Showing papers in "Turkish Journal of Mathematics in 2014"
TL;DR: In this paper, an extended Sprott E system was introduced by a general quadratic control scheme with three arbitrary parameters for the new system, which can exhibit codimension-one Hopf bifurcations as parameters vary.
Abstract: 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 with only one stable equilibrium, adaptive control laws are designed to stabilize the extended Sprott E system based on adaptive control theory and Lyapunov stability theory. Numerical simulations are shown to validate and demonstrate the effectiveness of the proposed adaptive control.
54 citations
TL;DR: In this paper, necessary and sufficient conditions for warped product manifolds (M,g) of dimension 4, with 1-dimensional base, and in particular for generalized Robertson-Walker spacetimes, to satisfy some generalized Einstein metric condition were given.
Abstract: We give necessary and sufficient conditions for warped product manifolds (M,g), of dimension \geqslant 4, with 1-dimensional base, and in particular, for generalized Robertson--Walker spacetimes, to satisfy some generalized Einstein metric condition. Namely, the difference tensor R . C - C . R, formed from the curvature tensor R and the Weyl conformal curvature tensor C, is expressed by the Tachibana tensor Q(S,R) formed from the Ricci tensor S and R. We also construct suitable examples of such manifolds. They are quasi-Einstein, i.e. at every point of M rank (S - a g) \leqslant 1, for some a \in R, or non-quasi-Einstein.
50 citations
TL;DR: In this article, the authors consider the analogue of these surfaces in the Minkowski 4-space and study general rotational surfaces with special invariants, and describe analytically the flat GRS surfaces and the general RRS surfaces with flat normal connection.
Abstract: 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.
32 citations
TL;DR: In this article, the authors extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution, and provide examples to show that the assumed restriction cannot be relaxed.
Abstract: A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
30 citations
TL;DR: In this paper, a W -direction curve and W -rectifying curve of a Frenet curve in 3-dimensional Euclidean space E3 by using the unit Darboux vector field W of the Frenet Curve and give some characterizations together with the relationships between the curvatures of each associated curve.
Abstract: In this paper, firstly, we define a W -direction curve and W -rectifying curve of a Frenet curve in 3-dimensional Euclidean space E3 by using the unit Darboux vector field W of the Frenet curve and give some characterizations together with the relationships between the curvatures of each associated curve. We also introduce a V -direction curve, which is associated with a curve lying on an oriented surface in E3. Later, some new associated curves of a Frenet curve are defined in E4.
27 citations
TL;DR: In this article, the authors generalize the result of the covering groups to a class of algebraic objects called topological groups with operations, and show that the crossed modules and internal categories within these classes are equivalent.
Abstract: 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 of an internal groupoid within topological groups with operations and those of the corresponding crossed module.
25 citations
TL;DR: In this paper, the Dirichlet problem for a discrete anisotropic equation with a nonlinear term f and a numerical parameter ∆ ( ∆ ∆ ) was considered.
Abstract: In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function , a nonlinear term f , and a numerical parameter : ∆ (
24 citations
TL;DR: In this article, the authors studied the geometry and topology of Grassmann manifolds with characteristic classes and the Poincare duality and showed that for k = 2 or n = 8, the cohomology groups H*(G(k,n), R) are generated by the first Pontrjagin class, the Euler classes of the canonical vector bundles.
Abstract: In this paper, we study the geometry and topology on the oriented Grassmann manifolds. In particular, we use characteristic classes and the Poincare duality to study the homology groups of Grassmann manifolds. We show that for k=2 or n \leq 8, the cohomology groups H*(G(k,n), R) are generated by the first Pontrjagin class, the Euler classes of the canonical vector bundles. In these cases, the Poincare duality: Hq(G(k,n), R) \to Hk(n-k)-q(G(k,n), R) can be expressed explicitly.
14 citations
TL;DR: In this article, it was shown that the Hilbert and Chow quotients are isomorphic to the universal family of morphisms, and that the induced morphism is an isomorphism onto its image.
Abstract: We provide a direct proof, valid in arbitrary characteristic, of the result originally proven by Kapranov over $\mathbb{C}$, that the Hilbert and Chow quotients $(\mathbb{P}^1)^n//PGL2$ are isomorphic to $\overline{M}_{0,n}$. In both cases this is done by explicitly constructing the universal family and then showing that the induced morphism is an isomorphism onto its image. The proofs of these results in many ways reduce to the case $n = 4$; in an appendix we outline a formalism of this phenomenon relating to certain operads.
13 citations
TL;DR: In this paper, the disjoint supercyclicity of finitely many different powers of weighted shifts acting on the weighted sequence spaces was characterized, where w=(wi)i is a positive weight sequence satisfying wi 1 for every i in N (or i in Z).
