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Articles 451 - 480 of 2595
Full-Text Articles in Mathematics
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 …
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 $c_{\beta}$.
On The Behaviour Of Solutions To A Kind Of Third Order Nonlinear Neutral Differential Equation With Delay, Adeleke Ademola, Peter Arawomo, Olufemi Adesina, Samuel Okoya
On The Behaviour Of Solutions To A Kind Of Third Order Nonlinear Neutral Differential Equation With Delay, Adeleke Ademola, Peter Arawomo, Olufemi Adesina, Samuel Okoya
Turkish Journal of Mathematics
This paper presents a novel class of third order nonlinear nonautonomous neutral differential equation with delay. The third order neutral differential equation is cut down to a system of first order, a suitable complete Lyapunov-Krasovskii's functional is constructed and used, to obtain standard conditions on the nonlinear functions to ensure stability and uniform asymptotic stability of the trivial solutions, the existence of a unique periodic solution, uniform boundedness and uniform ultimate boundedness of solutions when the forcing term is nonzero. The obtained results are new and include many prominent results on neutral and nonneutral delay differential equations in literature. Finally, …
Constant Angle Surfaces In The Lorentzian Warped Product Manifold $I \Times_{F} \Mathbb E^2_1$, Uğur Dursun
Constant Angle Surfaces In The Lorentzian Warped Product Manifold $I \Times_{F} \Mathbb E^2_1$, Uğur Dursun
Turkish Journal of Mathematics
Let $I \times_{f} \mathbb E^2_1$ be a 3-dimensional Lorentzian warped product manifold with the metric $\tilde g = dt^2 + f^2(t) (dx^2 - dy^2)$, where $I$ is an open interval, $f$ is a strictly positive smooth function on $I,$ and $\mathbb E^2_1$ is the Minkowski 2-plane. In this work, we give a classification of all space-like and time-like constant angle surfaces in $I \times_{f} \mathbb E^2_1$ with nonnull principal direction when the surface is time-like. In this classification, we obtain space-like and time-like surfaces with zero mean curvature, rotational surfaces, and surfaces with constant Gaussian curvature. Also, we have some …
Novel Exact Solutions To Navier-Stokes Momentum Equations Describing An Incompressible Fluid, Yahya Öz
Novel Exact Solutions To Navier-Stokes Momentum Equations Describing An Incompressible Fluid, Yahya Öz
Turkish Journal of Mathematics
An analytical solution to the incompressible Navier-Stokes momentum equations for a divergence-free flow $\boldsymbol{\nabla}\cdot \vec u\left(\vec x,t\right)=0$ with time-dependent dynamic viscosity $\mu\left(t\right)$ is presented. The demonstrated methodology holds for the physically relevent three dimensions. The constructed flow velocities $\vec u\left(\vec x,t\right)$ are eigenvectors of the vector operator curl. Moreover, vortex $\vec \omega\left(\vec x,t\right)$, helicity $H\left(\vec x,t\right)$, enstrophy $\mathcal{E}\left(t\right)$ and enstrophy evolution $\frac{\mathrm{d}\mathcal{E}\left(t\right)}{\mathrm{d}t}$ are explicitly determined.
Explicit Motion Planning In Digital Projective Product Spaces, Seher Fi̇şekci̇, İsmet Karaca
Explicit Motion Planning In Digital Projective Product Spaces, Seher Fi̇şekci̇, İsmet Karaca
Turkish Journal of Mathematics
We introduce digital projective product spaces based on Davis' projective product spaces. We determine an upper bound for the digital LS-category of digital projective product spaces. In addition, we obtain an upper bound for the digital topological complexity of these spaces through an explicit motion planning construction, which shows digital perspective validity of results given by S. Fişekci and L. Vandembroucq. We apply our outcomes on specific spaces in order to be more clear.
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 …
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.
