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Articles 2011 - 2040 of 10319
Full-Text Articles in Physical Sciences and Mathematics
A Class Of Fredholm Equations And Systems Of Equations Related To The Kontorovich-Lebedev And The Fourier Integral Transforms, Trinh Tuan, Nguyen Thanh Hong
A Class Of Fredholm Equations And Systems Of Equations Related To The Kontorovich-Lebedev And The Fourier Integral Transforms, Trinh Tuan, Nguyen Thanh Hong
Turkish Journal of Mathematics
In this article, we solve in closed form a class of Fredholm integral equations and systems of Fredholm integral equations with nondegenerate kernels by using techniques of convolutions and generalized convolutions related to the Kontorovich-Lebedev, Fourier sine, and Fourier cosine integral transforms.
Wirtinger Type Inequalities For Higher Order Differentiable Functions, Samet Erden
Wirtinger Type Inequalities For Higher Order Differentiable Functions, Samet Erden
Turkish Journal of Mathematics
Inthiswork,we establish a Wirtinger type inequality which gives the relation between the integral of square of its any order derivative via Taylor's formula. Then,we provide a similar inequality for mappings that are elements of Lr space with r > 1. Also, we indicate that special cases of these inequalities give some results presented in the earlier works.
Oscillation Criteria For Higher-Order Neutral Type Difference Equations, Turhan Köprübaşi, Zafer Ünal, Yaşar Bolat
Oscillation Criteria For Higher-Order Neutral Type Difference Equations, Turhan Köprübaşi, Zafer Ünal, Yaşar Bolat
Turkish Journal of Mathematics
In this paper, oscillation criteria are obtained for higher-order neutral-type nonlinear delay difference equations of the form% \begin{equation} \Delta (r_{n}(\Delta ^{k-1}(y_{n}+p_{n}y_{\tau _{n}}))+q_{n}f(y_{\sigma _{n}})=0\text{, }n\geq n_{0}\text{,} \tag{0.1} \end{equation}% where $r_{n},p_{n},q_{n}\in \lbrack n_{0},\infty ),$ $r_{n}>0$, $q_{n}>0$; $% 0\leq p_{n}\leq p_{0}0$; $\tau _{\sigma }=\sigma _{\tau }$; $\frac{f(u)}{u}\geq m>0$ for $u\neq 0$. Moreover, we provide some examples to illustrate our main results.
Inverse Problem For Sturm-Liouville Differential Operators With Finite Number Of Constant Delays, Mohammad Shahriari
Inverse Problem For Sturm-Liouville Differential Operators With Finite Number Of Constant Delays, Mohammad Shahriari
Turkish Journal of Mathematics
In this manuscript,we study nonself-adjoint second-order differential operators with finite number of constant delays. We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from their spectra. An inverse spectral problem is studied for recovering differential operator from the potential from spectra of two boundary value problems with one common boundary condition.The uniqueness theorem is proved for this inverse problem.
$Q$-Analogues Of Five Difficult Hypergeometric Evaluations, Xiaojing Chen, Wenchang Chu
$Q$-Analogues Of Five Difficult Hypergeometric Evaluations, Xiaojing Chen, Wenchang Chu
Turkish Journal of Mathematics
A nonterminating balanced $q$-series is examined by means of the modified Abel lemma on summation by parts that leads to $q$-analogues of five difficult identities for classical hypergeometric series, including three formulae conjectured by Gosper in 1977.
Stability In Commutative Rings, Başak Ay Saylam
Stability In Commutative Rings, Başak Ay Saylam
Turkish Journal of Mathematics
Let $R$ be a commutative ring with zero-divisors and $I$ an ideal of $R$. $I$ is said to be ES-stable if $JI=I^2$ for some invertible ideal $J \subseteq I$, and $I$ is said to be a weakly ES-stable ideal if there is an invertible fractional ideal $J$ and an idempotent fractional ideal $E$ of $R$ such that $I=JE$. We prove useful facts for weakly ES-stability and investigate this stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?
