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- Oscillation (23)
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- Collocation method (10)
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- Fractional derivative (10)
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- Green's function (9)
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Articles 31 - 60 of 2494
Full-Text Articles in Physical Sciences and Mathematics
Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractionaldifferential Equations At Resonance, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava
Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractionaldifferential Equations At Resonance, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava
Turkish Journal of Mathematics
Using the coincidence degree theory of Mawhin and constructing appropriate operators, we investigate the existence of solutions to Hadamard fractional differential equations (FRDEs) at resonance { − (HDγu ) (t) = f(t, u(t)), t ∈ (1, e), u(1) = 0, u(e) = ∫ e 1 u(t)dA(t), where 1 < γ < 2, f : [1, e]×R2 → R satisfies Carathéodory conditions, ∫ e 1 u(t)dA(t) is the Riemann–Stieltjes integration, and (HDγu ) is the Hadamard fractional derivation of u of order γ . An example is included to illustrate our result.
Lightcone Framed Curves In The Lorentz-Minkowski 3-Space, Liang Chen, Masatomo Takahashi
Lightcone Framed Curves In The Lorentz-Minkowski 3-Space, Liang Chen, Masatomo Takahashi
Turkish Journal of Mathematics
For a nonlightlike nondegenerate regular curve, we have the arc-length parameter and the Frenet-Serret type formula by using a moving frame like a regular space curve in the Euclidean space. If a point of the curve moves between spacelike and timelike regions, then there is a lightlike point. In this paper, we consider mixed types of not only regular curves but also curves with singular points. In order to consider mixed type of curves with singular points, we introduce a frame, so-called the lightcone frame, and lightcone framed curves. We investigate differential geometric properties of lightcone framed curves.
Special Subdiagrams Of Young Diagrams And Numerical Semigroups, Meral Süer, Mehmet Yeşi̇l
Special Subdiagrams Of Young Diagrams And Numerical Semigroups, Meral Süer, Mehmet Yeşi̇l
Turkish Journal of Mathematics
In this study, Young diagrams and their corresponding numerical sets are considered, and a new notion called special subdiagrams is described. Characterizations of special subdiagrams and their corresponding numerical sets, as well as the conditions when they are numerical semigroups, are provided. Young diagrams of symmetric, almost symmetric and Arf numerical semigroups are also considered and properties of their special subdiagrams are given.
Laguerre Type Twice-Iterated Appell Polynomials, Nesli̇han Bi̇ri̇ci̇k, Mehmet Ali̇ Özarslan, Bayram Çeki̇m
Laguerre Type Twice-Iterated Appell Polynomials, Nesli̇han Bi̇ri̇ci̇k, Mehmet Ali̇ Özarslan, Bayram Çeki̇m
Turkish Journal of Mathematics
In this study, we use discrete Appell convolution to define the sequence of Laguerre type twice-iterated Appell polynomials. We obtain explicit representation, recurrence relation, determinantal representation, lowering operator, integro-partial raising operator and integro-partial differential equation. In addition, the special cases of this new family are investigated using Euler and Bernoulli numbers. We also state their corresponding characteristic properties.
Twisted Sasaki Metric On The Unit Tangent Bundle And Harmonicity, Liana Lotarets
Twisted Sasaki Metric On The Unit Tangent Bundle And Harmonicity, Liana Lotarets
Turkish Journal of Mathematics
The paper deals with the twisted Sasaki metric on the unit tangent bundle of n–dimensional Riemannian manifold Mn . The main purpose of the research is to find deformations that preserve the existence harmonic left-invariant unit vector fields on 3-dimensional unimodular Lie groups G with the left invariant metric and harmonic maps G → T1G in case of twisted Sasaki metric on the unit tangent bundle. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map Mn → T1Mn are obtained. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map M2 …
Modules Over Invertible 1-Cocycles, José Manuel Fernández Vilaboa, Ramon Gonzalez Rodriguez, Brais Ramos Pérez, Ana Belén Rodríguez Raposo
Modules Over Invertible 1-Cocycles, José Manuel Fernández Vilaboa, Ramon Gonzalez Rodriguez, Brais Ramos Pérez, Ana Belén Rodríguez Raposo
Turkish Journal of Mathematics
In this paper, we introduce in a braided setting the notion of left module for an invertible 1-cocycle and we prove some categorical equivalences between categories of modules associated to an invertible 1-cocycle and categories of modules associated to Hopf braces.
