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Pseudosymmetric Lightlike Hypersurfaces, Sema Kazan, Bayram Şahi̇n
Pseudosymmetric Lightlike Hypersurfaces, Sema Kazan, Bayram Şahi̇n
Turkish Journal of Mathematics
We study lightlike hypersurfaces of a semi-Riemannian manifold satisfying pseudosymmetry conditions. We give sufficient conditions for a lightlike hypersurface to be pseudosymmetric and show that there is a close relationship of the pseudosymmetry condition of a lightlike hypersurface and its integrable screen distribution. We obtain that a pseudosymmetric lightlike hypersurface is a semisymmetric lightlike hypersurface or totally geodesic under certain conditions. Moreover, we give an example of pseudosymmetric lightlike hypersurfaces and investigate pseudoparallel lightlike hypersurfaces. Furthermore, we introduce Ricci-pseudosymmetric lightlike hypersurfaces, obtain characterizations, and give an example for such hypersurfaces.
On 4-Dimensional Almost Para-Complex Pure-Walker Manifolds, Murat İşcan, Hi̇lmi̇ Sarsilmaz, Si̇bel Turanli
On 4-Dimensional Almost Para-Complex Pure-Walker Manifolds, Murat İşcan, Hi̇lmi̇ Sarsilmaz, Si̇bel Turanli
Turkish Journal of Mathematics
This paper is concerned with almost para-complex structures on Walker 4-manifolds. For these structures, we study some problems of Kähler manifolds. We also give an example of a flat almost para-complex manifold, which consists of a nonintegrable almost para-complex structure on Walker 4-manifolds.
On The Equivariant Cohomology Algebra For Solenoidal Actions, Ali̇ Arslan Özkurt
On The Equivariant Cohomology Algebra For Solenoidal Actions, Ali̇ Arslan Özkurt
Turkish Journal of Mathematics
We prove, under certain conditions, that if a solenoidal group (i.e. 1-dimensional compact connected abelian group) acts effectively on a compact space then the fixed point set is nonempty and H_G^*(X,Q) has a presentation similar to the presentation of H^*(X,Q) as proven by Chang in the case of a circle group.
Functionals Of Gasser--Muller Estimators, Petre Babilua, Elizbar Nadaraya, Grigol Sokhadze
Functionals Of Gasser--Muller Estimators, Petre Babilua, Elizbar Nadaraya, Grigol Sokhadze
Turkish Journal of Mathematics
The asymptotic properties of a general functional of the Gasser--Muller estimator are investigated in the Sobolev space. The convergence rate, consistency, and central limit theorem are established.
On Minimal Poincaré 4-Complexes, Alberto Cavicchioli, Friedrich Hegenbarth, Dusan Repovs
On Minimal Poincaré 4-Complexes, Alberto Cavicchioli, Friedrich Hegenbarth, Dusan Repovs
Turkish Journal of Mathematics
We consider 2 types of minimal Poincaré 4-complexes. One is defined with respect to the degree 1-map order. This idea was already present in our previous papers, and more systematically studied later by Hillman. The second type of minimal Poincaré 4-complexes was introduced by Hambleton, Kreck, and Teichner. It is not based on an order relation. In the present paper we study existence and uniqueness questions.
Coverings And Crossed Modules Of Topological Groups With Operations, Osman Mucuk, Tunçar Şahan
Coverings And Crossed Modules Of Topological Groups With Operations, Osman Mucuk, Tunçar Şahan
Turkish Journal of Mathematics
It is a well-known result of the covering groups that a subgroup G of the fundamental group at the identity of a semilocally simply connected topological group determines a covering morphism of topological groups with characteristic group G. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also prove that the crossed modules and internal categories within topological groups with operations are equivalent. This equivalence enables us to introduce the cover of crossed modules within topological groups with operations. Finally, we draw relations between the coverings …
Central Configurations In The Collinear 5-Body Problem, Muhammad Shoaib, Anoop Sivasankaran, Abdulrehman Kashif
Central Configurations In The Collinear 5-Body Problem, Muhammad Shoaib, Anoop Sivasankaran, Abdulrehman Kashif
Turkish Journal of Mathematics
We study the inverse problem of central configuration of collinear general 4- and 5-body problems. A central configuration for n-body problems is formed if the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration. In the 3-body problem, it is always possible to find 3 positive masses for any given 3 collinear positions given that they are central. This is not possible for more than 4-body problems in general. We consider a collinear 5-body problem and identify regions in the phase space where it is possible to choose positive …
Hausdorff Dimension Of The Graph Of The Error-Sum Function Of \Alpha-Lüroth Series, Haibo Chen, Wenbo Wang, Min Yu
Hausdorff Dimension Of The Graph Of The Error-Sum Function Of \Alpha-Lüroth Series, Haibo Chen, Wenbo Wang, Min Yu
Turkish Journal of Mathematics
Let \alpha be a countable partition of the unit interval [0,1]. In this paper, we will introduce the error-sum function of \alpha-Lüroth series and determine the Hausdorff dimension of its graph when the partition \alpha is eventually decreasing. Some other properties of the error-sum function are also investigated.
