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Articles 121 - 150 of 2595
Full-Text Articles in Physical Sciences and Mathematics
On Vietoris’ Hybrid Number Sequence, Nurten Gürses, Gülsüm Yeli̇z Saçli, Sali̇m Yüce
On Vietoris’ Hybrid Number Sequence, Nurten Gürses, Gülsüm Yeli̇z Saçli, Sali̇m Yüce
Turkish Journal of Mathematics
This work is intended to establish a relation between Vietoris’ sequence, which is a rational sequence, andhybrid numbers. Then it provides some characteristic properties of the hybrid numbers with Vietoris’ number coefficients.Some relations between this hybrid number and its norm, the recurrence relations, the generating function, Binet-likeformula and Catalan-like identities are also indicated. Furthermore, a determinantal approach is presented to obtainelements of Vietoris’ hybrid number sequence.
Stacks In Einstein Gravity, Kadri̇ İlker Berktav
Stacks In Einstein Gravity, Kadri̇ İlker Berktav
Turkish Journal of Mathematics
In this paper, we examine stacky structures in certain Einstein gravity theories. In brief, using the classicalformulation of (vacuum) gravity, with vanishing cosmological constant, we first construct the stack of solutions to Einsteinfield equations on any given fixed manifold. Using a similar approach and setup, we also study Einstein’s gravity onfamilies of manifolds and define another stack encoding this situation. Later on, we focus on the gauge theoreticalinterpretation of 3D gravity and provide a natural stack associated with that interpretation. Finally, in a particularsetup, we give a natural morphism between the two stacks arising from different descriptions of 3D gravity.
New Oscillation Criteria For First-Order Differential Equations With General Delay Argument, Emad R. Attia, Irena Jadlovska
New Oscillation Criteria For First-Order Differential Equations With General Delay Argument, Emad R. Attia, Irena Jadlovska
Turkish Journal of Mathematics
This paper is concerned with the oscillation of solutions to a class of first-order differential equations withvariable coefficients and a general delay argument. New oscillation criteria are established, which improve and extendmany known results reported in the literature. A couple of illustrative examples are given to show the efficiency of thenewly obtained results. In particular, it is shown that our criteria partially fulfill a remaining gap in a recent sharp resultby Pituk et al. [31].
Bernstein-Nikol’Skii-Markov-Type Inequalities For Algebraic Polynomials In Aweighted Lebesgue Space In Regions With Cusps, Uğur Değer, Fahreddi̇n Abdullayev
Bernstein-Nikol’Skii-Markov-Type Inequalities For Algebraic Polynomials In Aweighted Lebesgue Space In Regions With Cusps, Uğur Değer, Fahreddi̇n Abdullayev
Turkish Journal of Mathematics
In this paper, we study Bernstein-Nikol’skii-Markov type inequalities for arbitrary algebraic polynomials withrespect to a weighted Lebesgue space, where the weight functions have some singularities on a given contour. We considercurves which can contain a finite number of exterior and interior corners with power law tangency of the boundary arcs atthose points where the weight functions have both zeros and poles of finite order. The estimates are given for the growthof the module of derivatives for algebraic polynomials on the closure of a region bounded by a given curve, dependingon the behavior of weight functions, on the property of curve, …
Some Qualitative Results For Nonlocal Dynamic Boundary Value Problem Of Thermistor Type, Svetlin G. Georgiev, Mahammad Khuddush, Sanket Tikare
Some Qualitative Results For Nonlocal Dynamic Boundary Value Problem Of Thermistor Type, Svetlin G. Georgiev, Mahammad Khuddush, Sanket Tikare
Turkish Journal of Mathematics
This paper is concerned with second-order nonlocal dynamic thermistor problem with two-point boundary conditions on time scales. By utilizing the fixed point theorems due to Schaefer and Rus, we establish some sufficient conditions for the existence and uniqueness of solutions. Further, we discuss the continuous dependence of solutions and four types of Ulam stability. We provide examples to support the applicability of our results.
