A centrosymmetric chaos

Symmetry plays an important part in the research of the dynamical behavior of nonlinear system. It is proved in this paper that, for a class of centrosymmetric systems with parametric excitation, chaos behaves in centrosymmetric manner, which implies that chaos need not to be an unsymmetric dynamical state. The project supported by National Natural Science Foundation of China     

中心对称型浑沌

对称性在非线性系统的动力学行为研究中起到重要作用。本文工作证实,对于一类具有中心对称型的参数激励系统,其混沌态也具有中心对称性质,从而说明了浑沌并非一定是一种非对称性的动力学形态。     

循环矩阵的一些性质

本文给出了循环矩阵的一些性质.     

Probability distributions of the fractional differences of the structure amplitudes and intensities of two related crystals

The probability distributions of the fractional intensities and amplitudes of x-ray reflections from a pair of imperfectly related structures are derived when both the structures satisfy the requirements of a given type of basic Wilson distribution. These two distributions are used to obtain theoretical expressions for 2 new fractional type ofR-indices which are expected to be useful in the final stages of refinement. The theoretical distributions are also used to deduce some theoretical distributions which are useful as tests for centrosymmetry via the random permutation method. The theoretical values of the relevant semi-cumulative functions are also tabulated.     

SHG from centrosymmetric supermolecular crystal

Supermolecular crystal composed of p-nitrophenol, hexamethylenetetramine, phosphoric acid and water was obtained by supermolecular assembly. The crystal has a centrosymmetric structure with space group P21/c. The relative intensity and integral value of green frequency doubling of light from the crystal powder compared with that from KDP powder measured by pico-second Nd:YAG laser are 757.3 (KDP: 183.4) and 1771.7 (KDP: 423.98), respectively. In supermolecular crystal, due to the arrangement of centrosymmetric p-nitrophenol molecules in the inorganic-organic host framework formed by hexamethylenetetramine, phosphoric acid and water, the distances between the p-nitrophenol molecules with centrosymmetry are changed (N1A-O1A: 0.8158 nm, N1B'-O1B: 1.4450 nm, N1A-N1A': 0.5837 nm, N1B'-N1B: 0.6898 nm), and the interaction between the dipoles becomes weak, which is easy for the ground state to turn into the excited state charge separated form, and generate the stable asymmetrical distribution of π-electron clo     

Comparison of azacyclic urea A-98881 as HIV-1 protease inhibitor with cage dimeric N-benzyl 4-(4-methoxyphenyl)-1,4- dihydropyridine as representative of a novel class of HIV-1 protease inhibitors: A molecular modeling study

The functional groups of cage dimeric N-alkyl substituted 3,5-bis(hydroxymethyl)-4-(4-methoxyphenyl)-1,4-dihydropyridines are similar to those of cyclic and azacyclic ureas that are potent inhibitors of HIV-1 protease of the dihydroxyethylene- and hydroxyethylene type, respectively. In the following study the conformity of common functional groups is investigated concerning their orientation in space as well as in the enzyme HIV-1 protease. Starting from X-ray crystal data of the centrosymmetric cage dimeric N-benzyl derivative with ester groups, the derivative with hydroxymethylene groups was built and a systematic conformational search was performed for the conformationally important torsion angles considering electrostatic and van der Waals interactions. From the huge number of conformations those comprising centrosymmetrical and C2-symmetrical energy minima were selected and minimized. The three remaining conformers were fitted to the azacyclic urea A-98881 selected from the HIV-1 protease enzyme- inhibitor complex using the centroids of the corresponding aromatic residues and additionally by the field fit option of the Advanced CoMFA module of SYBYL. Interestingly, the energetically most favourable one, which, additionally, possesses C2-symmetry like the active site cavity of HIV-1 protease, showed the best fit. Comparing the electrostatic potential (EP) of the latter with the EP of A-98881 the aromatic residues show excellent accordance. Slight differences in the extent of the EP were found in the areas of the hydroxymethylene groups of the cage dimer and the single hydroxy group as well as the urea carbonyl group of A- 98881, respectively. In order to compare the binding possibilities to the enzyme HIV-1 protease for the cage dimer and A-98881, their interaction fields with certain probes (CH3 for alkyl, NHamide, and carbonyl, O– of COO–), representing the decisive functional groups of the active site, have been calculated using GRID and projected into the enzyme placing the structures according to the position of A-98881 in the enzyme- inhibitor complex. The strongest calculated fields of the O– probe were found near Asp 25 for both structures. Another respective conformity consists in the overlap of the fields for the NHamide probe near Ile 50 and 50 for the investigated cage dimer and A-98881.