Fourth Order Differential Operators With Distributional Potentials, Eki̇n Uğurlu, Elgi̇z Bairamov
Fourth Order Differential Operators With Distributional Potentials, Eki̇n Uğurlu, Elgi̇z Bairamov
Turkish Journal of Mathematics
In this paper, regular and singular fourth order differential operators with distributional potentials are investigated. In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied. These symmetric operators are considered as acting on the single and direct sum Hilbert spaces. The latter one consists of three Hilbert spaces such that a squarely integrable space and two spaces of complex numbers. Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single …
On Bishop Frame Of A Pseudo Null Curve In Minkowski Space-Time, Jelena Djordjevic, Emilija Nesovic
On Bishop Frame Of A Pseudo Null Curve In Minkowski Space-Time, Jelena Djordjevic, Emilija Nesovic
Turkish Journal of Mathematics
In this paper, we introduce the Bishop frame of a pseudo null curve $\alpha$ in Minkowski space-time. We obtain the Bishop frame's equations and the relation between the Frenet frame and the Bishop frame. We find the third order nonlinear differential equation whose particular solutions determine the form of the Bishop curvatures. By using space-time geometric algebra, we derive the Darboux bivectors $D$ and $\tilde{D}$ of the Frenet and the Bishop frame of $\alpha$, respectively. We give geometric interpretations of the Frenet and the Bishop curvatures of $\alpha$ in terms of areas of the projections of the corresponding Darboux bivectors …
Inverse Problems For Differential Operators With Two Delays Larger Than Half The Length Of The Interval And Dirichlet Conditions, Biljana Vojvodic, Milenko Pikula, Vladimir Vladicic, Fatma Ayça Çeti̇nkaya
Inverse Problems For Differential Operators With Two Delays Larger Than Half The Length Of The Interval And Dirichlet Conditions, Biljana Vojvodic, Milenko Pikula, Vladimir Vladicic, Fatma Ayça Çeti̇nkaya
Turkish Journal of Mathematics
This paper deals with nonself-adjoint second-order differential operators with two constant delays from $\left[\frac{\pi}{2}, \pi\right)$ and two real-valued potentials from $L_{2} [0,\pi]$. An inverse spectral problem of recovering operators from the spectra of four boundary value problems is studied.
A Simple Derivation Of The Refined Sphere Packing Bound Under Certain Symmetry Hypotheses, Bariş Naki̇boğlu
A Simple Derivation Of The Refined Sphere Packing Bound Under Certain Symmetry Hypotheses, Bariş Naki̇boğlu
Turkish Journal of Mathematics
A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is $\mathit{\Omega}\left(n^{-0.5(1-E_{sp}'(R))}\right)$ for all codes on certain families of channels (including the Gaussian channels and the nonstationary Renyi symmetric channels) and for the constant composition codes on stationary memoryless channels. The resulting nonasymptotic bounds have definite approximation error terms. As a preliminary result that might be of interest on its own, the trade-off between type I and type II error probabilities in the hypothesis testing problem with (possibly non-stationary) independent samples is determined …
The Statistically Unbounded $\Tau$-Convergence On Locally Solid Riesz Spaces, Abdullah Aydin
The Statistically Unbounded $\Tau$-Convergence On Locally Solid Riesz Spaces, Abdullah Aydin
Turkish Journal of Mathematics
A sequence $(x_n)$ in a locally solid Riesz space $(E,\tau)$ is said to be statistically unbounded $\tau$-convergent to $x\in E$ if, for every zero neighborhood $U$, $\frac{1}{n}\big\lvert\{k\leq n:\lvert x_k-x\rvert\wedge u\notin U\}\big\rvert\to 0$ as $n\to\infty$. In this paper, we introduce the concept of the $st$-$u_\tau$-convergence and give the notions of $st$-$u_\tau$-closed subset, $st$-$u_\tau$-Cauchy sequence, $st$-$u_\tau$-continuous and $st$-$u_\tau$-complete locally solid vector lattice. Also, we give some relations between the order convergence and the $st$-$u_\tau$-convergence.
Erratum To "Study On Quasi-$\Gamma$-Hyperideals In $\Gamma$-Semihypergroups", Niovi Kehayopulu
Erratum To "Study On Quasi-$\Gamma$-Hyperideals In $\Gamma$-Semihypergroups", Niovi Kehayopulu
Turkish Journal of Mathematics
We wrote this note to show that the definition of $\Gamma$-hypersemigroups in [2] should be corrected, and that it is not enough to replace the hyperoperation $\circ$ of the hypersemigroup by $\Gamma$ to pass from a hypersemigroup to a $\Gamma$-hypersemigroup. Care should be taken about the definitions of $(m,n)$-quasi-$\Gamma$-hyperideal, the $m$-left $\Gamma$-hyperideal and the $n$-right $\Gamma$-hyperideal as well.