On The Continued Fraction Expansion Of Some Hyperquadratic Functions, Khalil Ayadi, Fatma Taktak
On The Continued Fraction Expansion Of Some Hyperquadratic Functions, Khalil Ayadi, Fatma Taktak
Turkish Journal of Mathematics
In this paper, we consider continued fraction expansions for algebraic power series over a finite field. Especially, we are interested in studying the continued fraction expansion of a particular subset of algebraic power series over a finite field, called hyperquadratic. This subset contains irrational elements \alpha satisfying an equation \alpha = f(\alpha^r), where r is a power of the characteristic of the base field and f is a linear fractional transformation with polynomials coefficients. The continued fraction expansion for these elements can sometimes be given fully explicitly. We will show this expansion for hyperquadratic power series satisfying certain types of …
The New Method Of Determining Koebe Domains For The Class Of Typically Real Functions Under Montel's Normalization, Leopold Koczan, Pawel Zaprawa
The New Method Of Determining Koebe Domains For The Class Of Typically Real Functions Under Montel's Normalization, Leopold Koczan, Pawel Zaprawa
Turkish Journal of Mathematics
We consider the class T(r) of typically real functions with the normalization f(0)=0 and f(r)=r for a fixed r \in (0,1). In the limiting case, when r tends to 0, the class T(r) coincides with the class T of typically real functions normalized by f(0)=f'(0)-1=0. In 1980, Lewandowski and Miazga determined the Koebe domain for T(r), i.e. the set of the form \bigcap_{f\in T(r)} f(\Delta). They used the method applied earlier by Goodman. In this paper we present a new, complete method of determining this set. As a corollary, we obtain the Koebe set for T.
An Existence Result For A Quasilinear System With Gradient Term Under The Keller--Osserman Conditions, Dragos Patru Covei
An Existence Result For A Quasilinear System With Gradient Term Under The Keller--Osserman Conditions, Dragos Patru Covei
Turkish Journal of Mathematics
We use some new technical tools to obtain the existence of entire solutions for the quasilinear elliptic system of type \Delta _pu_i+h_i(\vert x\vert) \vert \nabla u_i\vert ^{p-1}=a_i(\vert x\vert ) f_i(u_{1},u_2) on R^N (N\geq 3, i=1,2) where N-1\geq p>1, \Delta_p is the p-Laplacian operator, and h_i, a_i, f_i are suitable functions. The results of this paper supplement the existing results in the literature and complete those obtained by Jesse D Peterson and Aihua W Wood (Large solutions to non-monotone semilinear elliptic systems, Journal of Mathematical Analysis and Applications, Volume 384, pages 284--292, 2011).
Osserman Lightlike Hypersurfaces Of Indefinite S-Manifolds, Letizia Brunetti
Osserman Lightlike Hypersurfaces Of Indefinite S-Manifolds, Letizia Brunetti
Turkish Journal of Mathematics
We mainly deal with the problem of admissibility for screen distributions on a lightlike hypersurface of both a semi-Riemannian manifold and an indefinite S-manifold. In the latter case, we first show that a characteristic screen distribution is never admissible, and then we provide a characterization for admissible screen distributions on proper totally umbilical lightlike hypersurfaces. Finally, in studying Osserman conditions, we characterize Osserman totally umbilical hypersurfaces of a semi-Riemannian manifold, obtaining explicit results on the eigenvalues of the pseudo-Jacobi operators in the case of lightlike hypersurfaces with Lorentzian screen leaves.