Qualitative Results For A Generalized 2-Component Camassa-Holm System With Weak Dissipation Term, Nurhan Dündar
Qualitative Results For A Generalized 2-Component Camassa-Holm System With Weak Dissipation Term, Nurhan Dündar
Turkish Journal of Mathematics
Our main aim in the current study is to examine the mathematical properties of a generalized 2-component Camassa-Holm system with a weakly dissipative term. Firstly, we acquire the theorem of well-posedness in locally for the generalized system with weak dissipation. Then, we demonstrate that this system can reveal the blow-up phenomenon. Finally, we acquire the theorem of global existence utilizing a method of the Lyapunov function.
Isometries Of Length 1 In Purely Loxodromic Free Kleinian Groups And Trace Inequalities, İlker Savaş Yüce, Ahmet Nedi̇m Narman
Isometries Of Length 1 In Purely Loxodromic Free Kleinian Groups And Trace Inequalities, İlker Savaş Yüce, Ahmet Nedi̇m Narman
Turkish Journal of Mathematics
In this paper, we prove a generalization of a discreteness criteria for a large class of subgroups of PSL2(C) . In particular, given a finitely generated purely loxodromic free Kleinian group Γ = ⟨ξ1, ξ2, . . . , ξn⟩ for n ≥ 2, we show that |trace2(ξi) − 4| + |trace(ξiξjξ −1 i ξ −1 j ) − 2| ≥ 2 sinh2 ( 1 4 log αn ) for some ξi and ξj for i ̸= j in Γ provided that certain conditions on the hyperbolic displacements given by ξi , ξj and their length 3 conjugates formed by …
On The Reconstruction Of An Integro-Differential Dirac Operator With Parameter-Dependent Nonlocal Integral Boundary Conditions From The Nodal Data, Baki Keskin, Yu Ping Wang
On The Reconstruction Of An Integro-Differential Dirac Operator With Parameter-Dependent Nonlocal Integral Boundary Conditions From The Nodal Data, Baki Keskin, Yu Ping Wang
Turkish Journal of Mathematics
We consider the integro-differential Dirac operator with parameter-dependent nonlocal integral boundary conditions. We derive the asymptotic expressions for the eigenvalues and the zeros of eigenfunctions (nodal points or nodes) and develop a constructive procedure for solving the inverse nodal problem for this operator.
Timelike Surfaces With Parallel Normalized Mean Curvature Vector Field In The Minkowski 4-Space, Victoria Bencheva, Velichka Milousheva
Timelike Surfaces With Parallel Normalized Mean Curvature Vector Field In The Minkowski 4-Space, Victoria Bencheva, Velichka Milousheva
Turkish Journal of Mathematics
In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way, we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge …
Extremal Functions For A Singular Super-Critical Trudinger-Moser Inequality, Juan Zhao
Extremal Functions For A Singular Super-Critical Trudinger-Moser Inequality, Juan Zhao
Turkish Journal of Mathematics
In this paper, we deal with a singular super-critical Trudinger-Moser inequality on a unit ball of Rn , n ≥ 3. For any p > 1, we set λp(B) = inf u∈W1,n 0 (B),u̸≡0 ∫ B |∇u|ndx ( ∫ B |u|pdx)n/p as an eigenvalue related to the n-Laplacian. Let S be a set of radially symmetric functions. Precisely, if β ≥ 0 and α < (1 + p nβ)n−1+n/pλp(B) , then there exists a positive constant ϵ0 such that when λ ≤ 1 + ϵ0 , sup u∈W1,n 0 (B)∩S, ∫ B |∇u|ndx−α( ∫ B |u|p|x|pβdx) np ≤1 ∫ B |x|pβ ( eαn(1+ p n β)|u| n n−1 − λ Σm k=0 |αn(1 + p nβ)u n n−1 |k k! ) dx is attained, where αn = nω1/(n−1) n−1 , ωn−1 is the surface area of the unit ball in Rn . The proof is based on the method of blow-up analysis. The case λ = 0 was studied by Yang-Zhu in [38]. de Figueiredo [11] considered the case p = 2, β ≥ 0, and α = 0 in two dimension. The case λ = 0, p = n,−1 < β < 0, and α = 0 was considered by Adimurthi-Sandeep [1]. Our results extend those of the above cases.
