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Articles 1081 - 1110 of 10317
Full-Text Articles in Physical Sciences and Mathematics
Introducing Selective D-Separability In Bitopological Spaces, Selma Özçağ
Introducing Selective D-Separability In Bitopological Spaces, Selma Özçağ
Turkish Journal of Mathematics
We introduce $\sf D$-separability and its game-theoretic version, $\sf D^+$-separability in bitopological spaces, and investigate their relationships with $d$-separability and a weaker form of $\sf H$-separability which will be called ${\sf DH}$-separability. Further we give the connection of these notions with the selective versions of separability-types properties under the bitopological context. We also obtain some results about the $d$-separability properties of bitopological spaces which are slightly different from those one expects for the classical case
A Multidimensional Diffusion Coefficient Determination Problem For The Time-Fractional Equation, Durdimurod Durdiev, Askar Rahmonov
A Multidimensional Diffusion Coefficient Determination Problem For The Time-Fractional Equation, Durdimurod Durdiev, Askar Rahmonov
Turkish Journal of Mathematics
In this paper, we consider a multidimensional inverse problem for a fractional diffusion equation. The inverse problem is reduced to the equivalent integral equation. For solving this equation the Schauder principle is applied. The local existence and uniqueness results are obtained.
Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo
Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo
Turkish Journal of Mathematics
In this paper, we introduce new notions of symmetric operators such as semisymmetric shape operator and structure Jacobi operator in complex hyperbolic two-plane Grassmannians. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with such notions.
Universality Of An Absolutely Convergent Dirichlet Series With Modified Shifts, Antanas Laurincikas, Renata Macaitiene, Darius Siauciunas
Universality Of An Absolutely Convergent Dirichlet Series With Modified Shifts, Antanas Laurincikas, Renata Macaitiene, Darius Siauciunas
Turkish Journal of Mathematics
In the paper, a theorem on approximation of a wide class of analytic functions by generalized shifts $\zeta_{u_T}(s+i\varphi(\tau))$ of an absolutely convergent Dirichlet series $\zeta_{u_T}(s)$ which in the mean is close to the Riemann zeta-function is obtained. Here $\varphi(\tau)$ is a monotonically increasing differentiable function having a monotonic continuous derivative such that $\varphi(2\tau)\max\limits_{\tau\leqslant t\leqslant 2\tau} \frac{1}{\varphi'(t)} \ll \tau$ as $\tau\to\infty$, and $u_T\to\infty$ and $u_T\ll T^2$ as $T\to\infty$.
On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan
On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan
Turkish Journal of Mathematics
We introduce a certain type of warped-twisted product submanifolds which is called warped-twisted product hemislant submanifolds of the form $_{f_2}M^{\bot}\times_{f_1}M^{\theta}$ with warping function $f_2$ on $M^\theta$ and twisting function $f_1$, where $M^\bot$ is a totally real and $M^\theta$ is a slant submanifold of a globally conformal Kaehler manifold. We prove that a warped-twisted product hemislant submanifold of a globally conformal Kaehler manifold is a locally doubly warped product. Then we establish a general inequality for doubly warped product mixed geodesic hemislant submanifolds and get some results for such submanifolds by using the equality sign of the general inequality.
Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania
Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania
Turkish Journal of Mathematics
A Cauchy problem for a modification of the Swift-Hohenberg equation in $R^{N}$ with a mildly integrable potential is considered. Applying the dissipative mechanism of fourth order parabolic equations in unbounded domains, it is shown that the equation generates a semigroup of global solutions possessing a global attractor in the scale of Bessel potential spaces and in $H^2(R^{N})$ in particular.
A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici
A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici
Turkish Journal of Mathematics
A compact set $K\subset \mathbb C^n$ is called Bernstein set if, for some constant $M>0$, the following inequality $$ D^{\alpha}P _K\leq M^{ \alpha }(\deg P)^{ \alpha } P _K $$ is satisfied for every multiindex $\alpha\in \mathbb N^n$ and for every polynomial $P$. We provide here a lower bound for the transfinite diameter of Bernstein sets by using generalized extremal Leja points.
