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- Oscillation (22)
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- Fixed point theorem (17)
- Bi-univalent functions (16)
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Articles 211 - 240 of 2470
Full-Text Articles in Physical Sciences and Mathematics
Inverse Nodal Problem For Sturm-Liouville Operator On A Star Graph With Nonequal Edges, Sevi̇m Durak
Inverse Nodal Problem For Sturm-Liouville Operator On A Star Graph With Nonequal Edges, Sevi̇m Durak
Turkish Journal of Mathematics
In this study, Sturm-Liouville operator was investigated on a star graph with nonequal edges. First, the behaviors of sufficiently large eigenvalues were learned, then the solution of the inverse problem was given to determine the potantial functions and parameters of the boundary condition on the star graph with the help of a dense set of nodal points and obtain a constructive solution to the inverse problems of this class.
On Some Fractional Operators Generated From Abel's Formula, Eki̇n Uğurlu
On Some Fractional Operators Generated From Abel's Formula, Eki̇n Uğurlu
Turkish Journal of Mathematics
This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup properties for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.
On The Application Of Euler's Method To Linear Integro Differential Equations And Comparison With Existing Methods, Deni̇z Elmaci, Nurcan Baykuş Savaşaneri̇l, Fadi̇me Dal, Mehmet Sezer
On The Application Of Euler's Method To Linear Integro Differential Equations And Comparison With Existing Methods, Deni̇z Elmaci, Nurcan Baykuş Savaşaneri̇l, Fadi̇me Dal, Mehmet Sezer
Turkish Journal of Mathematics
In this study, a collocation method using Euler method for solving systems of linear integro-differential equations is presented. Thesolution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exactsolutions and solutions obtained by other methods show that the proposed method is an effective and highly promising for linear integro-differential equation systems. All of numerical calculations have been made on a computer using a program written in Matlab.
Examination Of Eigenvalues And Spectral Singularities Of A Discrete Dirac Operator With An Interaction Point, Şeri̇fenur Cebesoy
Examination Of Eigenvalues And Spectral Singularities Of A Discrete Dirac Operator With An Interaction Point, Şeri̇fenur Cebesoy
Turkish Journal of Mathematics
In this paper, the main content is the consideration of the concepts of eigenvalues and spectral singularities of an operator generated by a discrete Dirac system in $\ell_{2}(\mathbb{Z},\mathbb{C}^{2})$ with an interior interaction point. Defining a transfer matrix $ M $ enables us to present a relationship between the $ M_{22} $ component of this matrix and Jost functions of mentioned Dirac operator so that its eigenvalues and spectral properties can be studied. Finally, some special cases are examined where the impulsive condition possesses certain symmetries.
Various Operators In Relation To Fractional Order Calculus And Some Of Their Applications To Normalized Analytic Functions In The Open Unit Disk, Hüseyi̇n Irmak
Various Operators In Relation To Fractional Order Calculus And Some Of Their Applications To Normalized Analytic Functions In The Open Unit Disk, Hüseyi̇n Irmak
Turkish Journal of Mathematics
The main object of this scientific work is firstly to introduce various operators of fractional calculus (that is that fractional integral and fractional derivative(s)) in certain domains of the complex plane, then to determine certain results correlating with normalized analytic functions, which are analytic in certain domains in the complex plane, as a few applications of those operators, and also to present a number of extensive implications of them as special results.
To The Solution Of Integro-Differential Equations With Nonlocal Conditions, Kamil R. Aida-Zade, Vagif M. Abdullayev
To The Solution Of Integro-Differential Equations With Nonlocal Conditions, Kamil R. Aida-Zade, Vagif M. Abdullayev
Turkish Journal of Mathematics
We investigate linear integro-differential equations with ordinary derivatives. The kernels of the integrands depend only on the variable of integration, and the conditions involve the terms with the point and integral values of the unknown function. We drive necessary and sufficient conditions for the existence and uniqueness of the solution of the problem, which can be used both for analytical and numerical solutions. We present the results of solving an illustrative test problem.
Classical Solutions For 1-Dimensional And 2-Dimensional Boussinesq Equations, Svetlin Georgiev, Aissa Boukarou, Khaled Zennir
Classical Solutions For 1-Dimensional And 2-Dimensional Boussinesq Equations, Svetlin Georgiev, Aissa Boukarou, Khaled Zennir
Turkish Journal of Mathematics
In this article we investigate the IVPs for 1-dimensional and 2-dimensional Boussinesq equations. A new topological approach is applied to prove the existence of at least one classical solution and at least two nonnegative classical solutions for the considered IVPs. The arguments are based upon recent theoretical results.