From Ordered Semigroups To Ordered $\Gamma$-Hypersemigroups, Niovi Kehayopulu
From Ordered Semigroups To Ordered $\Gamma$-Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
In an attempt to show the way we pass from ordered semigroups to ordered $\Gamma$-hypersemigroups, we examine the results of Semigroup Forum (1992; 46: 341-346) for an ordered $\Gamma$-hypersemigroup. It has been shown that the concept of semisimple ordered $\Gamma$-hypersemigroup $S$ is identical with the concept "the ideals of $S$ are idempotent" and the ideals of $S$ are idempotent if and only if for all ideals $A, B$ of $S$, we have $A\cap B=(A\Gamma B]$. The main results of the paper are the following: The ideals of an ordered $\Gamma$-hypersemigroup $S$ are weakly prime if and only if they form …
Bessel Equation And Bessel Function On $\Mathbb{T}_{(Q,H)}$, Ahmet Yantir, Burcu Si̇li̇ndi̇r Yantir, Zehra Tuncer
Bessel Equation And Bessel Function On $\Mathbb{T}_{(Q,H)}$, Ahmet Yantir, Burcu Si̇li̇ndi̇r Yantir, Zehra Tuncer
Turkish Journal of Mathematics
This article is devoted to present nabla $(q, h)$-analogues of Bessel equation and Bessel function. In order to construct series solution of nabla $(q, h)$-Bessel equation, we present nabla $(q, h)$-analysis regarding nabla generalized quantum binomial, nabla $(q,h)$-analogues of Taylor's formula, Gauss's binomial formula, Taylor series, analytic functions, analytic exponential function with its fundamental properties, analytic trigonometric and hyperbolic functions. We emphasize that nabla $(q, h)$-Bessel equation recovers classical, $h$- and $q$-discrete Bessel equations. In addition, we establish nabla $(q, h)$-Bessel function which is expressed in terms of an absolutely convergent series in nabla generalized quantum binomials and intimately demonstrate …
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.
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.
On Generalized Fibonacci And Lucas Hybrid Polynomials, N. Rosa Ait-Amrane, Hacene Belbachir, Eli̇f Tan
On Generalized Fibonacci And Lucas Hybrid Polynomials, N. Rosa Ait-Amrane, Hacene Belbachir, Eli̇f Tan
Turkish Journal of Mathematics
In this paper, we introduce a new generalization of Fibonacci and Lucas hybrid polynomials. We investigate some basic properties of these polynomials such as recurrence relations, the generating functions, the Binet formulas, summation formulas, and a matrix representation. We derive generalized Cassini's identity and generalized Honsberger formula for generalized Fibonacci hybrid polynomials by using their matrix representation.
Numerical Solution Of A Singularly Perturbed Fredholm Integro Differential Equation With Robin Boundary Condition, Muhammet Enes Durmaz, Gabi̇l Ami̇rali̇, Mustafa Kudu
Numerical Solution Of A Singularly Perturbed Fredholm Integro Differential Equation With Robin Boundary Condition, Muhammet Enes Durmaz, Gabi̇l Ami̇rali̇, Mustafa Kudu
Turkish Journal of Mathematics
In this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions. By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh. The stability and convergence of the difference scheme have been analyzed in the discrete maximum norm. Some numerical examples have been solved and numerical outcomes are obtained.
Scattering Properties Of Impulsive Difference Dirac Equations, Şeyda Solmaz, Elgi̇z Bayram
Scattering Properties Of Impulsive Difference Dirac Equations, Şeyda Solmaz, Elgi̇z Bayram
Turkish Journal of Mathematics
In this paper, we explore the Jost solutions and the scattering matrix of the impulsive difference Dirac systems (IDDS) on the whole axis and study their analytic and asymptotic properties. Furthermore, characteristic properties of the scattering matrix of the IDDS have been examined.
Scattering Theory Of The Quadratic Eigenparameter Depending Impulsive Sturm-Liouville Equations, Güler Başak Öznur, Elgi̇z Bairamov
Scattering Theory Of The Quadratic Eigenparameter Depending Impulsive Sturm-Liouville Equations, Güler Başak Öznur, Elgi̇z Bairamov
Turkish Journal of Mathematics
We handle an impulsive Sturm-Liouville boundary value problem. We find the Jost solution, Jost function, and scattering function of this problem and examine the properties of scattering function. We also study eigenvalues and resolvent operator of this problem. Finally, we exemplify our work by taking a different problem.
Global Existence And Energy Decay For A Coupled System Of Kirchhoff Beam Equations With Weakly Damping And Logarithmic Source, Ducival Carvalho Pereira, Carlos Alberto Raposo Da Cunha, Adriano Pedreira Cattai
Global Existence And Energy Decay For A Coupled System Of Kirchhoff Beam Equations With Weakly Damping And Logarithmic Source, Ducival Carvalho Pereira, Carlos Alberto Raposo Da Cunha, Adriano Pedreira Cattai
Turkish Journal of Mathematics
This paper deals with the global solutions and exponential stability for a coupled system of Kirchhoff beam weakly damping and with a logarithmic source. We apply the potential well and establish the global well-posedness by using the Faedo--Galerkin approximations, taking into account that the initial data is located in a suitable set of stability created from the Nehari manifold. Moreover, by using Nakao's lemma, we prove the exponential stability of the solution.
