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Articles 1261 - 1290 of 2607
Full-Text Articles in Mathematics
Gadjieva's Conjecture, $K$-Functionals, And Someapplications In Weighted Lebesgue Spaces, Ramazan Akgün
Gadjieva's Conjecture, $K$-Functionals, And Someapplications In Weighted Lebesgue Spaces, Ramazan Akgün
Turkish Journal of Mathematics
We prove that Gadjieva's conjecture holds true as stated in her PhD thesis. The positive solution of this conjecture allows us to obtain improved versions of the Jackson--Stechkin type inequalities obtained in her thesis and some others. As an application, an equivalence of the modulus of smoothness with the realization functional is established. We obtain a characterization class for the modulus of smoothness.
Convolution And Jackson Inequalities In Musielak--Orlicz Spaces, Ramazan Akgün, Yunus Emre Yildirir
Convolution And Jackson Inequalities In Musielak--Orlicz Spaces, Ramazan Akgün, Yunus Emre Yildirir
Turkish Journal of Mathematics
In the present work we prove some direct and inverse theorems for approximation by trigonometric polynomials in Musielak-Orlicz spaces. Furthermore, we get a constructive characterization of the Lipschitz classes in these spaces.
Symmetry Of Numerical Range And Semigroup Generation Of Infinite Dimensional Hamiltonian Operators, Junjie Huang, Jie Liu, Alatancang Chen
Symmetry Of Numerical Range And Semigroup Generation Of Infinite Dimensional Hamiltonian Operators, Junjie Huang, Jie Liu, Alatancang Chen
Turkish Journal of Mathematics
This paper deals with the infinite dimensional Hamiltonian operator with unbounded entries. Using the core of its entries, we obtain the conditions under which the numerical range of such an operator is symmetric with respect to the imaginary axis. Based on the symmetry above, a necessary and sufficient condition for generating $C_0$ semigroups is further given.
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 …
An Effective Application Of Differential Quadrature Method Based Onmodified Cubic B-Splines To Numerical Solutions Of The Kdv Equation, Ali̇ Başhan
Turkish Journal of Mathematics
In this study, numerical solutions of the third-order nonlinear Korteweg--de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines. Five different problems are solved. To show the accuracy of the proposed method, $L_{2}$ and $L_{\infty }$ error norms of the problem, which has an analytical solution, and three lowest invariants are calculated and reported. The obtained solutions are compared with some earlier works. Stability analysis of the present method is also given.
Applications Of Extended Watson's Summation Theorem, Young Sup Kim, Sebastien Gaboury, Arjun Kumar Rathie
Applications Of Extended Watson's Summation Theorem, Young Sup Kim, Sebastien Gaboury, Arjun Kumar Rathie
Turkish Journal of Mathematics
In this research paper, several interesting applications of the extended classical summation theorem are given. As special cases, we recover several known results available in the literature.
Joint Densities Of Hitting Times For Finite State Markov Processes, Tomasz R. Bielecki, Monique Jeanblanc, Ali̇ Devi̇n Sezer
Joint Densities Of Hitting Times For Finite State Markov Processes, Tomasz R. Bielecki, Monique Jeanblanc, Ali̇ Devi̇n Sezer
Turkish Journal of Mathematics
For a finite state Markov process $X$ and a finite collection $\{ \Gamma_k, k \in K \}$ of subsets of its state space, let $\tau_k$ be the first time the process visits the set $\Gamma_k$. In general, $X$ may enter some of the $\Gamma_k$ at the same time and therefore the vector $\bm\tau :=(\tau_k, k \in K)$ may put nonzero mass over lower dimensional regions of ${\mathbb R}_+^{ K }$; these regions are of the form $R_s=\{{\bm t} \in {\mathbb R}_+^{ K }: t_i = t_j, ~~i,j \in s(1) \} \cap \bigcap_{l=2}^{ s } \{{\bm t}:t_m < t_i = t_j,~~ i,j \in s(l), m \in s(l-1) \}$ where $s$ is any ordered partition of the set $K$ and $s(j)$ denotes the $j^{th}$ subset of $K$ in the partition $s$. When $ s < K $, the density of the law of $\bm\tau$ over these regions is said to be ``singular'' because it is with respect to the $ s $-dimensional Lebesgue measure over the region $R_s.$ We derive explicit/recursive and simple to compute formulas for these singular densities and their corresponding tail probabilities over all $R_s$ as $s$ ranges over ordered partitions of $K$. We give a numerical example and indicate the relevance of our results to credit risk modeling.
