
Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal
Turkish Journal of Mathematics
The purpose of the present paper is to establish the rate of convergence for a Lipschitz-type space and obtain the degree of approximation in terms of Lipschitz-type maximal function for the Durrmeyer type modification of Jakimovski-Leviatan operators based on Appell polynomials. We also study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation.
On Radial Solutions For Monge-Ampére Equations, Ronghua Liu, Fanglei Wang, Yukun An
On Radial Solutions For Monge-Ampére Equations, Ronghua Liu, Fanglei Wang, Yukun An
Turkish Journal of Mathematics
In this paper,we obtain some new existence, uniqueness, and multiplicity results of radial solutions of an elliptic system coupled by Monge-Ampére equations using the fixed point theorem.
Extended Laguerre-Appell Polynomials Via Fractional Operators And Their Determinant Forms, Subuhi Khan, Shahid Ahmad Wani
Extended Laguerre-Appell Polynomials Via Fractional Operators And Their Determinant Forms, Subuhi Khan, Shahid Ahmad Wani
Turkish Journal of Mathematics
In this article, the extended form of Laguerre-Appell polynomials is introduced by means of generating function and operational definition. The corresponding results for the extended Laguerre-Bernoulli and Laguerre-Euler polynomials are obtained as applications. Further, the determinant forms of these polynomials are established by using operational techniques.
On Dominated Coloring Of Graphs And Some Nordhaus--Gaddum-Type Relations, Fatemeh Choopani, Abbas Jafarzadeh, Ahmad Erfanian, Doost Ali Mojdeh
On Dominated Coloring Of Graphs And Some Nordhaus--Gaddum-Type Relations, Fatemeh Choopani, Abbas Jafarzadeh, Ahmad Erfanian, Doost Ali Mojdeh
Turkish Journal of Mathematics
The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $\chi_{dom}(G)$. In this paper, dominated coloring of graphs is compared with (open) packing number of $G$ and it is shown that if $G$ is a graph of order $n$ with $diam(G)\geq3$, then $\chi_{dom}(G)\leq n-\rho(G)$ and if $\rho_0 (G)=2n/3$, then $\chi_{dom}(G)= \rho_0 (G)$, and if $\rho(G)=n/2$, then $\chi_{dom}(G)=\rho(G)$. The dominated chromatic numbers of the …
Certain Strongly Clean Matrices Over Local Rings, Tuğçe Pekacar Çalci, Huanyin Chen
Certain Strongly Clean Matrices Over Local Rings, Tuğçe Pekacar Çalci, Huanyin Chen
Turkish Journal of Mathematics
We are concerned about various strongly clean properties of a kind of matrix subrings $L_{(s)}(R)$ over a local ring $R$. Let $R$ be a local ring, and let $s\in C(R)$. We prove that $A\in L_{(s)}(R)$ is strongly clean if and only if $A$ or $I_2-A$ is invertible, or $A$ is similar to a diagonal matrix in $L_{(s)}(R)$. Furthermore, we prove that $A\in L_{(s)}(R)$ is quasipolar if and only if $A\in GL_2(R)$ or $A\in L_{(s)}(R)^{qnil}$, or $A$ is similar to a diagonal matrix $\left( \begin{array}{cc} \lambda&0\\ 0&\mu \end{array} \right)$ in $L_{(s)}(R)$, where $\lambda\in J(R)$, $\mu\in U(R)$ or $\lambda\in U(R)$, $\mu\in J(R)$, …
An Exponential Method To Solve Linear Fredholm-Volterraintegro-Differential Equations And Residual Improvement, Şuayi̇p Yüzbaşi
An Exponential Method To Solve Linear Fredholm-Volterraintegro-Differential Equations And Residual Improvement, Şuayi̇p Yüzbaşi
Turkish Journal of Mathematics
In this paper, a collocation approach based on exponential polynomials is introduced to solve linear Fredholm-Volterra integro-differential equations under the initial boundary conditions. First, by constructing the matrix forms of the exponential polynomials and their derivatives, the desired exponential solution and its derivatives are written in matrix forms. Second, the differential and integral parts of the problem are converted into matrix forms based on exponential polynomials. Later, the main problem is reduced to a system of linear algebraic equations by aid of the collocation points, the matrix operations, and the matrix forms of the conditions. The solutions of this system …
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Turkish Journal of Mathematics
Rotation minimizing (RM) vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even when the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed into a Riemannian manifold are studied when the ambient manifold is the Euclidean 3-space, the hyperbolic 3-space, and a Kähler manifold.