On A Solvable System Of Rational Difference Equations Of Higher Order, Merve Kara, Yasi̇n Yazlik
On A Solvable System Of Rational Difference Equations Of Higher Order, Merve Kara, Yasi̇n Yazlik
Turkish Journal of Mathematics
In this paper, we present that the following system of difference equations $$ x_{n}=\frac{x_{n-k}z_{n-l}}{b_{n}x_{n-k}+a_{n}z_{n-k-l}}, \ y_{n}=\frac{y_{n-k}x_{n-l}}{d_{n}y_{n-k}+c_{n}x_{n-k-l}}, \ z_{n}=\frac{z_{n-k}y_{n-l}}{f_{n}z_{n-k}+e_{n}y_{n-k-l}}, $$ where $n\in \mathbb{N}_{0}$, $k,l\in\mathbb{N}$, the initial values $x_{-i},y_{-i},z_{-i}$ are real numbers, for $i \in \overline{1,k+l}$, and sequences $\left( a_{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( b_{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( c_{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( d_{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( e_{n}\right) _{n\in \mathbb{N}_{0}}$ and $\left( f_{n}\right) _{n\in \mathbb{N}_{0}}$ are non-zero real numbers, for all $n\in \mathbb{N}_{0}$, which can be solved in closed form. We describe the forbidden set of the initial values using the obtained formulas and also determine the asymptotic behavior of solutions for the case …
Multiple Positive Solutions For Nonlinear Fractional $Q$-Difference Equation With $P$-Laplacian Operator, Zhongyun Qin, Shurong Sun, Zhenlai Han
Multiple Positive Solutions For Nonlinear Fractional $Q$-Difference Equation With $P$-Laplacian Operator, Zhongyun Qin, Shurong Sun, Zhenlai Han
Turkish Journal of Mathematics
In this paper, we investigate a class of four-point boundary value problems of fractional $q$-difference equation with $p$-Laplacian operator which is the first time to be studied and is extended from a bending elastic beam equation. By Avery-Peterson theorem and the method of lower and upper solutions associated with monotone iterative technique, we obtain some sufficient conditions for the existence of multiple positive solutions. As applications, examples are presented to illustrate the main results.
Existence And Transportation Inequalities For Fractional Stochastic Differential Equations, Abdelghani Ouahab, Mustapha Belabbas, Johnny Henderson, Fethi Souna
Existence And Transportation Inequalities For Fractional Stochastic Differential Equations, Abdelghani Ouahab, Mustapha Belabbas, Johnny Henderson, Fethi Souna
Turkish Journal of Mathematics
In this work, we establish the existence and uniqueness of solutions for a fractional stochastic differential equation driven by countably many Brownian motions on bounded and unbounded intervals. Also, we study the continuous dependence of solutions on initial data. Finally, we establish the transportation quadratic cost inequality for some classes of fractional stochastic equations and continuous dependence of solutions with respect Wasserstein distance.
Composition Laws On The Fricke Surface And Markov Triples, Abdurrahman Muhammed Uludağ, Esra Ünal Yilmaz
Composition Laws On The Fricke Surface And Markov Triples, Abdurrahman Muhammed Uludağ, Esra Ünal Yilmaz
Turkish Journal of Mathematics
We determine some composition laws related to the Fricke surface and the "double" Fricke surface. This latter surface admits the squares of Markov triples as its solutions.
Necessary Conditions For Extended Spectral Decomposable Multivalued Linear Operators, Yosra Barkaoui, Maher Mnif
Necessary Conditions For Extended Spectral Decomposable Multivalued Linear Operators, Yosra Barkaoui, Maher Mnif
Turkish Journal of Mathematics
In this paper, we use subsets of the Riemann sphere and specific types of invariant linear subspaces to introduce the extended spectral decomposable multivalued linear operators (linear relations) in Banach spaces. We also introduce the extended Bishop's property, the extended relatively single-valued extension property and the extended Dunford's property. More importantly, we show that these properties are three necessary conditions for a linear relation to be extended spectral decomposable.