Abstract: We characterize the disjoint supercyclicity of finitely many different powers of weighted shifts acting on the weighted sequence spaces l2(N,w), c0(N,w) , and l2(Z,w), c0(Z,w), where w=(wi)i is a positive weight sequence satisfying wi \geq 1 for every i\in N (or i\in Z).
13 citations
TL;DR: In this paper, the regular poles of the L-factors of the admissible and irreducible representations of the group GSp4, which admit a nonsplit Bessel functional and have a Jacquet module length of at most 2 with respect to the unipotent radical of the Siegel parabolic, over a non-Archimedean local field of odd characteristic, were computed.
Abstract: We compute the regular poles of the L-factors of the admissible and irreducible representations of the group GSp4, which admit a nonsplit Bessel functional and have a Jacquet module length of at most 2 with respect to the unipotent radical of the Siegel parabolic, over a non-Archimedean local field of odd characteristic. We also compute the L-factors of the generic representations of GSp4.
TL;DR: In this paper, the authors studied biharmonic Legendre curves in S-space forms and found curvature characterizations of these special curves in four cases, i.e.
Abstract: We study biharmonic Legendre curves in S-space forms. We find curvature characterizations of these special curves in 4 cases.
TL;DR: In this article, the lifting problem of projectable geometric objects on M to the semi-cotangent bundle is considered and relations between lifted objects and a degenerate symplectic structure are also presented.
Abstract: Using the ber bundle M over a manifold B, we dene a semi-cotangent (pull-back) bundle t B, which has a degenerate symplectic structure. We consider lifting problem of projectable geometric objects on M to the semi-cotangent bundle. Relations between lifted objects and a degenerate symplectic structure are also presented.
TL;DR: In this paper, the authors consider the existence, both locally and globally in time, the global nonexistence, and the asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term.
Abstract: We consider the existence, both locally and globally in time, the global nonexistence, and the asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term.
TL;DR: In this article, moment equalities for sums of independent and identically distributed random variables including, in particular, centered and specifically symmetric summands are derived for self-normalized sums.
Abstract: We give moment equalities for sums of independent and identically distributed random variables including, in particular, centered and specifically symmetric summands. Two different types of proofs, combinatorial and analytical, lead to 2 different types of formulas. Furthermore, the combinatorial method allows us to find the optimal lower and upper constants in the Marcinkiewicz--Zygmund inequalities in the case of even moment-orders. Our results are applied to give elementary proofs of the classical central limit theorem (CLT) and of the CLT for the empirical bootstrap. Moreover, we derive moment and exponential inequalities for self-normalized sums.
TL;DR: In this article, the authors investigated half-light-like submanifolds with planar normal sections of 4-dimensional pseudo-Euclidean space, and they obtained necessary and sufficient conditions for a halflightlike sub-manifold of R24 such that it has degenerate or non-degenerate normal sections.
Abstract: We investigate half-lightlike submanifolds with planar normal sections of 4-dimensional pseudo-Euclidean space. We obtain necessary and sufficient conditions for a half-lightlike submanifold of R24 such that it has degenerate or nondegenerate planar normal sections.
TL;DR: In this paper, minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms are considered and shown to be totally geodesic under certain conditions.
Abstract: We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms. We show that the submanifolds are totally geodesic under certain conditions.
TL;DR: In this paper, the authors studied various continuity properties for t-Wigner transform on Lorentz spaces and t-Weyl operator Wta with symbols belonging to appropriate LMs.
Abstract: We study various continuity properties for t-Wigner transform on Lorentz spaces and t-Weyl operators Wta with symbols belonging to appropriate Lorentz spaces. We also study the action of t-Wigner transform on Lorentz mixed normed modulation spaces.
TL;DR: In this paper, it was shown that the nonabelian tensor square G \otimes G of a group G of |G| = pn and |G'| = pm (p prime and n,m \ge 1) satisfies a classic bound of the form |G \toimes G|\le pn(n-m).
Abstract: The nonabelian tensor square G \otimes G of a group G of |G| = pn and |G'| = pm (p prime and n,m \ge 1) satisfies a classic bound of the form |G \otimes G|\le pn(n-m). This allows us to give an upper bound for the order of the third homotopy group p3(SK(G,1)) of the suspension of an Eilenberg--MacLane space K(G,1), because p3(K(G,1)) is isomorphic to the kernel of k : 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 pn(n-m) but also supporting a recent result of Jafari on the topic. Consequently, we discuss restrictions on the size of p3(SK(G,1)) based on this new estimation.
TL;DR: In this article, the authors used some new technical tools to obtain the existence of entire solutions for the quasilinear elliptic system of type D pui+hi(\vert x\vert) \vert
abla ui\vert p-1=ai(u1,u2) on RN (N\geq 3, i=1,2) where N-1/geq p>1, Dp is the p-Laplacian operator, and hi, ai, fi are suitable functions.