On The Invariance Of Hyperstoneanness Under Lattice Isomorphisms, Banu Güntürk
On The Invariance Of Hyperstoneanness Under Lattice Isomorphisms, Banu Güntürk
Turkish Journal of Mathematics
Let X and Y be compact Hausdorff spaces with Y hyperstonean. In this paper, we prove that if C(X,R) and C(Y,R) are lattice isomorphic then these Banach spaces are linearly isometric, and, consequently, X and Y are homeomorphic, which in turn implies that X is also hyperstonean. Actually, we prove more than what is announced in the headline above. This result, in some ways, is a generalization of the well-known Banach-Stone theorem.
Invariant Symplectic Forms On Number Fields, Ahmad Rafiqi, Ayberk Zeyti̇n
Invariant Symplectic Forms On Number Fields, Ahmad Rafiqi, Ayberk Zeyti̇n
Turkish Journal of Mathematics
We show that a number field of the form Q(λ) admits a symplectic form which is invariant under multiplication by λ if and only if the minimal polynomial of λ is palindromic of even degree. In particular, if λ is an algebraic integer, it is forced to be a unit. In the case when the minimal polynomial of λ is palindromic of degree 2d, we show that there is a d-dimensional space of invariant symplectic forms on Q(λ) .
Globally Generated Vector Bundles On The Del Pezzo Threefold Of Degree 6 With Picard Number 2, Takuya Nemoto
Globally Generated Vector Bundles On The Del Pezzo Threefold Of Degree 6 With Picard Number 2, Takuya Nemoto
Turkish Journal of Mathematics
We classify globally generated vector bundles on a general hyperplane section of P2 × P2 embedded by the Segre embedding, considering small first Chern classes c1 = (1, 1) and c1 = (2, 1).
On Strong Solvability Of One Nonlocal Boundary Value Problem For Laplace Equation In Rectangle, Telman Gasymov, Baharchin Akhmadli, Ümi̇t Ildiz
On Strong Solvability Of One Nonlocal Boundary Value Problem For Laplace Equation In Rectangle, Telman Gasymov, Baharchin Akhmadli, Ümi̇t Ildiz
Turkish Journal of Mathematics
One nonlocal boundary value problem for the Laplace equation in a bounded domain is considered in this work. The concept of a strong solution to this problem is introduced. The correct solvability of this problem in the Sobolev spaces generated by the weighted mixed norm is proved by the Fourier method. In a classic statement, this problem has been
On The Qualitative Analysis Of Nonlinear Q-Fractional Delay Descriptor Systems, Abdullah Yi̇ği̇t
On The Qualitative Analysis Of Nonlinear Q-Fractional Delay Descriptor Systems, Abdullah Yi̇ği̇t
Turkish Journal of Mathematics
In this manuscript, we obtain some sufficient conditions for a nonlinear q fractional integro singular system with constant delays to be asymptotically admissible and a nonlinear q fractional non-singular system to be asymptotically stable. We use Lyapunov-Krasovskii functionals and some inequalities to obtain these conditions. At the same time, we present some numerical examples that confirm the sufficient conditions we obtained theoretically, with their annotated solutions and graphs.
