The iteration-approximation decoupling in the reversible KAM theory

General theorems on the persistence of quasiperiodic motions in reversible flows and diffeomorphisms satisfying very weak nondegeneracy conditions are obtained by a new method. The essence of this method is that the reversible system under consideration is embedded in a multiparameter family of reversible systems, and standard results on Diophantine approximations of dependent quantities are then applied to Whitney-smooth Cantor foliations of invariant tori of this family. Invariant tori are constructed for all the permissible values of m, p, q (for vector fields V) or m, p, q, P, Q (for diffeomorphisms A) where m is the torus dimension, (q,p) is the type of the reversing involution G, and (Q,P) is the type of the involution AG. The excitation of elliptic normal modes is also considered. (c) 1995 American Institute of Physics.     

Quasielastic reactions around the coulomb barrier in 16O+118Sn

Measurement of elastic and quasielastic reaction cross sections were done in ¹⁶O + ¹¹⁸Sn system at two different energies above the barrier. Attempts are being made to understand the results in the framework of coupled reaction channel model.     

Single-layer graphene oxide films on a silicon surface

A method is proposed to produce large-area single-layer graphene oxide films on the surface of semiconductor silicon wafers by precipitation from aqueous suspensions. Graphene oxide is synthesized from natural crystalline graphite during chemical oxidation and represents a wide-gap insulator. Single-layer graphene with a homogeneous-fragment size up to 50 μm can be formed by the reduction of graphene oxide films, and this size is significantly larger than those achieved to date.     

ICP-AES分析光谱条件对中药蒲公英无机元素吸收的影响

在全密闭植物工厂中水培种植中药蒲公英,以发射不同波段光谱的荧光灯及LED灯作为药材生长光源,并结合ICP–AES技术分析了不同光谱条件对蒲公英无机元素吸收和积累的影响。结果表明:(1)相近的光合有效辐射(PAR)条件下,单一红光R及混合光FLRB有利于水培蒲公英可食生物量的积累,单一蓝光B处理下可食生物量最低;(2)荧光灯FL条件下蒲公英地上部分常量无机元素含量比值为K∶Ca∶P∶Mg∶Na=79.74∶32.39∶24.32∶10.55∶1.00,微量无机元素含量比值为Fe∶Mn∶B∶Zn∶Cu=9.28∶9.71∶3.82∶2.08∶1.00;(3)峰值为660nm的红光有利于蒲公英对Ca,Fe,Mn,Zn元素的吸收,Cu元素含量受光谱条件的影响不明显;(4)蒲公英地上部分对Ca,Na,Mn,Zn四种元素的积累量均在纯红光R下最高,而对其余六种元素的积累量以混合光FLRB条件下最高。     

Dynamical mechanisms of direct three-body recombination

Despite the ubiquity of recombination processes in nature and various technologies, presently little is known about the dynamics of these processes. This article reports on a quasi-classical trajectory study of the dynamics of the direct three-body recombination of Cs(+) and Br(-) ions in the presence of a Xe atom at energies of the ion encounter and that of the third body ranging from 0.2 to 10 eV. Several dynamical mechanisms of stabilization of the recombining ion pair have been found. Head-on ion encounters are characterized by two mechanisms of removing the energy from the recombining pair. In the case of nonzero impact parameters of ion encounters, the dynamics leading to the stabilization of the nascent CsBr molecule becomes much more complicated and three new mechanisms appear. They depend mainly on the energy of the ion encounter, on the energy of the collision of the ion pair with the third body, and on the impact parameter of the ion encounter and the impact parameter of the third body. The common feature of all the three mechanisms is the transfer of a fraction of the rotational energy of the recombining pair to the third body. This transfer plays a key role in the stabilization of the molecule. The dynamical peculiarities observed are expected to be common for the recombination of the charged and neutral particles.     

Statistical characteristics of the motion of a pair of heavy ions in non-convex cavities of complicated geometry with fixed crosspieces and charges

Using the method of classical trajectories, the motion of a pair of ions Cs⁺ and Cl^– in three non-convex closed cavities of complicated geometry containing neutral cylindrical “crosspieces” and charged spherical “nuclei” is simulated. The collisions of the ions with the cavity boundary, crosspieces, and nuclei are supposed to be inelastic. The signs of the charges of the nuclei are varied. In each cavity, in one of the calculation series, the nuclei are assumed to be shielded (to carry charges smaller than 1 a.u. in absolute value), whereas in another calculation series, the possibility of the mutual neutralization of an ion and an oppositely charged nucleus at their encounter is taken into account. The statistics of various events, such as the “stickings” of ions to nuclei, neutralizations of ions and nuclei, collisions of ions with obstacles, recombinations of ions, and dissociations of the CsCl ionic-bond molecule are analyzed.     

The reversible context 2 in KAM theory: the first steps

The reversible context 2 in KAM theory refers to the situation where dim FixG < 1/2 codim T, here FixG is the fixed point manifold of the reversing involution G and T is the invariant torus one deals with. Up to now, this context has been entirely unexplored. We obtain a first result on the persistence of invariant tori in the reversible context 2 (for the particular case where dim Fix G = 0) using J. Moser’s modifying terms theorem of 1967.     

Reversible linear systems and their versal deformations

Let R be a fixed linear involution (R ²=id) of the spaceR ⁿ . A linear operator M is said to bereversible with respect to R if RM R=M^–1 and infinitesimally reversible with respect to R if M R=–RM. A linear differential equation dx/dt=B(t)x is said to be reversible with respect to R if V(t)R –RV(–t). We construct normal forms and versal deformations for reversible and infinitesimally reversible operators. The results are applied to describe the homotopy classes of strongly stable reversible linear differential equations with periodic coefficients. The analogous theory for linear Hamiltonian systems was developed by J. Williamson, M. G. Krein, I.M. Gel'fand, V. B. Lidskii, D. M. Galin, and H. Koçak.Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 33–54, 1991. Original article submitted April 27, 1988.