Existence And Uniqueness Of Mild Solutions For Mixed Caputo And Riemann-Liouville Semilinear Fractional Integrodifferential Equations With Nonlocal Conditions, Ashraf H. A. Radwan
Existence And Uniqueness Of Mild Solutions For Mixed Caputo And Riemann-Liouville Semilinear Fractional Integrodifferential Equations With Nonlocal Conditions, Ashraf H. A. Radwan
Turkish Journal of Mathematics
The purpose of this paper is to investigate the existence and uniqueness of the mild solution to a class of semilinear fractional integrodifferential equations with state-dependent nonlocal fractional conditions. Our problem includes both Caputo and Riemann-Liouville fractional derivatives. Continuous dependence of solutions on initial conditions and $\epsilon$-approximate mild solutions of the considered problem will be discussed.
Oscillation Of Third-Order Neutral Differential Equations With Oscillatory Operator, Miroslav Bartusek
Oscillation Of Third-Order Neutral Differential Equations With Oscillatory Operator, Miroslav Bartusek
Turkish Journal of Mathematics
A third-order damped neutral sublinear differential equation for which its differential operator is oscillatory is studied. Sufficient conditions are given under which every solution is either oscillatory or the derivative of its neutral term is oscillatory (or it tends to zero).
$K$-Generalized Pell Numbers Which Are Repdigits In Base $B$, Zafer Şi̇ar, Refi̇k Keski̇n
$K$-Generalized Pell Numbers Which Are Repdigits In Base $B$, Zafer Şi̇ar, Refi̇k Keski̇n
Turkish Journal of Mathematics
Let $k\geq 2$ be an integer and let $(P_{n}^{(k)})_{n\geq 2-k}$ be the $k$ -generalized Pell sequence defined by \begin{equation*} P_{n}^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+...+P_{n-k}^{(k)} \end{equation*} for $n\geq 2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(k)}=P_{-(k-3)}^{(k)}=\cdot \cdot \cdot =P_{-1}^{(k)}=P_{0}^{(k)}=0,P_{1}^{(k)}=1. \end{equation*} In this study, we deal with the Diophantine equation \begin{equation*} P_{n}^{(k)}=d\left( \frac{b^{m}-1}{b-1}\right) \end{equation*} in positive integers $n,m,k,b,d$ such that $m\geq 2,$ $2\leq b\leq 9$ and $ 1\leq d\leq b-1$. We show that the repdigits in the base $b$ in the $k-$ generalized Pell sequence, which have at least two digits, are the numbers \begin{eqnarray*} \ P_{7}^{(4)} &=&228=(444)_{7},\text{ }P_{4}^{(2)}=12=(22)_{5}\text{, }% P_{6}^{(2)}=70=(77)_{9}\text{;} \\ P_{4}^{(k)} &=&13=(111)_{3}\text{ } \end{eqnarray*} for $k\geq …
A Galerkin-Type Approach To Solve Systems Of Linear Volterra-Fredholm Integro-Differential Equations, Murat Karaçayir, Şuayi̇p Yüzbaşi
A Galerkin-Type Approach To Solve Systems Of Linear Volterra-Fredholm Integro-Differential Equations, Murat Karaçayir, Şuayi̇p Yüzbaşi
Turkish Journal of Mathematics
The main interest of this paper is to propose a numerical scheme in order to solve linear systems of Volterra-Fredholm integro-differential equations given with mixed conditions. The proposed method is a weighted residual scheme which uses monomials up to a prescribed degree $N$ as the basis functions. By taking inner product of the equation system with the elements of this basis set in a Galerkin-like fashion, the original problem is transformed into a linear algebraic equation system. After a suitable incorporation of the mixed conditions, a final algebraic system is obtained, from which the approximate solutions of the problem are …
On A Subclass Of The Analytic And Bi-Univalent Functions Satisfying Subordinate Condition Defined By $Q$-Derivativ, Ni̇zami̇ Mustafa, Semra Korkmaz
On A Subclass Of The Analytic And Bi-Univalent Functions Satisfying Subordinate Condition Defined By $Q$-Derivativ, Ni̇zami̇ Mustafa, Semra Korkmaz
Turkish Journal of Mathematics
In this paper, we introduce and examine certain subclass $\ M_{q,\Sigma }\left( \varphi ,\beta \right) $ of analytic and bi-univalent functions on the open unit disk in the complex plane. Here, we give coefficient bound estimates, upper bound estimate for the second Hankel determinant and Fekete-Szegö inequality for the function belonging to this class. Some interesting special cases of the results obtained here are also discussed.