The Natural Brackets On Couples Of Vector Fields And $1$-Forms, Miroslav Doupovec, Jan Kurek, Wlodzimierz Mikulski
The Natural Brackets On Couples Of Vector Fields And $1$-Forms, Miroslav Doupovec, Jan Kurek, Wlodzimierz Mikulski
Turkish Journal of Mathematics
All natural bilinear operators transforming pairs of couples of vector fields and $1$-forms into couples of vector fields and $1$-forms are found. All natural bilinear operators as above satisfying the Leibniz rule are extracted. All natural Lie algebra brackets on couples of vector fields and $1$-forms are collected.
On The Exponential Diophantine Equation $(18m^2+1)^X+(7m^2-1)^Y=(5m)^Z$, Murat Alan
On The Exponential Diophantine Equation $(18m^2+1)^X+(7m^2-1)^Y=(5m)^Z$, Murat Alan
Turkish Journal of Mathematics
Let $m$ be a positive integer. We show that the exponential Diophantine equation $ (18m^2+1)^x+(7m^2-1)^y=(5m)^z $ has only the positive integer solution $(x,y,z)=(1,1,2)$ except for $m \equiv 23,47,63, 87 \pmod {120}$. For $m\not\equiv 0 \pmod5$ we use some elementary methods and linear forms in two logarithms. For $m \equiv 0 \pmod 5$ we apply a result for linear forms in $p$-adic logarithms.
Existence And Uniqueness Of Solution Fordifferential Equation Of Fractional Order $2, Ghazala Akram, Fareeha Anjum
Existence And Uniqueness Of Solution Fordifferential Equation Of Fractional Order $2, Ghazala Akram, Fareeha Anjum
Turkish Journal of Mathematics
This paper is devoted to the study of nonlinear fractional differential equation involving Caputo fractional derivative of order $2
The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi
The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi
Turkish Journal of Mathematics
Karoubi's density theorem was first proved in Benayat's thesis and then cited and used in several books and articles. As K-theory is a special case of hermitian $_{\varepsilon }L$-theory, a natural question is whether such a theorem is still true in the latter theory. The purpose of this article is to show that it is indeed the case.
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.
Bargraphs In Bargraphs, Toufik Mansour, Armend Shabani
Bargraphs In Bargraphs, Toufik Mansour, Armend Shabani
Turkish Journal of Mathematics
Bargraphs are lattice paths in $\mathbb{N}_0^2$ that start at the origin and end upon their first return to the $x$-axis. Each bargraph is represented by a sequence of column heights $\pi_1\pi_2\cdots\pi_m$ such that column $j$ contains $\pi_j$ cells. In this paper, we study the number of bargraphs with $n$ cells and $m$ columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.
The Productively Lindelöf Property In The Remainders Of Topological Spaces, Seçi̇l Tokgöz
The Productively Lindelöf Property In The Remainders Of Topological Spaces, Seçi̇l Tokgöz
Turkish Journal of Mathematics
A topological space $X$ is called productively Lindelöf if $X\times Y$ is Lindelöf for every Lindelöf space $Y$. We study with remainders and investigate topological spaces with productively Lindelöf remainders.
Semisymmetric Contact Metric Manifolds Of Dimension $\Geq 5$, Nasrin Malekzadeh, Esmaiel Abedi
Semisymmetric Contact Metric Manifolds Of Dimension $\Geq 5$, Nasrin Malekzadeh, Esmaiel Abedi
Turkish Journal of Mathematics
We classify semisymmetric contact metric manifolds $M^{2n+1}(\varphi, \xi, \eta, g),~n\geq2$ with $\xi$-parallel tensor $h$, where $2h$ denotes the Lie derivative of the structure tensor $\varphi$ in the direction of the characteristic vector field $\xi$.