The Arens-Michael Envelopes Of Laurent Ore Extensions, Petr Kosenko
The Arens-Michael Envelopes Of Laurent Ore Extensions, Petr Kosenko
Turkish Journal of Mathematics
For an Arens-Michael algebra $A$ we consider a class of $A$-$\hat{\otimes}$-bimodules which are invertible with respect to the projective bimodule tensor product. We call such bimodules topologically invertible over $A$. Given a Frechet-Arens-Michael algebra $A$ and a topologically invertible Frechet $A$-$\hat{\otimes}$-bimodule $M$, we construct an Arens-Michael algebra $\widehat{L}_A(M)$ which serves as a topological version of the Laurent tensor algebra $L_A(M)$. Also, for a fixed algebra $B$ we provide a condition on an invertible $B$-bimodule $N$ which allows us to explicitly describe the Arens-Michael envelope of $L_B(N)$ as a topological Laurent tensor algebra. In particular, we provide an explicit description of …
On The Blow-Up Of Solutions To A Fourth-Order Pseudoparabolic Equation, Mustafa Polat
On The Blow-Up Of Solutions To A Fourth-Order Pseudoparabolic Equation, Mustafa Polat
Turkish Journal of Mathematics
In this note, we consider a fourth-order semilinear pseudoparabolic differential equation including a strong damping term together with a nonlocal source term. The problem is considered under the periodic boundary conditions and a finite time blow-up result is established. Also a lower bound estimate for the blow-up time is obtained.
Second Main Theorem For Meromorphic Mappings Intersecting Moving Targets On Parabolic Manifolds, Jiali Chen, Qingcai Zhang
Second Main Theorem For Meromorphic Mappings Intersecting Moving Targets On Parabolic Manifolds, Jiali Chen, Qingcai Zhang
Turkish Journal of Mathematics
In this paper, we establish a new second main theorem for meromorphic mappings from $M$ into $\mathbb{P}(V)$ intersecting moving targets $g_{j}:M\rightarrow\mathbb{P}(V^{\ast}),\ 1\leq j\leq q,$ where $M$ is a parabolic manifold and $V$ is a Hermitian vector space. As an application, we prove the algebraic dependence problem for meromorphic mappings with moving targets in general position.
Ricci-Yamabe Solitons And 3-Dimensional Riemannian Manifolds, Uday Chand De, Arpan Sardar, Krishnendu De
Ricci-Yamabe Solitons And 3-Dimensional Riemannian Manifolds, Uday Chand De, Arpan Sardar, Krishnendu De
Turkish Journal of Mathematics
In this paper, we classify 3-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are Ricci-Yamabe solitons and gradient Ricci-Yamabe solitons, respectively. Finally, we construct an example to illustrate our result.
A Parametric Family Of Ternary Purely Exponential Diophantine Equation $A^X+B^Y=C^Z$, Yasutsugu Fujita, Maohua Le
A Parametric Family Of Ternary Purely Exponential Diophantine Equation $A^X+B^Y=C^Z$, Yasutsugu Fujita, Maohua Le
Turkish Journal of Mathematics
Let $a,b,c$ be fixed positive integers such that $a+b=c^2$, $2 \nmid c$ and $(b/p)\ne 1$ for every prime divisor $p$ of $c$, where $(b/p)$ is the Legendre symbol. Further let $m$ be a positive integer with $m>1$. In this paper, using the Baker method, we prove that if $m>\max\{10^8,c^2\}$, then the equation $(am^2+1)^x+(bm^2-1)^y=(cm)^z$ has only one positive integer solution $(x,y,z)=(1,1,2)$.
Inverse Coefficient Identification Problem For A Hyperbolic Equation With Nonlocal Integral Condition, Azizbayov Elvin
Inverse Coefficient Identification Problem For A Hyperbolic Equation With Nonlocal Integral Condition, Azizbayov Elvin
Turkish Journal of Mathematics
This paper is concerned with an inverse coefficient identification problem for a hyperbolic equation in a rectangular domain with a nonlocal integral condition. We introduce the definition of the classical solution, and then the considered problem is reduced to an auxiliary equivalent problem. Further, the existence and uniqueness of the solution of the equivalent problem are proved using a contraction mapping principle. Finally, using equivalency, the unique existence of a classical solution is proved.