Some Estimates On The Spin−Submanifolds, Serhan Eker
Some Estimates On The Spin−Submanifolds, Serhan Eker
Turkish Journal of Mathematics
In this paper, an optimal lower bound is given for the Submanifold Dirac operator in terms of the trace of an Energy−Momentum tensor, scalar curvature and mean curvature. In the equality case, it is proven that the submanifold is Einstein if the normal bundle is flat. Key words: Spin geometry, eigenvalues,
On Lyapunov-Type Inequalities For Five Different Types Of Higher Order Boundary Value Problems, Mustafa Fahri̇ Aktaş, Bariş Berkay Erçikti
On Lyapunov-Type Inequalities For Five Different Types Of Higher Order Boundary Value Problems, Mustafa Fahri̇ Aktaş, Bariş Berkay Erçikti
Turkish Journal of Mathematics
In this paper, we establish the uniqueness and existence of the classical solution to higher-order boundary value problems. Then, we give a new Lyapunov-type inequalities for higher order boundary value problems. Our study is based on Green’s functions corresponding to the five different types of two-point boundary value problems. In addition, some applications of the obtained inequalities are given.
An Extensive Note On Characteristic Properties And Possible Implications Of Some Operators Designated By Various Type Derivatives, Ömer Faruk Kulali, Hüseyi̇n Irmak
An Extensive Note On Characteristic Properties And Possible Implications Of Some Operators Designated By Various Type Derivatives, Ömer Faruk Kulali, Hüseyi̇n Irmak
Turkish Journal of Mathematics
In this extensive note, various differential-type operators in certain domains of the complex plane will be first introduced, a number of their comprehensive characteristic properties will be next pointed out and an extensive theorem dealing with some argument properties for several multivalent(ly) analytic functions will be also presented. In addition, numerous implications and suggestions, which can be obtained with the help of general result, will be determined.
Fibonomial Matrix And Its Domain In The Spaces $\Ell_P$ And $\Ell_{\Infty}$, Muhammet Ci̇hat Dağli, Taja Yaying
Fibonomial Matrix And Its Domain In The Spaces $\Ell_P$ And $\Ell_{\Infty}$, Muhammet Ci̇hat Dağli, Taja Yaying
Turkish Journal of Mathematics
In this paper, we introduce the fibonomial sequence spaces $b_{p}^{r,s,F}$ and $b_{\infty}^{r,s,F},$ and show that these are BK-spaces. Also, we prove that these new spaces are linearly isomorphic to $\ell_{p}$ and $\ell_{\infty}.$ Moreover, we determine the $\alpha$-, $\beta$-, $\gamma$-duals for these new spaces and characterize some matrix classes. The final section is devoted to the investigation of some geometric properties of the newly defined space $b_{p}^{r,s,F}.$
Best Proximity For Proximal Operators On $B$-Metric Spaces, Ariana Pitea, Monica Stanciu
Best Proximity For Proximal Operators On $B$-Metric Spaces, Ariana Pitea, Monica Stanciu
Turkish Journal of Mathematics
The paper presents existence results of $(\phi,\varphi)$ best proximity points for operators that fulfill implicit type inequalities. Classes of mappings endowed with continuity, monotone or monotone-type properties, and which additionally satisfy some adequate inequalities are studied from this point of view. Applications of our results are given with regard to fixed point theory.