On Oscillation Of Two-Dimensional Time-Scale Systems With A Forcing Term, Özkan Öztürk
On Oscillation Of Two-Dimensional Time-Scale Systems With A Forcing Term, Özkan Öztürk
Turkish Journal of Mathematics
The oscillation and nonoscillation theories for nonlinear systems have recently received a lot of attention. We consider a two-dimensional time-scale system and find the oscillation criteria for solutions of the system by using some improper integrals and inequalities. We also give a few examples in order to highlight our main results.
On A Biharmonic Equation Involving Slightly Supercritical Exponent, Kamal Ould Bouh
On A Biharmonic Equation Involving Slightly Supercritical Exponent, Kamal Ould Bouh
Turkish Journal of Mathematics
We consider the biharmonic equation with supercritical nonlinearity $ (P_\varepsilon ):$ $\Delta^{2} u = K u ^{8/(n-4)+\varepsilon}u$ in $\Omega$, $\Delta u =u = 0$ on $\partial \Omega $, where $\Omega $ is a smooth bounded domain in $\mathbb{R}^n $, $n \geq 5 $, $K$ is a $C^3$ positive function, and $\varepsilon$ is a positive real parameter. In contrast with the subcritical case, we prove the nonexistence of sign-changing solutions of $ (P_\varepsilon )$ that blow up at two near points. We also show that $(P_\varepsilon)$ has no bubble-tower sign-changing solutions.
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.
$R$-Submodules And $Sr$-Submodules, Suat Koç, Ünsal Teki̇r
$R$-Submodules And $Sr$-Submodules, Suat Koç, Ünsal Teki̇r
Turkish Journal of Mathematics
In this article, we introduce new classes of submodules called $r$-submodule and special $r$-submodule, which are two different generalizations of $r$-ideals. Let $M $be an $R$-module, where $R $is a commutative ring$. $We call a proper submodule $N\ $of $M$ an $r$-submodule (resp., special $r$-submodule) if the condition $am\in N$ with $ann_{M}(a)=0_{M} $(resp., $ann_{R}(m)=0$) implies that $m\in N$ (resp., $a\in(N:_{R} M)$) for each $a\in R $and $m\in M. $ We also give various results and examples concerning $r$-submodules and special $r$-submodules.
Accelerating Diffusion By Incompressible Drift On The Two-Dimensional Torus, Yaakoubi Nejib
Accelerating Diffusion By Incompressible Drift On The Two-Dimensional Torus, Yaakoubi Nejib
Turkish Journal of Mathematics
In this paper we construct an explicit sequence of divergence-free vector fields $\rm{b}_{n}$ that pushes the spectral gap of the nonself-adjoint operator $A_{\rm{b}_{n}}=\Delta +\rm{b}_{n}\cdot\nabla $ to infinity. The spectral gap is an indicator for the speed at which this diffusion converges toward its equilibrium, which corresponds to the uniform distribution.
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
Formal Residue And Computer-Assisted Proofs Of Combinatorial Identities, Jin Haitao
Formal Residue And Computer-Assisted Proofs Of Combinatorial Identities, Jin Haitao
Turkish Journal of Mathematics
The coefficient of $x^{-1}$ of a formal Laurent series $f(x)$ is called the formal residue of $f(x)$. Many combinatorial numbers can be represented by the formal residues of hypergeometric terms. With these representations and the extended Zeilberger algorithm, we generate recurrence relations for summations involving combinatorial sequences such as Stirling numbers and their $q$-analog. As examples, we give computer proofs of several known identities and derive some new identities. The applicability of this method is also studied.
On The Higher Derivatives Of The Inverse Tangent Function, Mohamed Amine Boutiche, Mourad Rahmani
On The Higher Derivatives Of The Inverse Tangent Function, Mohamed Amine Boutiche, Mourad Rahmani
Turkish Journal of Mathematics
In this paper, we find explicit formulas for higher-order derivatives of the inverse tangent function. More precisely, we study polynomials that are induced from the higher-order derivatives of $\arctan(x)$. Successively, we give generating functions, recurrence relations, and some particular properties for these polynomials. Connections to Chebyshev, Fibonacci, Lucas, and matching polynomials are established.