Global Existence And Blow-Up Of Solutions Of The Time-Fractional Space-Involution Reaction-Diffusion Equation, Rami̇z Tapdigoğlu, Berikbol Torebek
Global Existence And Blow-Up Of Solutions Of The Time-Fractional Space-Involution Reaction-Diffusion Equation, Rami̇z Tapdigoğlu, Berikbol Torebek
Turkish Journal of Mathematics
A time-fractional space-nonlocal reaction-diffusion equation in a bounded domain is considered. First, the existence of a unique local mild solution is proved. Applying Poincaré inequality it is obtained the existence and boundedness of global classical solution for small initial data. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time.
Degree Of Approximation By Means Of Hexagonal Fourier Series, Ali̇ Güven
Degree Of Approximation By Means Of Hexagonal Fourier Series, Ali̇ Güven
Turkish Journal of Mathematics
Let $f$ be a continuous function which is periodic with respect to the hexagon lattice, and let $A$ be a lower triangular infinite matrix of nonnegative real numbers with nonincreasing rows. The degree of approximation of the function $f$ by matrix means $T_{n}^{\left( A\right) }\left( f\right) $ of its hexagonal Fourier series is estimated in terms of the modulus of continuity of $f.$
New Multiple Solutions For A Schrödinger-Poisson System Involving Concave-Convex Nonlinearities, Chun-Yu Lei, Gao-Sheng Liu, Chang-Mu Chu, Hong-Min Suo
New Multiple Solutions For A Schrödinger-Poisson System Involving Concave-Convex Nonlinearities, Chun-Yu Lei, Gao-Sheng Liu, Chang-Mu Chu, Hong-Min Suo
Turkish Journal of Mathematics
In this paper, we study the following critical growth Schrödinger-Poisson system with concave-convex nonlinearities term $\left\{\begin{array} -\Delta u + u + \eta\varphi u = \lambda f(x) u^{q-1} + u^5, in R^3, \\ -\Delta \varphi = u^2, in R^3,\end{array}\right. $ where $1 < q < 2, \eta\in \mathbb{R}, \lambda > 0$ is a real parameter and $f \in L^{\frac{6}{6-q}} (\mathbb{R}^3)$ is a nonzero nonnegative function. Using the variational method, we obtain that there exists a positive constant $\lambda_* > 0$ such that for all $\lambda \in (0,\lambda_*)$, the system has at least two positive solutions.
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces, Yusuf Zeren, Miqdad Ismailov, Cemi̇l Karaçam
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces, Yusuf Zeren, Miqdad Ismailov, Cemi̇l Karaçam
Turkish Journal of Mathematics
The analogs of Korovkin theorems in grand-Lebesgue spaces are proved. The subspace $G^{p)} (-\pi ;\pi )$ of grand Lebesgue space is defined using shift operator. It is shown that the space of infinitely differentiable finite functions is dense in $G^{p)}(-\pi ;\pi )$. The analogs of Korovkin theorems are proved in $G^{p)} (-\pi ;\pi )$. These results are established in $G^{p)} (-\pi ;\pi )$ in the sense of statistical convergence. The obtained results are applied to a sequence of operators generated by the Kantorovich polynomials, to Fejer and Abel-Poisson convolution operators.