On The Size Of The Third Homotopy Group Of The Suspension Of An Eilenberg--Maclane Space, Peyman Niroomand, Francesco Russo
On The Size Of The Third Homotopy Group Of The Suspension Of An Eilenberg--Maclane Space, Peyman Niroomand, Francesco Russo
Turkish Journal of Mathematics
The nonabelian tensor square G \otimes G of a group G of G = p^n and G' = p^m (p prime and n,m \ge 1) satisfies a classic bound of the form G \otimes G \le p^{n(n-m)}. This allows us to give an upper bound for the order of the third homotopy group \pi_3(SK(G,1)) of the suspension of an Eilenberg--MacLane space K(G,1), because \pi_3(K(G,1)) is isomorphic to the kernel of \kappa : x \otimes y \in G \otimes G \mapsto [x,y] \in G'. We prove that G \otimes G \le p^{(n-1)(n-m)+2}, sharpening not only G \otimes G \le p^{n(n-m)} but …
Degenerate Hopf Bifurcations, Hidden Attractors, And Control In The Extended Sprott E System With Only One Stable Equilibrium, Zhouchao Wei, Irene Moroz, Anping Liu
Degenerate Hopf Bifurcations, Hidden Attractors, And Control In The Extended Sprott E System With Only One Stable Equilibrium, Zhouchao Wei, Irene Moroz, Anping Liu
Turkish Journal of Mathematics
In this paper, we introduce an extended Sprott E system by a general quadratic control scheme with 3 arbitrary parameters for the new system. The resulting system can exhibit codimension-one Hopf bifurcations as parameters vary. The control strategy used can be applied to create degenerate Hopf bifurcations at desired locations with preferred stability. A complex chaotic attractor with only one stable equilibrium is derived in the sense of having a positive largest Lyapunov exponent. The chaotic attractor with only one stable equilibrium can be generated via a period-doubling bifurcation. To further suppress chaos in the extended Sprott E system coexisting …
Continuity Of Wigner-Type Operators On Lorentz Spaces And Lorentz Mixed Normed Modulation Spaces, Ayşe Sandikçi
Continuity Of Wigner-Type Operators On Lorentz Spaces And Lorentz Mixed Normed Modulation Spaces, Ayşe Sandikçi
Turkish Journal of Mathematics
We study various continuity properties for \tau-Wigner transform on Lorentz spaces and \tau-Weyl operators W_{\tau}^{a} with symbols belonging to appropriate Lorentz spaces. We also study the action of \tau-Wigner transform on Lorentz mixed normed modulation spaces.
On Semiparallel Anti-Invariant Submanifolds Of Generalized Sasakian Space Forms, Ci̇han Özgür, Fatma Gürler, Cengi̇zhan Murathan
On Semiparallel Anti-Invariant Submanifolds Of Generalized Sasakian Space Forms, Ci̇han Özgür, Fatma Gürler, Cengi̇zhan Murathan
Turkish Journal of Mathematics
We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms. We show that the submanifolds are totally geodesic under certain conditions.
Seiberg--Witten-Like Equations On 5-Dimensional Contact Metric Manifolds, Nedi̇m Deği̇rmenci̇, Şenay Bulut
Seiberg--Witten-Like Equations On 5-Dimensional Contact Metric Manifolds, Nedi̇m Deği̇rmenci̇, Şenay Bulut
Turkish Journal of Mathematics
In this paper, we write Seiberg--Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spin^c-structure, we use the generalized Tanaka--Webster connection on a Spin^c spinor bundle of a contact metric manifold to define the Dirac-type operators and write the Dirac equation. The self-duality of 2-forms needed for the curvature equation is defined by using the contact structure. These equations admit a nontrivial solution on 5-dimensional strictly pseudoconvex CR manifolds whose contact distribution has a negative constant scalar curvature.
Adjoints Of Rationally Induced Composition Operators On Bergman And Dirichlet Spaces, Aliakbar Goshabulaghi, Hamid Vaezi
Adjoints Of Rationally Induced Composition Operators On Bergman And Dirichlet Spaces, Aliakbar Goshabulaghi, Hamid Vaezi
Turkish Journal of Mathematics
We will state a connection between the adjoints of a vast variety of bounded operators on 2 different weighted Hardy spaces. We will apply it to determine the adjoints of rationally induced composition operators on Dirichlet and Bergman spaces.
Essential Norms Of Weighted Composition Operators Between Zygmund-Type Spaces And Bloch-Type Spaces, Amir Hossein Sanatpour, Mostafa Hassanlou
Essential Norms Of Weighted Composition Operators Between Zygmund-Type Spaces And Bloch-Type Spaces, Amir Hossein Sanatpour, Mostafa Hassanlou
Turkish Journal of Mathematics
We investigate the boundedness of weighted composition operator u C_{\varphi} mapping the Zygmund-type space Z^{\alpha} into the Bloch-type space B^{\beta}. Then we give essential norm estimates of such an operator in terms of u and \varphi.