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.
Combinatorial Results For Semigroups Of Orientation-Preserving Transformations, Ayşegül Dağdevi̇ren, Gonca Ayik
Combinatorial Results For Semigroups Of Orientation-Preserving Transformations, Ayşegül Dağdevi̇ren, Gonca Ayik
Turkish Journal of Mathematics
Let Xn denote the chain {1, 2, . . . , n} under its natural order. We denote the semigroups consisting of all order-preserving transformations and all orientation-preserving transformations on Xn by On and OPn , respectively. We denote by E(U) the set of all idempotents of a subset U of a semigroup S . In this paper, we first determine the cardinalities of Er(On) = {α ∈ E(On) : |im(α)| = |fix(α)| = r}, E ∗ r (On) = {α ∈ Er(On) : 1, n ∈ fix(α)}, Er(OPn) = {α ∈ E(OPn) : |fix(α)| = r}, E ∗ r …
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 …
Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin
Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin
Turkish Journal of Mathematics
This paper is devoted to defining the delayed analogue of the Mittag-Leffler type function with three parameters and investigating a representation of a solution to Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders, which are first introduced and investigated, by means of the Laplace integral transform. It is verified by showing the solution satisfies the introduced system. Special cases which are also novel are presented as examples. The findings are illustrated with the help of the RLC circuits.
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.
On The Oscillation And Asymptotic Behavior Of Solutions Of Third Order Nonlineardifferential Equations With Mixed Nonlinear Neutral Terms, Shaimaa Salem, Mohamed M. A. El-Sheikh, Ahmed Mohamed Hassan
On The Oscillation And Asymptotic Behavior Of Solutions Of Third Order Nonlineardifferential Equations With Mixed Nonlinear Neutral Terms, Shaimaa Salem, Mohamed M. A. El-Sheikh, Ahmed Mohamed Hassan
Turkish Journal of Mathematics
This paper is concerned with the oscillation and asymptotic behavior of solutions of third-order nonlinear neutral differential equations with a middle term and mixed nonlinear neutral terms in the case of the canonical operator. We establish several oscillation criteria that guarantee that all solutions are oscillatory or converge to zero. The given results are obtained by applying the comparison method, the Riccati transformation and the integral averaging technique. The results improve significantly and extend existing ones in the literature. Finally, illustrative examples are given.
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.
Duality And Norm Completeness In The Classes Of Limitedly Lwc Anddunford–Pettis Lwc Operators, Ömer Şafak Alpay, Eduard Emelyanov, Svetlana Gorokhova
Duality And Norm Completeness In The Classes Of Limitedly Lwc Anddunford–Pettis Lwc Operators, Ömer Şafak Alpay, Eduard Emelyanov, Svetlana Gorokhova
Turkish Journal of Mathematics
We study the duality and norm completeness in the new classes of limitedly L-weakly compact and Dunford–Pettis L-weakly compact operators from Banach spaces to Banach lattices.
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.
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 …
Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz
Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz
Turkish Journal of Mathematics
Let H be a supersolvable Hall π -subgroup of a finite group G. We prove that G has a normal π -complement if and only if H controls G-fusion in H.
An Extension Of The Definition On The Compositions Of The Singular Distributions, Emi̇n Özçağ
An Extension Of The Definition On The Compositions Of The Singular Distributions, Emi̇n Özçağ
Turkish Journal of Mathematics
Gelfand and Shilov give the definition of the composition δ(g(x)) for an infinitely differentiable function g(x) having any number of simple roots. In the paper, we consider their definition for an infinitely differentiable function having any number of multiple roots by using the method of the discarding of unwanted infinite quantities from asymptotic expansions and give some examples. Further, we define the compositions δ(g+) and δ(g−) for a locally summable function g(x).
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.
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.
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.
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 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.
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.
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
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 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.
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.
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.