On The Convergence And Stability Analysis Of Finite-Difference Methods For The Fractional Newell-Whitehead-Segel Equations, İnci̇ Çi̇li̇ngi̇r Süngü, Emre Aydin
On The Convergence And Stability Analysis Of Finite-Difference Methods For The Fractional Newell-Whitehead-Segel Equations, İnci̇ Çi̇li̇ngi̇r Süngü, Emre Aydin
Turkish Journal of Mathematics
In this study, standard and non-standard finite-difference methods are proposed for numerical solutions of the time-spatial fractional generalized Newell-Whitehead-Segel equations describing the dynamical behavior near the bifurcation point of the Rayleigh-Benard convection of binary fluid mixtures. The numerical solutions have been found for high values of $p$ which shows the degree of nonlinear terms in the equations. The stability and convergence conditions of the obtained difference schemes are determined for each value of $p$. Errors of methods for various values of $p$ are given in tables. The compatibility of exact solutions and numerical solutions and the effectiveness of the methods …
On The Bmo Spaces Associated With The Laplace-Bessel Differential Operator, Si̇nem Sezer, Si̇mten Bayrakçi, Güldane Yildiz, Recep Kahraman
On The Bmo Spaces Associated With The Laplace-Bessel Differential Operator, Si̇nem Sezer, Si̇mten Bayrakçi, Güldane Yildiz, Recep Kahraman
Turkish Journal of Mathematics
In this paper, the characteristic properties of the space of functions of bounded mean oscillation called the $B$-$BMO$ associated with the Laplace-Bessel differential operator are obtained. The John-Nirenberg type inequality on the $B$-$BMO$ space and a relation between the $B$-Poisson integral and the $B$-$BMO$ functions are proved.
Nonunique Best Proximity Point Results With An Application To Nonlinear Fractional Differential Equations, Mustafa Aslantaş
Nonunique Best Proximity Point Results With An Application To Nonlinear Fractional Differential Equations, Mustafa Aslantaş
Turkish Journal of Mathematics
In this paper, we point out an error in proving famous Achari type nonunique fixed point results. Also, we prove some best proximity point results in $b$ -metric spaces by introducing new concepts. Hence, we develop some results existing in the literature. Finally, we give a result for the existence of the solution of nonlinear fractional differential equations.
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.
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.
New Form Of Laguerre Fractional Differential Equation And Applications, Zahra Kavooci, Kazem Ghanbari, Hanif Mirzaei
New Form Of Laguerre Fractional Differential Equation And Applications, Zahra Kavooci, Kazem Ghanbari, Hanif Mirzaei
Turkish Journal of Mathematics
Laguerre differential equation is a well known equation that appears in the quantum mechanical description of the hydrogen atom. In this paper, we aim to develop a new form of Laguerre Fractional Differential Equation (LFDE) of order $2\alpha$ and we investigate the solutions and their properties. For a positive real number $\alpha$, we prove that the equation has solutions of the form $L_{n,\alpha}(x)=\sum_{k=0}^na_kx^k$, where the coefficients of the polynomials are computed explicitly. For integer case $\alpha=1$ we show that these polynomials are identical to classical Laguerre polynomials. Finally, we solve some fractional differential equations by defining a suitable integral transform.
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.
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 …
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 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 …
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.
A Novel Energy Consumption Model For Autonomous Mobile Robot, Gürkan Gürgöze, İbrahi̇m Türkoğlu
A Novel Energy Consumption Model For Autonomous Mobile Robot, Gürkan Gürgöze, İbrahi̇m Türkoğlu
Turkish Journal of Electrical Engineering and Computer Sciences
In this study, a novel predictive energy consumption model has been developed to facilitate the development of tasks based on efficient energy consumption strategies in mobile robot systems. For the proposed energy consumption model, an advanced mathematical system model that takes into account all parameters during the motion of the mobile robot is created. The parameters of inclination, load, dynamic friction, wheel slip and speed-torque saturation limit, which are often neglected in existing models, are especially used in our model. Thus, the effects of unexpected disruptors on energy consumption in the real world environment are also taken into account. As …
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.
Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan
Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan
Turkish Journal of Mathematics
We study hyperelastic curves known as a generalization of elastic curves in $3-$dimensional lightlike cone which is a degenerate hypersurface in Minkowski $4-$space as critical points of the cone curvature energy functional constructed with the $r-$th power of the cone curvature depending on the given boundary conditions for the natural number $r \geq 2$. We derive the Euler-Lagrange equations for the critical points of this functional that is namely the hyperelastic curves and solve completely the Euler-Lagrange equations by quadratures. Then, we construct Killing vector fields along the hyperelastic curves. Lastly, we give explicitly the hyperelastic curves by integral according …
On Isolated Gaps In Numerical Semigroups, Harold J. Smith
On Isolated Gaps In Numerical Semigroups, Harold J. Smith
Turkish Journal of Mathematics
A numerical semigroup is said to be perfect if it does not contain any isolated gaps. In this paper, we will look at some basic properties of isolated gaps in numerical semigroups. In particular, we will see how they are related to elements of the Apery set. We will use these properties to find all of the isolated gaps in a numerical semigroup of embedding dimension two and demonstrate a simple method of generating some examples of perfect numerical semigroups of embedding dimension three.
On Bounded Solutions Of A Second-Order Iterative Boundary Value Problem, Safa Chouaf, Ahleme Bouakkaz, Rabah Khemis
On Bounded Solutions Of A Second-Order Iterative Boundary Value Problem, Safa Chouaf, Ahleme Bouakkaz, Rabah Khemis
Turkish Journal of Mathematics
In this article, we investigate a second-order iterative differential equation with boundary conditions. The use of the principle of contraction mappings and the Schauder's fixed point theorem allows us to prove some existence and uniqueness results. Finally, an example is given to check the validity of our findings, which are new, and complete some published manuscripts to some degree.