General Rotational Surfaces In The 4-Dimensional Minkowski Space, Georgi Ganchev, Velichka Milousheva
General Rotational Surfaces In The 4-Dimensional Minkowski Space, Georgi Ganchev, Velichka Milousheva
Turkish Journal of Mathematics
General rotational surfaces as a source of examples of surfaces in the 4-dimensional Euclidean space were introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the basis of our invariant theory of spacelike surfaces we study general rotational surfaces with special invariants. We describe analytically the flat general rotational surfaces and the general rotational surfaces with flat normal connection. We classify completely the minimal general rotational surfaces and the general rotational surfaces consisting of parabolic points.
\Xi^{\Perp}-Submanifolds Of Para-Sasakian Manifolds, Selcen Yüksel Perktaş, Mukut Mani Tripathi, Erol Kiliç, Sadik Keleş
\Xi^{\Perp}-Submanifolds Of Para-Sasakian Manifolds, Selcen Yüksel Perktaş, Mukut Mani Tripathi, Erol Kiliç, Sadik Keleş
Turkish Journal of Mathematics
Almost semiinvariant \xi^{\perp}-submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant \xi^{\perp}-submanifolds and semiinvariant \xi^{\perp}-submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant \xi^{\perp}-submanifold of a normal almost paracontact metric (and hence para-Sasakian) manifold with the proper invariant distribution always possesses a para-\textit{CR}-structure. A counter example is also given. Integrability conditions for certain natural distributions arising on almost semiinvariant \xi^{\perp} -submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.
A Characterization Of The Projective Transformation In Minkowski 3-Space, Yasemi̇n Alagöz
A Characterization Of The Projective Transformation In Minkowski 3-Space, Yasemi̇n Alagöz
Turkish Journal of Mathematics
We consider transformations preserving asymptotic directions of surfaces in Minkowski 3-space and show that a transformation preserves the asymptotic directions of a surface if only if it is the projective one. Therefore, we obtain a characterization of the projective transformation.
A Cohen Type Inequality For Laguerre--Sobolev Expansions With A Mass Point Outside Their Oscillatory Regime, Edmundo José Huertas Cejudo, Francisco Marcellán Espanol, María Francisca Pérez Valero, Yamilet Quintana
A Cohen Type Inequality For Laguerre--Sobolev Expansions With A Mass Point Outside Their Oscillatory Regime, Edmundo José Huertas Cejudo, Francisco Marcellán Espanol, María Francisca Pérez Valero, Yamilet Quintana
Turkish Journal of Mathematics
Let consider the Sobolev type inner product \langle f, g\rangle_S = \int_0^{\infty} f(x)g(x)d \mu (x) + Mf(c)g(c) + Nf^{\prime}(c) g^{\prime}(c), where d\mu (x) = x^{\alpha} e^{-x}dx, \alpha > -1, is the Laguerre measure, c < 0, and M, N \geq 0. In this paper we get a Cohen-type inequality for Fourier expansions in terms of the orthonormal polynomials associated with the above Sobolev inner product. Then, as an immediate consequence, we deduce the divergence of Fourier expansions and Cesàro means of order \delta in terms of this kind of Laguerre--Sobolev polynomials.
Highly Nonconcurrent Longest Paths And Cycles In Lattices, Yasir Bashir
Highly Nonconcurrent Longest Paths And Cycles In Lattices, Yasir Bashir
Turkish Journal of Mathematics
We investigate here the connected graphs with the property that any pair of vertices are missed by some longest paths (or cycles), embeddable in n-dimensional lattices L^n where L denotes the set of integers.
On Transformations Of Index 1, Leyla Bugay, Osman Kelekci̇
On Transformations Of Index 1, Leyla Bugay, Osman Kelekci̇
Turkish Journal of Mathematics
The index and the period of an element a of a finite semigroup are defined as the smallest values of m \geq 1 and r \geq 1 such that a^{m+r}=a^m, respectively. If m=1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in T_n, which we call transformations of index 1.
On Biharmonic Legendre Curves In S-Space Forms, Ci̇han Özgür, Şaban Güvenç
On Biharmonic Legendre Curves In S-Space Forms, Ci̇han Özgür, Şaban Güvenç
Turkish Journal of Mathematics
We study biharmonic Legendre curves in S-space forms. We find curvature characterizations of these special curves in 4 cases.
On The Maximal Operators Of Vilenkin-Fejéer Means, George Tephnadze
On The Maximal Operators Of Vilenkin-Fejéer Means, George Tephnadze
Turkish Journal of Mathematics
The main aim of this paper is to prove that the maximal operator \overset{\sim}{\sigma}^{\ast}f:=\underset{n \in P} \sup\frac{ \sigma _nf }{\log^2 (n+1)} is bounded from the Hardy space H_{1/2} to the space L_{1/2}, where \sigma _nf are Fejér means of bounded Vilenkin-Fourier series.