The Homogenization Of Diffusion-Convection Equations In Non-Periodic Structures, Anvarbek Meirmanov, Oleg Galtsev
The Homogenization Of Diffusion-Convection Equations In Non-Periodic Structures, Anvarbek Meirmanov, Oleg Galtsev
Turkish Journal of Mathematics
We consider the homogenization of diffusion-convective problems with given divergence-free velocities in nonperiodic structures defined by sequences of characteristic functions(the first sequence). These quence of concentration (the second sequence)is uniformly bounded in the space of square-summable functions with square-summable derivatives with respect to spatial variables. At the same time, the sequence of time-derivative of product of these concentrations on the characteristic functions, that define a nonperiodic structure, is bounded in the space of square-summable functions from time interval into the conjugated space of functions depending on spatial variables, withsquare-summable derivatives. We prove the strong compactness of the second sequences in …
Pell-Lucas Collocation Method To Solve High-Order Linear Fredholm-Volterra Integro-Differential Equations And Residual Correction, Şuayi̇p Yüzbaşi, Gamze Yildirim
Pell-Lucas Collocation Method To Solve High-Order Linear Fredholm-Volterra Integro-Differential Equations And Residual Correction, Şuayi̇p Yüzbaşi, Gamze Yildirim
Turkish Journal of Mathematics
In this article, a collocation method based on Pell-Lucas polynomials is studied to numerically solve higher order linear Fredholm-Volterra integro differential equations (FVIDE). The approximate solutions are assumed in form of the truncated Pell-Lucas polynomial series. By using Pell-Lucas polynomials and relations of their derivatives, the solution form and its derivatives are brought to matrix forms. By applying the collocation method based on equally spaced collocation points, the method reduces the problem to a system of linear algebraic equations. Solution of this system determines the coefficients of assumed solution. Error estimation is made and also a method with the help …
Analytic Functions Associated With Cardioid Domain, Sarfraz Nawaz Malik, Mohsan Raza, Janusz Sokol, Saira Zainab
Analytic Functions Associated With Cardioid Domain, Sarfraz Nawaz Malik, Mohsan Raza, Janusz Sokol, Saira Zainab
Turkish Journal of Mathematics
In this article, we define and study new domain for analytic functions which is named as cardioid domain for being of cardioid structure. Analytic functions producing cardioid domain are defined and studied to some extent. The Fekete-Szegö inequality is also investigated for such analytic functions.
Dual And Canonical Dual Of Controlled K-G-Frames In Hilbert Spaces, Hessam Hosseinnezhad
Dual And Canonical Dual Of Controlled K-G-Frames In Hilbert Spaces, Hessam Hosseinnezhad
Turkish Journal of Mathematics
This paper is devoted to studying the controlled dual K-g-Bessel sequences of controlled K-g-frames. In fact, we introduce the concept of dual K-g-Bessel sequences of controlled K-g-frames and then, we present some necessary and/or sufficient conditions under which a controlled g-Bessel sequence is a controlled dual K-g-frame of a given controlled K-g-frame. Subsequently, we pay attention to investigating the structure of the canonical controlled dual K-g-Bessel sequence of a Parseval controlled K-g-frame and some other related results.
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy
Turkish Journal of Mathematics
In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its applications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when the order m is odd.
On A Three-Dimensional Solvable System Of Difference Equations, Yacine Halim, Massaoud Berkal, Amira Khelifa
On A Three-Dimensional Solvable System Of Difference Equations, Yacine Halim, Massaoud Berkal, Amira Khelifa
Turkish Journal of Mathematics
In this paper we solve the following system of difference equations \begin{equation*} x_{n+1}=\dfrac{z_{n-1}}{a+by_nz_{n-1}},\quad y_{n+1}=\dfrac{x_{n-1}}{a+bz_nx_{n-1}},\quad z_{n+1}=\dfrac{y_{n-1}}{a+bx_ny_{n-1}},\quad n\in \mathbb{N}_{0} \end{equation*} where parameters $a, b$ and initial values $x_{-1},x_{0},y_{-1},y_{0},z_{-1},z_{0}$ are nonzero real numbers, and give a representation of its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constant coefficients associated to the system.
Oscillatory And Asymptotic Behavior Of Third-Order Nonlinear Differential Equations With A Superlinear Neutral Term, Said R. Grace, Iren Jadlovska, Ercan Tunç
Oscillatory And Asymptotic Behavior Of Third-Order Nonlinear Differential Equations With A Superlinear Neutral Term, Said R. Grace, Iren Jadlovska, Ercan Tunç
Turkish Journal of Mathematics
Sufficient conditions are derived for all solutions of a class of third-order nonlinear differential equations with a superlinear neutral term to be either oscillatory or convergent to zero asymptotically. Examples illustrating the results are included and some suggestions for further research are indicated.