Multiplication Of Closed Balls In $\Mathbb{C}^N$, Patrícia Damas Beites, Alejandro Piñera Nicolás, José Da Silva Lourenço Vitória
Multiplication Of Closed Balls In $\Mathbb{C}^N$, Patrícia Damas Beites, Alejandro Piñera Nicolás, José Da Silva Lourenço Vitória
Turkish Journal of Mathematics
Motivated by circular complex interval arithmetic, some operations on closed balls in $\mathbb{C}^n$ are considered. Essentially, the properties of possible multiplications for closed balls in $\mathbb{C}^n$, related either to the Hadamard product of vectors or to the $2$-fold vector cross product when $n \in \{3, 7\}$, are studied. In addition, certain equations involving the defined multiplications are solved.
On Polynomially Partial-$A$-Isometric Operators, Mohamed Amine Aouichaoui, Dijana Mosic
On Polynomially Partial-$A$-Isometric Operators, Mohamed Amine Aouichaoui, Dijana Mosic
Turkish Journal of Mathematics
This paper presents a generalization of the concepts of partial-$A$-isometry and left polynomially partial isometry. Our investigation is inspired by previous work in the field [5, 30, 31]. By extending the definition of partial-$A$-isometry, we provide new insights into the properties and applications of these mathematical objects. In particular, we define the notion of left $p$-partial-$A$-isometry as a broader class of operators, including partial-$A$-isometry and left polynomially partial isometry. Some basic properties of a left $p$-partial-$A$-isometry are proven, as well as its relation with $A$-isometry. Several decompositions of a left $p$-partial-$A$-isometry are developed. We consider spectral properties and matrix representation …
Various Types Of Continuity And Their Interpretations In Ideal Topological Spaces, Anika Njamcul, Aleksandar Pavlovi?
Various Types Of Continuity And Their Interpretations In Ideal Topological Spaces, Anika Njamcul, Aleksandar Pavlovi?
Turkish Journal of Mathematics
In this paper we work on preserving various types of continuity in ideal topological spaces. The accent will be on $\theta$-continuity and weak continuity. We will give their translations in ideal topological spaces. As a consequence of those results, we will prove that every $\theta$-continuous function is continuous if topologies are generated by $\theta$-open sets and we will give an example of a weakly continuous function which is not $\tau_\theta$-continuous. This will complete the diagram of relations between continuous, $\tau_\theta$-continuous, $\theta$-continuous, weakly continuous, and faintly continuous functions.
A New Approaching Method For Linear Neutral Delay Differential Equations By Using Clique Polynomials, Şuayi̇p Yüzbaşi, Mehmet Emi̇n Tamar
A New Approaching Method For Linear Neutral Delay Differential Equations By Using Clique Polynomials, Şuayi̇p Yüzbaşi, Mehmet Emi̇n Tamar
Turkish Journal of Mathematics
This article presents an efficient method for obtaining approximations for the solutions of linear neutral delay differential equations. This numerical matrix method, based on collocation points, begins by approximating $y^{\prime}(u)$ using a truncated series expansion of Clique polynomials. This method is constructed using some basic matrix relations, integral operations, and collocation points. Through this method, the neutral delay problem is transformed into a system of linear algebraic equations. The solution of this algebraic system determines the coefficients of the approximate solution obtained by this method. The efficiency, accuracy, and error analysis of this method are demonstrated by applying it to …
Involutive Automorphisms And Derivations Of The Quaternions, Eyüp Kizil, Adriano Da Silva, Okan Duman
Involutive Automorphisms And Derivations Of The Quaternions, Eyüp Kizil, Adriano Da Silva, Okan Duman
Turkish Journal of Mathematics
Let $Q=(\frac{a,b}{{\Bbb R}})$ denote the quaternion algebra over the reals which is by the Frobenius Theorem either split or the division algebra $H$ of Hamilton's quaternions. We have presented explicitly in \cite{Kizil-Alagoz} the matrix of a typical derivation of $Q$. Given a derivation $d\in Der(H)$, we show that the matrix $D\in M_{3}({\Bbb R})$ that represents $d$ on the linear subspace $% H_{0}\simeq {\Bbb R}^{3}$ of pure quaternions provides a pair of idempotent matrices $AdjD$ and $-D^{2}$ that correspond bijectively to the involutary matrix $\Sigma $ of a quaternion involution $\sigma $ and present several equations involving these matrices. In particular, …
Invariant Subspaces Of Operators Via Berezin Symbols And Duhamel Product, Mübari̇z T. Garayev
Invariant Subspaces Of Operators Via Berezin Symbols And Duhamel Product, Mübari̇z T. Garayev
Turkish Journal of Mathematics
The Berezin symbol $\tilde{A}$ of an operator $A$ on the reproducing kernel Hilbert space $\mathcal{H}\left( \Omega\right) $ over some set $\Omega$ with the reproducing kernel $k_{\lambda}$ is defined by \[ \tilde{A}(\lambda)=\left\langle {A\frac{{k_{\lambda}}}{{\left\Vert {k_{\lambda}}\right\Vert }},\frac{{k_{\lambda}}}{{\left\Vert {k_{\lambda}% }\right\Vert }}}\right\rangle ,\ \lambda\in\Omega. \] We study the existence of invariant subspaces for Bergman space operators in terms of Berezin symbols.