Continuous Wavelet Transform On Triebel-Lizorkin Spaces, Antonio L. Baisón Olmo, Víctor A. Cruz Barriguete, Jaime Navarro
Continuous Wavelet Transform On Triebel-Lizorkin Spaces, Antonio L. Baisón Olmo, Víctor A. Cruz Barriguete, Jaime Navarro
Turkish Journal of Mathematics
The continuous wavelet transform in higher dimensions is used to prove the regularity of weak solutions $u \in L^p(\mathbb R^n)$ under $Qu = f$ where $f$ belongs to the Triebel-Lizorkin space $F^{r,q}_p(\mathbb R^n)$ where $1 < p,q < \infty$, $0< r 0$ with positive constant coefficients $c_{\beta}$.
The Fourier Spectral Method For Determining A Heat Capacity Coefficient In A Parabolic Equation, Durdimurod Durdiev, Dilshod Durdiev
The Fourier Spectral Method For Determining A Heat Capacity Coefficient In A Parabolic Equation, Durdimurod Durdiev, Dilshod Durdiev
Turkish Journal of Mathematics
In this paper, the comparison of finite difference and Fourier spectral numerical methods for an inverse problem of simultaneously determining an unknown coefficient in a parabolic equation with the usual initial and boundary conditions is proposed. We represent the detailed description of the methods and their algorithms. The research work conducted in this paper shows that the Fourier spectral method is highly accurate.
$3d$-Flows Generated By The Curl Of A Vector Potential & Maurer-Cartan Equations, Oğul Esen, Partha Guha, Hasan Gümral
$3d$-Flows Generated By The Curl Of A Vector Potential & Maurer-Cartan Equations, Oğul Esen, Partha Guha, Hasan Gümral
Turkish Journal of Mathematics
We examine $3D$ flows $\mathbf{\dot{x}}=\mathbf{v}({\bf x})$ admitting vector identity $M\mathbf{v} = \nabla \times \mathbf{A}$ for a multiplier $M$ and a potential field $\mathbf{A}$. It is established that, for those systems, one can complete the vector field $\mathbf{v}$ into a basis fitting an $\mathfrak{sl}(2)$-algebra. Accordingly, in terms of covariant quantities, the structure equations determine a set of equations in Maurer-Cartan form. This realization permits one to obtain the potential field as well as to investigate the (bi-)Hamiltonian character of the system. The latter occurs if the system has a time-independent first integral. In order to exhibit the theoretical results on some …
A Matrix-Collocation Method For Solutions Of Singularly Perturbed Differential Equations Via Euler Polynomials, Deni̇z Elmaci, Şuayi̇p Yüzbaşi, Nurcan Baykuş Savaşaneri̇l
A Matrix-Collocation Method For Solutions Of Singularly Perturbed Differential Equations Via Euler Polynomials, Deni̇z Elmaci, Şuayi̇p Yüzbaşi, Nurcan Baykuş Savaşaneri̇l
Turkish Journal of Mathematics
In this paper, a matrix-collocation method which uses the Euler polynomials is introduced to find the approximate solutions of singularly perturbed two-point boundary-value problems (BVPs). A system of algebraic equations is obtained by converting the boundary value problem with the aid of the collocation points. After this algebraic system, the coefficients of the approximate solution are determined. This error analysis includes two theorems which consist of an upper bound of errors and an error estimation technique. The present method and error analysis are applied to three numerical examples of singularly perturbed two-point BVPs. Numerical examples and comparisons with other methods …
Translating Solitons Of Translation And Homothetical Types, Muhi̇tti̇n Evren Aydin, Rafael Lopez
Translating Solitons Of Translation And Homothetical Types, Muhi̇tti̇n Evren Aydin, Rafael Lopez
Turkish Journal of Mathematics
We prove that if a translating soliton can be expressed as the sum of two curves and one of these curves is planar, then the other curve is also planar and consequently the surface must be a plane or a grim reaper. We also investigate translating solitons that can be locally written as the product of two functions of one variable. We extend the results in Lorentz-Minkowski space.