Construction Of Some New Families Of Apostol-Type Numbers And Polynomials Via Dirichlet Character And $P$-Adic $Q$-Integrals, Yilmaz Şi̇mşek
Construction Of Some New Families Of Apostol-Type Numbers And Polynomials Via Dirichlet Character And $P$-Adic $Q$-Integrals, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
In this paper, by applying the $p$-adic $q$-integrals to a family of continuous differentiable functions on the ring of $p$-adic integers, we construct new generating functions for generalized Apostol-type numbers and polynomials attached to the Dirichlet character of a finite abelian group. By using these generating functions with their functional equations, we derive various new identities and relations for these numbers and polynomials. These results are generalizations of known identities and relations including some well-known families of special numbers and polynomials such as the generalized Apostol-type Bernoulli, the Apostol-type Euler, the Frobenius-Euler numbers and polynomials, the Stirling numbers, and other …
Some Results On Hecke And Extended Hecke Groups, Recep Şahi̇n
Some Results On Hecke And Extended Hecke Groups, Recep Şahi̇n
Turkish Journal of Mathematics
Let $q\geq 3$ be a prime number and let $\overline{H}(\lambda _{q})$ be the extended Hecke group associated with $q.$ In this paper, we determine the presentation of the commutator subgroup ($H$($\lambda _{q})\alpha )^{\prime } $ of the normal subgroup $H$($\lambda _{q})\alpha $, where $H$($\lambda _{q})\alpha $ is a subgroup of index $2$ in $\overline{H}$($\lambda _{q}).$ Next we discuss the commutator subgroup ($\overline{H}_{2})^{\prime }$($% \lambda _{q})$ of the principal congruence subgroup $\overline{H}_{2}$($% \lambda _{q})$ of $\overline{H}$($\lambda _{q})$. Then we show that some quotient groups of $\overline{H}$($\lambda _{q})$ are generalized $M^{\ast }- $groups. Finally, we prove some results related to some normal …
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Turkish Journal of Mathematics
In this paper, on one hand, we propose a new type of symmetric function to interpret the bi$^{s}$nomial coefficients and their analogs. On other hand, according to this function, we give an interpretation of these coefficients by lattice paths and tiling. Some identities of these coefficients are also established. This work is an extension of the results of Belbachir and Benmezai's ''A $\mathit{q}$-analogue for bi$^{\mathit{s}}$nomial coefficients and generalized Fibonacci sequences".
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Turkish Journal of Mathematics
The iterative equation $f^{q}(x)=g(x)$, $x\in X$ for a given function $g$ and a positive integer $q$ is solved in the following two main cases: (i) $X=\mathbb{Z}$, $g(x)=ax+b$, ($a,b\in\mathbb{Z}$; $a\neq0,1$); (ii) $X=\mathbb{N}\cup\left\{ 0\right\} $, $g$ is increasing with no fixed point.
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Turkish Journal of Mathematics
A variant of Weyl- and Horn-type inequalities for cyclically compact operators on Kaplansky-Hilbert modules is given.
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Turkish Journal of Mathematics
Let $E$ be a Banach space, $\lambda$ a perfect sequence space, and $M$ an Orlicz function. Denote by $\lambda \left(E, M\right)_{r}$ the space of all weakly $(M, \lambda)$-summable sequences from $E$ that are the limit of their finite sections. In this paper, we describe the continuous linear functionals on $\lambda \left(E, M\right)_{r}$ in terms of strongly $(N, \lambda^{\ast})$-summable sequences in the dual $E^{*}$ of $E$, and then we give a characterization of the reflexivity of $\lambda \left(E, M\right)$ in terms of that of $\lambda$ and of $E$ and the AK-property.
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
Turkish Journal of Mathematics
Using generalized hypergeometric functions to perform symbolic manipulations of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, that function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new …
On The Monodromy Of Milnor Open Books, Selma Altinok Bhupal, Mohan Lal Bhupal
On The Monodromy Of Milnor Open Books, Selma Altinok Bhupal, Mohan Lal Bhupal
Turkish Journal of Mathematics
We present some techniques that can be used to factorize the monodromy of certain Milnor open books. We also describe a class of Milnor open books for which we can explicitly express the monodromy as a product of Dehn twists.