A Taylor Operation Method For Solutions Of Generalized Pantograph Type Delay Differential Equations, Şuayi̇p Yüzbaşi, Nurbol Ismailov
A Taylor Operation Method For Solutions Of Generalized Pantograph Type Delay Differential Equations, Şuayi̇p Yüzbaşi, Nurbol Ismailov
Turkish Journal of Mathematics
In this paper, a new operational matrix method based on the Taylor polynomials is presented to solve generalized pantograph type delay differential equations. The method is based on operational matrices of integration and product for Taylor polynomials. These matrices are obtained by using the best approximation of function by the Taylor polynomials. The advantage of the method is that the method does not require collocation points. By using the proposed method, the generalized pantograph equation problem is reduced to a system of linear algebraic equations. The solving of this system gives the coefficients of our solution. Numerical examples are given …
A Generalization Of The Alexander Polynomial As An Application Of The Delta Derivative, İsmet Altintaş, Kemal Taşköprü
A Generalization Of The Alexander Polynomial As An Application Of The Delta Derivative, İsmet Altintaş, Kemal Taşköprü
Turkish Journal of Mathematics
In this paper, we define the delta derivative in the integer group ring and we show that the delta derivative is well defined on the free groups. We also define a polynomial invariant of oriented knot and link by carrying the delta derivative to the link group. Since the delta derivative is a generalization of the free derivative, this polynomial invariant called the delta polynomial is a generalization of the Alexander polynomial. In addition, we present a new polynomial called the difference polynomial of oriented knot and link, which is similar to the Alexander polynomial and is a special case …
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
A Result On The Maximal Length Of Consecutive 0 Digits In $\Beta$-Expansions, Xiang Gao, Hui Hu, Zhihui Li
A Result On The Maximal Length Of Consecutive 0 Digits In $\Beta$-Expansions, Xiang Gao, Hui Hu, Zhihui Li
Turkish Journal of Mathematics
Let $\beta>1$ be a real number. For any $x\in[0,1]$, let $r_{n}(x,\beta)$ be the maximal length of consecutive zero digits in the first $n$ digits of the $\beta$-expansion of $x$. In this note, it is proved that for any $0
On The Unit Index Of Some Real Biquadratic Number Fields, Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous
On The Unit Index Of Some Real Biquadratic Number Fields, Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous
Turkish Journal of Mathematics
Let $p_1\equiv p_2\equiv1 \pmod 4$ be different prime numbers such that $\left(\dfrac{2}{p_2}\right)=\left(\dfrac{p_1}{p_2}\right)=-\left(\dfrac{2}{p_1}\right)=-1$. Put $\kk=\QQ(\sqrt{2p_1p_2})$ and let $\KK$ be a quadratic extension of $\kk$ contained in its absolute genus field $\kk^{(*)}$. Denote by $k_j$, $1\leq j\leq 3$, the three quadratic subfields of $\KK$. Let $E_{\KK}$ (resp. $E_{k_j}$) be the unit group of $\KK$ (resp. $k_j$). The unit index $\left[E_{\KK}: \prod_{j=1}^3E_{k_j}\right]$ is characterized in terms of biquadratic residue symbols between $2$, $p_1$ and $p_2$ or by the capitulation of $\mathfrak{2}$, the prime ideal of $\QQ(\sqrt{2p_1})$ above $2$, in $\KK$. These results are used to describe the $2$-rank of some CM-fields.
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 …
Multivariate Lucas Polynomials And Ideal Classes Inquadratic Number Fields, Ayberk Zeyti̇n
Multivariate Lucas Polynomials And Ideal Classes Inquadratic Number Fields, Ayberk Zeyti̇n
Turkish Journal of Mathematics
In this work, by using Pauli matrices, we introduce four families of polynomials indexed over the positive integers. These polynomials have rational or imaginary rational coefficients. It turns out that two of these families are closely related to classical Lucas and Fibonacci polynomial sequences and hence to Lucas and Fibonacci numbers. We use one of these families to give a geometric interpretation of the 200-year-old class number problems of Gauß, which is equivalent to the study of narrow ideal classes in real quadratic number fields.