The Interior-Boundary Strichartz Estimate For The Schrödinger Equation On The Half-Line Revisited, Bi̇lge Köksal, Türker Özsari
The Interior-Boundary Strichartz Estimate For The Schrödinger Equation On The Half-Line Revisited, Bi̇lge Köksal, Türker Özsari
Turkish Journal of Mathematics
In recent papers, it was shown for the biharmonic Schrödinger equation and 2D Schrödinger equation that Fokas method-based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interior-boundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with …
2-Colored Rogers-Ramanujan Partition Identities, Mohammad Zadehdabbagh
2-Colored Rogers-Ramanujan Partition Identities, Mohammad Zadehdabbagh
Turkish Journal of Mathematics
In this paper, we combined two types of partitions and introduced 2-colored Rogers-Ramanujan partitions. By finding some functional equations and using a constructive method, some identities have been found. Some overpartition identities coincide with our findings. A correspondence between colored partitions and overpartitions is provided.
Notes On The Quadraticity Of Linear Combinations Of A Cubic Matrix And A Quadratic Matrix That Commute, Tuğba Peti̇k, Hali̇m Özdemi̇r, Burak Tufan Gökmen
Notes On The Quadraticity Of Linear Combinations Of A Cubic Matrix And A Quadratic Matrix That Commute, Tuğba Peti̇k, Hali̇m Özdemi̇r, Burak Tufan Gökmen
Turkish Journal of Mathematics
Let $A_{1}$ and $A_{2}$ be an $\{\alpha_{1}, \beta_{1}, \gamma_{1}\}$-cubic matrix and an $\{\alpha_{2}, \beta_{2}\}$-quadratic matrix, respectively, with $\alpha_{1} \neq \beta_{1}$, $\beta_{1} \neq \gamma_{1}$, $\alpha_{1} \neq \gamma_{1}$ and $\alpha_{2}\neq \beta_{2}$. In this work, we characterize all situations in which the linear combination $A_{3}=a_{1}A_{1}+a_{2}A_{2}$ with the assumption $A_{1}A_{2}=A_{2}A_{1}$ is an $\{\alpha_{3}, \beta_{3}\}$-quadratic matrix, where $a_{1}$ and $a_{2}$ are unknown nonzero complex numbers.
Maximising The Number Of Connected Induced Subgraphs Of Unicyclic Graphs, Audace A V Dossou Olory
Maximising The Number Of Connected Induced Subgraphs Of Unicyclic Graphs, Audace A V Dossou Olory
Turkish Journal of Mathematics
Denote by $\mathcal{G}(n,c,g,k)$ the set of all connected graphs of order $n$, having $c$ cycles, girth $g$, and $k$ pendant vertices. In this paper, we give a partial characterisation of the structure of those graphs in $\mathcal{G}(n,c,g,k)$ maximising the number of connected induced subgraphs. For the special case where $c=1$, we find a complete characterisation of all maximal unicyclic graphs. We also derive a precise formula for the corresponding maximum number given the following parameters: (1) order, girth, and number of pendant vertices; (2) order and girth; (3) order.
Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren
Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren
Turkish Journal of Mathematics
In this paper, we present some relationships between statistical boundedness and statistical monotonicity of a given sequence and its subsequences. The results concerning statistical boundedness and monotonicity presented here are also closely related to earlier results regarding statistical convergence and are dealing with the Lebesgue measure and with the Baire category.
Ranks And Presentations For Order-Preserving Transformations With One Fixed Point, Joerg Koppitz, Somnuek Worawiset
Ranks And Presentations For Order-Preserving Transformations With One Fixed Point, Joerg Koppitz, Somnuek Worawiset
Turkish Journal of Mathematics
In the present paper, we consider the semigroup $O_{n,p}$ of all order-preserving full transformations $\alpha $ on an n-elements chain $X_{n}$% , where $p\in X_{n}$ is the only fixed point of $\alpha $. The nilpotent semigroup $O_{n,p}$ was first studied by Ayik et al. in 2011. Moreover, $% O_{n,1}$ is the maximal nilpotent subsemigroup of the Catalan Monoid $C_{n}$. Its rank is the difference of the $(n-1)$th and the $(n-2)$th Catalan number. The aim of the present paper is to provide further fundamental information about the nilpotent semigroup $O_{n,p}$. We will calculate the rank of $O_{n,p}$ for $% p>1$ …
On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök
On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök
Turkish Journal of Mathematics