Solvability Of Gripenberg's Equations Of Fractional Order With Perturbation Term In Weighted $L_P$-Spaces On ${\Mathbb{R}}^+$, Mohamed M. A. Metwali
Solvability Of Gripenberg's Equations Of Fractional Order With Perturbation Term In Weighted $L_P$-Spaces On ${\Mathbb{R}}^+$, Mohamed M. A. Metwali
Turkish Journal of Mathematics
This article deals with the solvability of Gripenberg's equations of fractional order with a perturbation term in weighted Lebesgue spaces on ${\mathbb{R}}^+=[0,\infty)$ via the fixed point hypothesis and the measure of noncompactness. The uniqueness of the solutions for the studied problem is discussed. An example is included to validate our results. The results presented in the article extend and generalize some former results in the available literature.
Some Notes On Crossed Semimodules, Sedat Temel
Some Notes On Crossed Semimodules, Sedat Temel
Turkish Journal of Mathematics
In this paper, we introduce the notion of lifting via a homomorphism of monoids for a crossed semimodule and give some properties. Further, we characterize actions and coverings of Schreier internal categories in the category Mon of monoids and prove the natural equivalence between their categories. Then, we prove that liftings of a certain crossed semimodule are naturally equivalent to the actions of Schreier internal category in Mon, where the Schreier internal category corresponds to the crossed semimodule. Finally, we give a relation between crossed semimodules and simplicial monoids.
A Köthe-Toeplitz Dual Of A Generalized Cesaro Difference Sequence Space, A Degenerate Lorentz Space, Their Corresponding Function Spaces And Fpp, Veysel Nezi̇r, Ni̇zami̇ Mustafa
A Köthe-Toeplitz Dual Of A Generalized Cesaro Difference Sequence Space, A Degenerate Lorentz Space, Their Corresponding Function Spaces And Fpp, Veysel Nezi̇r, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In 1970, Cesaro sequence spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for ${\ell }^{\infty }$, ${\mathrm{c}}_0$ and $\mathrm{c}$. Then, in 1983, Orhan introduced Cesaro difference sequence spaces. Both works used difference operator and investigated the Köthe-Toeplitz dual for the new Banach spaces they introduced. Later, various authors generalized these new spaces, especially the one introduced by Orhan. In this study, first we discuss the fixed point property for these spaces and for the corresponding function space of the Köthe-Toeplitz dual. Moreover, we consider another generalized space which is a degenerate Lorentz space because the spaces …
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 …
Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds, Tüli̇n Altunöz
Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds, Tüli̇n Altunöz
Turkish Journal of Mathematics
We consider simply connected $4$-manifolds admitting Lefschetz fibrations over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are exotic symplectic $4$-manifolds in the homeomorphism classes of $\mathbb{C} P^{2}\#8\overline{\mathbb{C} P^{2}}$ and $\mathbb{C} P^{2}\#9\overline{\mathbb{C} P^{2}}$, respectively. From these, we provide upper bounds for the minimal number of singular fibers of such fibrations. In addition, we prove that this number is equal to $18$ for $g=3$ when such fibrations are hyperelliptic. Moreover, we discuss these numbers for higher genera.
Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds, Deng Yihua
Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds, Deng Yihua
Turkish Journal of Mathematics
In this paper, we consider gradient estimates for positive solutions to the following equation $$\triangle_V u+au^p\log u=0$$ on complete noncompact Riemannian manifold with $k$-dimensional Bakry-Emery Ricci curvature bounded from below. Using the Bochner formula and the Cauchy inequality, we obtain upper bounds of $ \nabla u $ with respect to the lower bound of the Bakry-Emery Ricci curvature.
Existence And Multiplicity Of Solutions For P(.)-Kirchhoff-Type Equations, Rabi̇l Ayazoğlu, Sezgi̇n Akbulut, Ebubeki̇r Akkoyunlu
Existence And Multiplicity Of Solutions For P(.)-Kirchhoff-Type Equations, Rabi̇l Ayazoğlu, Sezgi̇n Akbulut, Ebubeki̇r Akkoyunlu
Turkish Journal of Mathematics
his paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for $p(.)$-Kirchhoff-type equation% \begin{equation*} \left\{ \begin{array}{c} M\left( \int_{\Omega }\frac{\left\vert \nabla u\right\vert ^{p(x)}}{p(x)}% dx\right) \left( -\Delta _{p(x)}u\right) =f(x,u),\text{ in }\Omega , \\ u=0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{on }\partial \Omega .% \end{array}% \right. \end{equation*}% Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of …