Lower And Upper Solutions Method For A Problem Of An Elastic Beam Whose One End Is Simply Supported And The Other End Is Sliding Clamped, Man Xu, Ruyun Ma, Jin Wen
Lower And Upper Solutions Method For A Problem Of An Elastic Beam Whose One End Is Simply Supported And The Other End Is Sliding Clamped, Man Xu, Ruyun Ma, Jin Wen
Turkish Journal of Mathematics
In this paper we develop the lower and upper solutions method for the fourth-order boundary value problem of the form $$ \left\{ \aligned &y^{(4)}(x)+(k_{1}+k_{2})y''(x)+k_{1}k_{2}y(x)=f(x,y(x)), \ \ x\in (0,1),\\ &y(0)=y'(1)=y''(0)=y'''(1)=0,\\ \endaligned \right. $$ which models a statically elastic beam with one of its ends simply supported and the other end clamped by sliding clamps, where $k_{1}
Generation Of Efficient And $\Epsilon$-Efficient Solutionsin Multiple Objective Linear Programming, Zohra Sabrina Delhoum, Sonia Radjef, Fatima Boudaoud
Generation Of Efficient And $\Epsilon$-Efficient Solutionsin Multiple Objective Linear Programming, Zohra Sabrina Delhoum, Sonia Radjef, Fatima Boudaoud
Turkish Journal of Mathematics
We develop an algorithm to solve a multiple objective linear programming problem with bounded variables. It is based on the scalarization theorem of optimal solutions of multiobjective linear programs and the single objective adaptive method. We suggest a process for the search for the first efficient solution without having to calculate a feasible solution, and we elaborate a method to generate efficient solutions, weakly efficient solutions, and $\epsilon$-efficient solutions. Supporting theoretical results are established and the method is demonstrated on a numerical example.
Just Non-Artinian Modules Over Some Group Rings, Leonid A. Kurdachenko, Marco Trombetti
Just Non-Artinian Modules Over Some Group Rings, Leonid A. Kurdachenko, Marco Trombetti
Turkish Journal of Mathematics
Let $D$ be a Dedekind domain and $G$ be a periodic Abelian-by-finite group. In this paper we study $DG$-modules in which every factor-module, apart from the trivial one, is $DG$-Artinian. In particular we prove that such modules cannot be $D$-periodic and that $G$ must be subject to some restrictions. Finally, we give a detailed description of such modules when $G$ is periodic Abelian and the spectrum of $D$ is infinite.
Fréchet-Hilbert Spaces And The Property Scbs, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul
Fréchet-Hilbert Spaces And The Property Scbs, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul
Turkish Journal of Mathematics
In this note, we obtain that all separable Fréchet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioğlu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Fréchet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Fréchet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Fréchet-Hilbert space still takes place up to a complemented Hilbert subspace. Moreover, the strong dual of a real Fréchet-Hilbert space has the SCBS property.
Diagonal Lift In The Semi-Cotangent Bundle And Its Applications, Furkan Yildirim
Diagonal Lift In The Semi-Cotangent Bundle And Its Applications, Furkan Yildirim
Turkish Journal of Mathematics
The present paper is devoted to some results concerning the diagonal lift of tensor fields of type (1,1) from manifold M to its semi-cotangent bundle t*M. In this context, cross-sections in the semi-cotangent (pull-back) bundle t*M of cotangent bundle T*M by using projection (submersion) of the tangent bundle TM can be also defined.
A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
Turkish Journal of Mathematics
Motivated by their importance and potential for applications in a variety of research fields, recently, various polynomials and their extensions have been introduced and investigated. In this sequel, we modify the known generating functions of polynomials, due to both Milne-Thomson and Dere and Simsek, to introduce a new class of generalized polynomials and present some of their involved properties. As obvious special cases of the newly introduced polynomials, we also introduce so-called power sum-Laguerre--Hermite polynomials and generalized Laguerre and Euler polynomials and we present some of their involved identities and formulas. The results presented here, being very general, are pointed …
On The Local Superconvergence Of The Fully Discretized Multiprojection Method For Weakly Singular Volterra Integral Equations Of The Second Kind, Hossein Beyrami, Taher Lotfi
On The Local Superconvergence Of The Fully Discretized Multiprojection Method For Weakly Singular Volterra Integral Equations Of The Second Kind, Hossein Beyrami, Taher Lotfi
Turkish Journal of Mathematics
In this paper, we extend the well-known multiprojection method for solving the second kind of weakly singular Volterra integral equations. We apply this method based on the collocation projection and develop a fully discretized version using appropriate quadrature rules. This method has a superconvergence property that the classic collocation method lacks. Although the new approach results in a significant increase in computational cost, when performing the related matrix-matrix products in parallel the computational time can be reduced. We provide a rigorous mathematical discussion about error analysis of this method. Finally, we present some numerical examples to confirm our theoretical results.