Generalized Pell Graphs, Vesna Irsi̇c, Sandi Klavzar, Eli̇f Tan
Generalized Pell Graphs, Vesna Irsi̇c, Sandi Klavzar, Eli̇f Tan
Turkish Journal of Mathematics
In this paper, generalized Pell graphs $\Pi _{n,k}$, $k\ge 2$, are introduced. The special case of $k=2$ are the Pell graphs $\Pi _{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $\Pi _{n,k}$ and the generating function of its cube polynomial are determined. The center of $\Pi _{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $\Gamma_{n}$. It is also shown that $\Pi _{n,k}$ is a median graph, and that $\Pi _{n,k}$ embeds into a Fibonacci cube.
Interpolation Polynomials Associated To Linear Recurrences, Muhammad Syifa'ul Mufid, Laszlo Szalay
Interpolation Polynomials Associated To Linear Recurrences, Muhammad Syifa'ul Mufid, Laszlo Szalay
Turkish Journal of Mathematics
Assume that $(G_n)_{n\in\mathbb{Z}}$ is an arbitrary real linear recurrence of order $k$. In this paper, we examine the classical question of polynomial interpolation, where the basic points are given by $(t,G_t)$ ($n_0\le t\le n_1$). The main result is an explicit formula depends on the explicit formula of $G_n$ and on the finite difference sequence of a specific sequence. It makes it possible to study the interpolation polynomials essentially by the zeros of the characteristic polynomial of $(G_n)$. During the investigations, we developed certain formulae related to the finite differences.
Free Ordered Products-Ordered Semigroup Amalgams-Ordered Dominions, Michael Tsingelis
Free Ordered Products-Ordered Semigroup Amalgams-Ordered Dominions, Michael Tsingelis
Turkish Journal of Mathematics
Given an indexed family $\left\{ \left( {{S}_{i}},{{\cdot }_{i}},{{\le }_{i}} \right),i\in I \right\}$ of disjoint ordered semigroups, we construct an ordered semigroup having $\left( {{S}_{i}},{{\cdot }_{i}},{{\le }_{i}} \right)$, $i\in I$ as subsemigroups (with respect to the operation and order relation of each $\left( {{S}_{i}},{{\cdot }_{i}},{{\le }_{i}} \right)$, $i\in I$). This ordered semigroup is the free ordered product ${{\underset{i\in I}{\mathop{\Pi }}\,}^{*}}{{S}_{i}}$ of the family $\left\{ {{S}_{i}},i\in I \right\}$ and we give the crucial property which essentially characterizes the free products. Next we study the same problem in the case that the family $\left\{ \left( {{S}_{i}},{{\cdot }_{i}},{{\le }_{i}} \right),i\in I \right\}$ of ordered …