Abstract: We use some new technical tools to obtain the existence of entire solutions for the quasilinear elliptic system of type D pui+hi(\vert x\vert) \vert
abla ui\vert p-1=ai(\vert x\vert ) fi(u1,u2) on RN (N\geq 3, i=1,2) where N-1\geq p>1, Dp is the p-Laplacian operator, and hi, ai, fi 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).
TL;DR: In this article, a linear system for irreducible words and the Hilbert series of the braid monoid MB4 were constructed and solved using a Grobner-Shirshov basis.
Abstract: L. A. Bokut gave a Grobner--Shirshov basis of the braid group Bn in band generators. Using this presentation and solving all the ambiguities we construct a linear system for irreducible words and compute the Hilbert series of the braid monoid MB4.
TL;DR: In this article, the pomonoid over which various flatness properties of S-posets are preserved under direct products is characterized, and the flatness property of Sposets is analyzed.
Abstract: In this paper we characterize pomonoids over which various flatness properties of S-posets are preserved under direct products.
TL;DR: In this paper, the authors studied the initial-boundary value problem for a system of nonlinear viscoelastic Petrovsky equations and proved uniform decay of solution energy under some restrictions on the initial data and the relaxation functions.
Abstract: In this paper, we study the initial-boundary value problem for a system of nonlinear viscoelastic Petrovsky equations. Introducing suitable perturbed energy functionals and using the potential well method we prove uniform decay of solution energy under some restrictions on the initial data and the relaxation functions. Moreover, we establish a growth result for certain solutions with positive initial energy.
TL;DR: In this paper, the authors review the Spin(7) geometry in relation to solvmanifolds and present an example of a homogeneous conformally parallel spin-7 metric on an associated solv manifold.
Abstract: In this paper we review the Spin(7) geometry in relation to solvmanifolds. Starting from a 7-dimensional nilpotent Lie group N endowed with an invariant G2 structure, we present an example of a homogeneous conformally parallel Spin(7) metric on an associated solvmanifold. It is thought that this paper could lead to very interesting and exciting areas of research and new results in the direction of (locally conformally) parallel Spin(7) structures.
TL;DR: In this paper, the inverse problem of central configuration of collinear general 4-and 5-body problems is studied and a critical value for the central mass above which no central configurations exist is derived.
Abstract: 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 masses that will make the configuration central. In the symmetric case we derive a critical value for the central mass above which no central configurations exist. We also show that in general there is no such restriction on the value of the central mass.
TL;DR: In this article, the existence condition of para-Kahler structures for Norden{Hessian metrics has been studied and it has been shown that for any manifold f = r 2 f the function f is holomorphic (para-holomorphic).
Abstract: In this paper, we show that Kahler (para-Kahler) manifolds admit a Norden{Hessian metric h = r 2 f if the function f is holomorphic (para-holomorphic), and we further consider the existence condition of para-Kahler structures for Norden{Hessian metrics.
TL;DR: In this paper, the boundedness of weighted composition operator uC φ mapping the Zygmund-type space Z into the Bloch-like space B � was investigated and essential norm estimates of such an operator in terms of u and φ were given.
Abstract: We investigate the boundedness of weighted composition operator uC φ mapping the Zygmund-type space Zinto the Bloch-type space B � . Then we give essential norm estimates of such an operator in terms of u and φ.
TL;DR: In this paper, a stochastic logistic model driven by martingales with jumps is considered, and the critical value of extinction, nonpersistence in the mean, and weak persistence is established.
Abstract: This paper is concerned with a stochastic logistic model driven by martingales with jumps. In the model, generalized noise and jump noise are taken into account. This model is new and more feasible. The explicit global positive solution of the system is presented, and then sufficient conditions for extinction and persistence are established. The critical value of extinction, nonpersistence in the mean, and weak persistence in the mean are obtained. The path-wise and moment properties are also investigated. Finally, some simulation figures are introduced to illustrate the main results.
TL;DR: In this paper, the authors discuss several recent results about the properties of a nite group G admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of CG(H) and focusing mainly on bounds for the Fitting height and related parameters.
Abstract: A nite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH=(F;F) is a Frobenius group with Frobenius kernel F=(F;F). Such subgroups and sections are abundant in any nonnilpotent nite group. We discuss several recent results about the properties of a nite group G admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of CG(H) and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for Frobenius groups of automorphisms; new theorems for Frobenius-like groups are based on new representation-theoretic results. Apart from a brief survey, the paper contains the new theorem on almost nilpotency of a nite group admitting a Frobenius-like group of automorphisms with xed-point-free almost extraspecial kernel.
TL;DR: In this paper, the generalized Tanaka-Webster connection on a Spinc spinor bundle of a contact metric manifold is used to define the Dirac-type operators and define the self-duality of 2-forms needed for the curvature equation.
Abstract: In this paper, we write Seiberg--Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spinc-structure, we use the generalized Tanaka--Webster connection on a Spinc 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.