Let $U$ and $V$ be two Archimedean Riesz spaces. An operator $S:U\rightarrow V$ is said to be unbounded order continuous ($uo$-continuous), if $r_{\alpha }\overset{uo}{\rightarrow }0$ in $U$ implies $Sr_{\alpha }\overset{uo}{% \rightarrow }0$ in $V$. In this paper, we give some properties of the $uo$% -continuous dual $U_{uo}^{\sim }$ of $U$. We show that a nonzero linear functional $f$ on $U$ is $uo$-continuous if and only if $f$ is a linear combination of finitely many order continuous lattice homomorphisms. The result allows us to characterize the $uo$-continuous dual $U_{uo}^{\sim }.$ In general, by giving an example that the $uo$-continuous dual $U_{uo}^{\sim …
Hyperelastic Curves Along Riemannian Maps, Tunahan Turhan, Gözde Özkan Tükel, Bayram Şahi̇n
Hyperelastic Curves Along Riemannian Maps, Tunahan Turhan, Gözde Özkan Tükel, Bayram Şahi̇n
Turkish Journal of Mathematics
The main purpose of this paper is to examine what kind of information the smooth Riemannian map defined between two Riemannian manifolds provides about the character of the Riemannian map when a horizontal hyperelastic curve on the total manifold is carried to a hyperelastic curve on the base manifold. For the solution of the mentioned problem, firstly, the behavior of an arbitrary horizontal curve on the total manifold under a Riemannian map is investigated and the equations related to pullback connection are obtained. The necessary conditions are given for the Riemannian map to be h-isotropic or totally umbilical when a …
A Simple And Constructive Proof To A Generalization Of Lüroth's Theorem, Francois Ollivier, Brahim Sadik
A Simple And Constructive Proof To A Generalization Of Lüroth's Theorem, Francois Ollivier, Brahim Sadik
Turkish Journal of Mathematics
A generalization of Lüroth's theorem expresses that every transcendence degree $1$ subfield of the rational function field is a simple extension. In this note we show that a classical proof of this theorem also holds to prove this generalization.
An Application Of Modified Sigmoid Function To A Class Of $Q-$ Starlike And $Q-$ Convex Analytic Error Functions, Arzu Akgül
Turkish Journal of Mathematics
In this study, in the open unit disc $\Lambda$, by applying the $q-$ derivative operator and the fractional $q-$ derivative operator and by using the principle of subordination between analytic functions, we introduce some new interesting subclasses of $q-$ starlike and $q-$ convex analytic functions associated with error functions and modified sigmoid functions.
Study Of The $\Phi$-Generalized Type $K$-Fractional Integrals Or Derivatives And Some Of Their Properties, Mustafa Aydin, Nazim I. Mahmudov
Study Of The $\Phi$-Generalized Type $K$-Fractional Integrals Or Derivatives And Some Of Their Properties, Mustafa Aydin, Nazim I. Mahmudov
Turkish Journal of Mathematics
A novel fractional integral in the sense of Riemann-Liouville integral and two new fractional derivatives in the sense of Riemann-Liouville derivative and Caputo derivative with respect to another function and two parameters are introduced. Some significant properties of them are presented like semigroup property, inverse property, etc. The solution of the Cauchy-type problem for the nonhomogenous linear differential equation with the $\phi$-generalized Caputo $k$-fractional derivative is given by using the method of successive approximation.
Representation Variety Of Free Or Surface Groups And Reidemeister Torsion, Fati̇h Hezenci̇, Yaşar Sözen
Representation Variety Of Free Or Surface Groups And Reidemeister Torsion, Fati̇h Hezenci̇, Yaşar Sözen
Turkish Journal of Mathematics
For $G \in \left\{ \mathrm{GL}(n,\mathbb{C}) , \mathrm{SL}(n,\mathbb{C})\right\} ,$ we consider $G-$valued representations of free or surface group with genus $ >1.$ We establish a formula for computing Reidemeister torsion of such representations in terms of Atiyah-Bott-Goldman symplectic form for $G.$ Furthermore, we apply the obtained results to hyperbolic 3-manifolds.
Numerical Simulations Of Traveling Waves In A Counterflow Filtration Combustion Model, Fati̇h Özbağ
Numerical Simulations Of Traveling Waves In A Counterflow Filtration Combustion Model, Fati̇h Özbağ
Turkish Journal of Mathematics
We focused on traveling combustion waves that appear in a simplified, one-dimensional combustion model in porous media. The system we consider is a reaction-convection-diffusion system that can be reduced into two-dimension in order to prove traveling waves by phase plane analysis. In previous studies combustion wave velocity was assumed positive and their existence was proven. Also, all possible wave sequences that solve boundary value problems on infinite intervals with constant boundary data were identified. In this study, we generalize the previous work by including the case of negative combustion wave speed and taking the assumption that oxygen is carried faster …