Bilateral-Type Solutions To The Fixed-Circle Problem With Rectified Linear Units Application, Ni̇hal Taş
Bilateral-Type Solutions To The Fixed-Circle Problem With Rectified Linear Units Application, Ni̇hal Taş
Turkish Journal of Mathematics
In this paper, we prove new fixed-circle (resp. fixed-disc) results using the bilateral type contractions on a metric space. To do this, we modify some known contractive conditions called the Jaggi-type bilateral contraction and the Dass-Gupta type bilateral contraction. We give some examples to show the validity of our obtained results. Also, we construct an application to rectified linear units activation functions used in the neural networks. This application shows the importance of studying "fixed-circle problem".
Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam
Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the $n$th$~(n\geq 3)$ Taylor-Maclaurin coefficients $\left\vert a_{n}\right\vert $ of functions belong to these new subclasses with $a_{k}=0$ for $2\leq k\leq n-1$, also we find non-sharp estimates on the first two coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $. The results, which are presented in this paper, would generalize those in related earlier works of several authors.
On Lyapunov-Type Inequalities For Boundary Value Problems Of Fractional Caputo-Fabrizio Derivative, Şuayi̇p Toprakseven
On Lyapunov-Type Inequalities For Boundary Value Problems Of Fractional Caputo-Fabrizio Derivative, Şuayi̇p Toprakseven
Turkish Journal of Mathematics
In this study, Lyapunov-type inequalities for fractional boundary value problems involving the fractional Caputo Fabrizio differential equation with mixed boundary conditions when the fractional order of $\beta \in (1,2]$ and Dirichlet-type boundary condition when the fractional order of $\sigma \in (2,3]$ have been derived. Some consequences of the results related to the fractional Sturm?Liouville eigenvalue problems have also been given. Additionally, we examine the nonexistence of the solution of the fractional boundary value problem.
Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator, Wei-Chuan Chen, Yanhsiou Cheng
Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator, Wei-Chuan Chen, Yanhsiou Cheng
Turkish Journal of Mathematics
In this paper, we study the inverse nodal problem and the eigenvalue gap for the one-dimensional sloshing problem with the $p$-Laplacian operator. By applying the Prüfer substitution, we first derive the reconstruction formula of the depth function by using the information of the nodal data. Furthermore, we employ the Tikhonov regularization method to consider how to reconstruct the depth function using only zeros of one eigenfunction. Finally, we investigate the eigenvalue gap under the restriction of symmetric single-well depth functions. We show the gap attains its minimum when the depth function is constant.
On The Variational Curves Due To The Ed-Frame Field In Euclidean 4-Space, Muradi̇ye Çi̇mdi̇ker, Yasi̇n Ünlütürk
On The Variational Curves Due To The Ed-Frame Field In Euclidean 4-Space, Muradi̇ye Çi̇mdi̇ker, Yasi̇n Ünlütürk
Turkish Journal of Mathematics
In this study, we define a variational field for constructing a family of Frenet curvesof the length l lying on a connected oriented hypersurface and calculate the length of the variational curves due to the ED-frame field in Euclidean 4-space. And then, we derive the intrinsic equations for the variational curves and also obtain boundary conditions for this type of curves due to the ED-frame field in Euclidean 4-space.
Units And 2-Class Field Towers Of Some Multiquadratic Number Fields, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi
Units And 2-Class Field Towers Of Some Multiquadratic Number Fields, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi
Turkish Journal of Mathematics
In this paper, we investigate the unit groups, the 2-class groups, the 2-class field towers and the structures of the second 2-class groups of some multiquadratic number fields of degree 8 and 16.
On Ulam's Type Stability Criteria For Fractional Integral Equations Including Hadamard Type Singular Kernel, Yasemi̇n Başci, Süleyman Öğrekçi̇, Adi̇l Misir
On Ulam's Type Stability Criteria For Fractional Integral Equations Including Hadamard Type Singular Kernel, Yasemi̇n Başci, Süleyman Öğrekçi̇, Adi̇l Misir
Turkish Journal of Mathematics
In this paper, we deal with the Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU) stability of Hadamard type fractional integral equations on compact intervals. The stability conditions are developed using a new generalized metric (GM) definition and the fixed point technique by motivating Wang and Lin Ulam's type stability of Hadamard type fractional integral equations. Filomat 2014; 28(7): 1323-1331. Moreover, our approach is efficient and ease in use than to the previously studied approaches. Finally, we give two examples to explain our main results.