THE ALMOST PERIODIC SOLUTION AND BOUNDED SOLUTION OF PERTURBED SYSTEMS

ＴＨＥＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＡＮＤＢＯＵＮＤＥＤＳＯＬＵＴＩＯＮＯＦＰＥＲＴＵＲＢＥＤＳＹＳＴＥＭＳＬｉｎＭｕｒｅｎ（林木仁）（ＦｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ福州大学，邮编：３５０００２）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅ...     

New solutions of classical problems in rigid body dynamics

The equations of motion of a rigid body acted upon by general conservative potential and gyroscopic forces were reduced by Yehia to a single second-order differential equation. The reduced equation was used successfully in the study of stability of certain simple motions of the body. In the present work we use the reduced equation to construct a new particular solution of the dynamics of a rigid body about a fixed point in the approximate field of a far Newtonian centre of attraction. Using a transformation to a rotating frame we also construct a new solution of the problem of motion of a multiconnected rigid body in an ideal incompressible fluid. It turns out that the solutions obtained generalize a known solution of the simplest problem of motion of a heavy rigid body about a fixed point due to Dokshevich.     

群代数Ore扩张的量子群

本文讨论由Beattie通过群代数的Ore扩张所构造的量子群的中心和Yang－Baxter模范畴．此外,完全刻画了这类量子群的不可约表示．     

关于一致凸空间中联合逼近的一个特征

文中给出了一致凸空间中 Chebyshev中心的一个特征 ,推广了 D.Amir和 J.Mach关于 Hilbert空间中的一个结果 .     

Banach upper density recurrent points of <Emphasis Type="Italic">C</Emphasis><Superscript>0</Superscript>-flows

Let X denote a compact metric space with distance d and F:X×R→X or F_t:X→X denote a C⁰-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C⁰-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.     

NMR Study of Hetero‐Association Accompanying Self‐Association of 2‐Hydroxyl‐4‐methyl‐pyridine and 2‐Pyrrolidone in Acetonitrile

This work in vestigated not only the equilibrium of self‐association of 2‐pyrrolidone (A) and that of 2‐hydroxyl‐4‐methyl‐pyridine (B), but also the hetero‐association between A and B in [²H₃]acetonitrile through hydrogen bonding using high‐resolution nuclear magnetic resonance spectroscopy. Dilution shift data for the protons of the NH group of A and OH group of B were measured over a wide range of temperatures and concentrations. In addition, the monomer shifts, dimer shifts and dimerization constants of self‐association and hetero‐association were evaluated using a graphic method operating on the dilution chemical shift data. The enthalpy and entropy of dimerization of self‐association and hetero‐association were also obtained from the van't Hoff plot.     

Crystal structure of a dimeric copper(II) complex with N,N -diethylethylenediamine (dien): a model for the thermally and photoinduced violet forms of the bis(dien)copper(II) cation

The molecular structure of the violet dimer bis(μ-hydroxo)bis(N,N-diethylethyl- enediamine)dicopper(II) perchlorate supports the hypothesis that the photoinduced phase of the monomer bis(N,N-diethylethylenediamine)copper(II) perchlorate, similar to the corresponding, high temperature, thermally induced phase, features tetrahedral distortion of the square planar coordination.     

Photophysics of Genistein isoflavone: Solvent and concentration effects studied by UV–visible spectroscopy and theoretical simulation

Genistein isoflavone is shown to exist in two different conformations which are the 90° completely twisted geometry and the 50° less twisted one. Specific interactions with the solvent cage as well as self-association processes seem shifting the isoflavone from the perpendicular conformation towards the less twisted one. The theoretical simulation, using analytical atom–atom pair potential, predicts a self-dimer in a slipped non-sandwich, face to river, perpendicular structure. From the UV–visible photophysics investigations it is revealed that monomeric species cannot exist alone even at very low solute concentration (10⁻⁶ M), the self-association process occurs already in this concentration range.     

A Quadruply Bridged Non-Offset Face-to-Face Porphyrin Dimer and Cross-Shaped Pentameric Porphyrin Tapes Based on 2,7,12,17-Tetrakis(pinacolatoboryl) NiII Porphyrin

2,7,12,17-Tetrakis(pinacolatoboryl) Ni^II porphyrin 5 Ni was synthesized in 75 % yield by Ir-catalyzed borylation of porphine followed by Ni^II metalation and has been demonstrated to be a useful synthon, giving 2,7,12,17-tetraaryated Ni^II porphyrins 6 a – d , peripherally octaarylated Ni^II porphyrins 8 a – d , quadruply bridged face-to-face non-offset Ni^II-porphyrin dimer 12 , and cross-shaped β-meso singly linked porphyrin pentamers and nonamers. Oxidation of cross-shaped β-meso singly linked porphyrin pentamers 14 Ni and 14 Zn gave fused pentameric tapes 15 Ni and 15 Zn . The structures of 12 , 14 Zn , and 15 Ni have been revealed by X-ray diffraction analysis. Optical separation of 12 has been accomplished, showing a bisignate coupling pattern for exciton-coupled blue-shifted Soret band. Pentameric porphyrin tape 15 Zn exhibits a red-shifted absorption band at 1156 nm and seven reversible redox waves.     

Lattice gas activity series from secular equations

The secular equations for finite tori of lattice sites are obtained by computer expansion of determinants for a hard-particle lattice gas. The secular equations yield all of the thermodynamic functions for finite systems and the beginning terms of activity expansions for all of the eigenvalues of the infinite system. The same secular equation that yields the low-density series for the equation of state of the infinite-circumference system also yields the beginning terms in the highdensity expansion. As examples we treat two hard-particle lattice gases in two dimensions, the lattice gas with nearest-neighbor exclusion (which has a secondorder transition), and the case of dimers (which is analytic all the way to close packing).