Harmonic Functions Associated With Some Polynomials In Severalvariables, Fatma Taşdelen Yeşi̇ldal, Rabi̇a Aktaş, Esra Erkus Duman
Harmonic Functions Associated With Some Polynomials In Severalvariables, Fatma Taşdelen Yeşi̇ldal, Rabi̇a Aktaş, Esra Erkus Duman
Turkish Journal of Mathematics
The aim of this paper is to give various properties of homogeneous operators associated with Chan-Chyan-Srivastava polynomials and, by using these results, to obtain harmonic functions by applying Laplace and ultrahyperbolic operators to the Chan-Chyan-Srivastava polynomials.
If $4$-Convex Vectors Are Closed In Uniform Norms Then Their Second Derivatives Are Also Closed In Weighted $L^2$-Norm, Muhammad Shoaib Saleem, Josip Pecaric, Hamood Ur Rehman, Mobeen Munir, Muhammad Wahab Khan
If $4$-Convex Vectors Are Closed In Uniform Norms Then Their Second Derivatives Are Also Closed In Weighted $L^2$-Norm, Muhammad Shoaib Saleem, Josip Pecaric, Hamood Ur Rehman, Mobeen Munir, Muhammad Wahab Khan
Turkish Journal of Mathematics
In this paper, we develop the weighted energy estimates for arbitrary 4-convex vectors and the vectors having both 4-convex and 4-concave functions as their arguments. To do this, we first develop these estimates for smooth 4-convex vectors and then, through mollification, extend the results for arbitrary 4-convex vectors. This type of estimates are valuable in problems of financial mathematics for the establishment of optimal investment strategies
Equivalence Problem For Compatible Bi-Hamiltonian Structures On Three-Dimensional Orientable Manifolds, Tuna Bayrakdar, Abdullah Azi̇z Ergi̇n
Equivalence Problem For Compatible Bi-Hamiltonian Structures On Three-Dimensional Orientable Manifolds, Tuna Bayrakdar, Abdullah Azi̇z Ergi̇n
Turkish Journal of Mathematics
We solve the equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds via Cartan's method of equivalence. The problem separates into two branches on total space, one of which ends up with the intransitive involutive structure equations. For the transitive case, we obtain an $\{e\}$-structure on both total and base spaces.
Iteration Method Of Approximate Solution Of The Cauchy Problem Fora~Singularly Perturbed Weakly Nonlinear Differential Equation Of An Arbitrary Order, Alexey Alimov, Evgeny Bukhzhalev
Iteration Method Of Approximate Solution Of The Cauchy Problem Fora~Singularly Perturbed Weakly Nonlinear Differential Equation Of An Arbitrary Order, Alexey Alimov, Evgeny Bukhzhalev
Turkish Journal of Mathematics
We construct an iteration sequence converging (in the uniform norm in the space of continuous functions) to the solution of the Cauchy problem for a~singularly perturbed weakly nonlinear differential equation of an arbitrary order (the weak nonlinearity means the presence of a~small parameter in the nonlinear term). The sequence thus constructed is also asymptotic in the sense that the departure of its $n$th element from the solution of the problem is proportional to the $(n+1)$th power of the perturbation parameter.
Adaptive Collaborative Speed Control Of Pmdc Motor Using Hyperbolic Secant Functions And Particle Swarm Optimization, Omer Saleem, Khalid Mahmood-Ul-Hasan
Adaptive Collaborative Speed Control Of Pmdc Motor Using Hyperbolic Secant Functions And Particle Swarm Optimization, Omer Saleem, Khalid Mahmood-Ul-Hasan
Turkish Journal of Electrical Engineering and Computer Sciences
This paper presents an adaptive collaborative speed controller for a permanent magnet direct-current (PMDC) motor. The proposed scheme beneficially combines the control efforts of a proportional-integral (PI) controller and a linear-quadratic regulator (LQR) via a weighted summing module. Initially, the weightages of the summing module are kept fixed. They are optimally tuned and tested via the particle swarm optimization algorithm. In order to synergize the controller combination, these weightages are adaptively modulated as well, using hyperbolic secant functions of the error dynamics of the motor's angular speed. The adaptive combination renders significant enhancement in the transient response, steady-state response, input-energy …