Synchronization of generalized Hénon map using polynomial controller

This Letter presents the chaos synchronization of two discrete-time generalized Hénon map, namely the drive and response systems. A polynomial controller is proposed to drive the system states of the response system to follow those of the drive system. The system stability of the error system formed by the drive and response systems and the synthesis of the polynomial controller are investigated using the sum-of-squares (SOS) technique. Based on the Lyapunov stability theory, stability conditions in terms of SOS are derived to guarantee the system stability and facilitate the controller synthesis. By satisfying the SOS-based stability conditions, chaotic synchronization is achieved. The solution of the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. A simulation example is given to illustrate the merits of the proposed polynomial control approach.     

Hill Four-Body Problem with Oblate Bodies: An Application to the Sun–Jupiter–Hektor–Skamandrios System

We consider a restricted four-body problem, with a precise hierarchy between the bodies: two larger bodies and a smaller one, all three of oblate shape, and a fourth, infinitesimal body, in the neighborhood of the smaller of the three bodies. The three heavy bodies are assumed to move in a plane under their mutual gravity, and the fourth body to move in the three-dimensional space under the gravitational influence of the three heavy bodies, but without affecting them. We first find that the triangular central configuration of the three heavy oblate bodies is a scalene triangle (rather than an equilateral triangle as in the point mass case). Then, assuming that these three bodies are in such a central configuration, we perform a Hill approximation of the equations of motion describing the dynamics of the infinitesimal body in a neighborhood of the smaller body. Through the use of Hill’s variables and a limiting procedure, this approximation amounts to sending the two larger bodies to infinity. Finally, for the Hill approximation, we find the equilibrium points for the motion of the infinitesimal body and determine their stability. As a motivating example, we identify the three heavy bodies with the Sun, Jupiter, and the Jupiter’s Trojan asteroid Hektor, which are assumed to move in a triangular central configuration. Then, we consider the dynamics of Hektor’s moonlet Skamandrios.

     

Synthesis of, light emission from, and optical power limiting in soluble single-walled carbon nanotubes functionalized by disubstituted polyacetylenes

Single-walled carbon nanotubes are covalently functionalized by conjugated polyacetylenes through their cyclization reactions with poly(1-phenyl-1-alkyne) and poly(diphenylacetylene) derivatives carrying azido functional groups at the ends of their alkyl pendants. The resultant polyene nanotube addends are soluble in common solvents, emit intense visible lights and strongly attenuate the power of harsh laser pulses.     

Diastereoselective cobalt-catalyzed reductive aldol cyclizations using diethylzinc as the stoichiometric reductant

[reaction: see text] Cobalt catalysis enables a new method for the generation of zinc enolates using diethylzinc to reduce alpha,beta-unsaturated amides. This method has been applied to a high-yielding diastereoselective reductive aldol cyclization.     

On σ(·, W)-Holomorphic Functions and Theorems of Vitali-Type

The aim of this paper is to give some criterions for holomorphy of F-valued σ(F, W)-holomorphic functions which are bounded on bounded sets in a domain D of Fréchet spaces E (resp. ${\mathbb{C}^n}$ ) where ${W \subset F'}$ defines the topology of Fréchet space F. Base on these results we consider the problem on holomorphic extension of F-valued σ(F, W)-holomorphic functions from non-rare subsets of D and from subsets of D which determines uniform convergence in H(D). As an application of the above, some theorems of Vitali-type for a locally bounded sequence ${\{f_i\}_{i \in \mathbb{N}}}$ of Fréchet-valued holomorphic functions are also proved.     

On voa associated with special jordan algebras

For a given simple Jordan algebra A of type A, B or C over C, we construct a vertex operator algebra V such that the weight two space V ₂ ? A by using the structure of Heisenberg algebras. In addition, we compute the automorphism groups of these vertex operator algebras.     

On the rate constants of OH + HO2 and HO2 + HO2: A comprehensive study of H2O2 thermal decomposition using multi-species laser absorption

Hydrogen peroxide (H₂O₂) and hydroperoxy (HO₂) reactions present in the H₂O₂ thermal decomposition system are important in combustion kinetics. H₂O₂ thermal decomposition has been studied behind reflected shock waves using H₂O and OH diagnostics in previous studies (Hong et al. (2009) [9] and Hong et al. (2010) [6,8]) to determine the rate constants of two major reactions: H₂O₂ + M → 2OH + M (k₁) and OH + H₂O₂ → H₂O + HO₂ (k₂). With the addition of a third diagnostic for HO₂ at 227 nm, the H₂O₂ thermal decomposition system can be comprehensively characterized for the first time. Specifically, the rate constants of two remaining major reactions in the system, OH + HO₂ → H₂O + O₂ (k₃) and HO₂ + HO₂ → H₂O₂ + O₂ (k₄) can be determined with high-fidelity.No strong temperature dependency was found between 1072 and 1283 K for the rate constant of OH + HO₂ → H₂O + O₂, which can be expressed by the combination of two Arrhenius forms: k₃ = 7.0 × 10¹² exp(550/T) + 4.5 × 10¹⁴ exp(?5500/T) [cm³ mol^?1 s^?1]. The rate constants of reaction HO₂ + HO₂ → H₂O₂ + O₂ determined agree very well with those reported by Kappel et al. (2002) [5]; the recommendation therefore remains unchanged: k₄ = 1.0 × 10¹⁴ exp(?5556/T) + 1.9 × 10¹¹⁺exp(709/T) [cm³ mol^?1 s^?1]. All the tests were performed near 1.7 atm.     

Perfect-absorber metamaterial based on flower-shaped structure

We theoretically and experimetally investigated the narrow-band peak of perfect absorber (PA), which was realized with a metal–dielectric–metal scheme based on a flower-shaped structure (FSS). The PA slabs were designed and fabricated to work in the GHz range of electromagnetic radiation. The absorption is due to the magnetic influence and therefore, the resonance frequency can be easily controlled without affecting the efficiency of the absorption peak by changing the dimensional parameters of the FSS. In addition, the FSS also results in polarization independence of electromagnetic waves, as expected due to its geometry.     

Semicontinuity of the Approximate Solution Sets of Multivalued Quasiequilibrium Problems

We consider two kinds of approximate solutions and approximate solution sets to multivalued quasiequilibrium problems. Sufficient conditions for the lower semicontinuity, Hausdorff lower semicontinuity, upper semicontinuity, Hausdorff upper semicontinuity, and closedness of these approximate solution sets are established. Applications in approximate quasivariational inequalities, approximate fixed points, and approximate quasioptimization problems are provided.