Euler operator and homogeneous hida distributions

Let (S)⊄L ²(S′(∔),μ)⊄(S)^* be the Gel'fand triple over the white noise space (S′(∔),μ). Let (e _n ,n>-0) be the ONB ofL ²(∔) consisting of the eigenfunctions of the s.a. operator . In this paper the Euler operator Δ _E is defined as the sum , where ∂ _i stands for the differential operatorD _{e i}. It is shown that Δ _E is the infinitesimal generator of the semigroup (T _t ), where (T _t ϕ)(x)=ϕ(e ^t x) for ϕ∈(S). Similarly to the finite dimensional case, the λ-order homogeneous test functionals are characterized by the Euler equation: Δ _Eϕ =λ_ϕ. Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out. Supported by the National Natural Science Foundation of China.     

Chaotic electronic scattering with He(+)

We investigate classical electronic collisions with a He(+) ion. Scattering functions, such as the scattering angle, collisional time, or energy of the outgoing electron, all exhibit an interesting hierarchial self-similar structure, which can be interpreted in terms of the indefinite number of electronic returns to the vicinity of the nucleus, encounters between electrons, and Keplerian excursions of electrons during the collisional processes. Based on this mechanism a binary coding is introduced to organize the dynamics of this three-body system and to provide an understanding of the self-similarity among generations of scale magnification, which yields escape rates that vary with the sectional cut into the parameter space. The self-similarity displayed within a single generation, on the other hand, can be simply tied to the periods of the two independent electronic excursions. The physical interpretation and the symbolic dynamics introduced here are generally useful for three-body collisional systems, including atomic, molecular, or stellar collisions.     

HIGHLY SENSITIVE SPECTROPHOTOMETRY OF NIOBIUM

In pH2.0-3.0,niobium(V)forms molybdonlobic acid with sodiummolybdate.A spectrophotometric method has been developed for the deter-mination of niobium based on the formation of ion-associate compound ofmolybdoniobate with Butyl Rhodamine B in aqueous solution in the presenceof polyvinyl alcohol and 0.4-0.7 mol/L H_2SO_4.The maximum absorption ofion-associate compound exhioits at 85 nm and the molar absorptivity is7.5×1.0~5 L.mol~(-1).cm~(-1)for niobium.The new method has been applied tothe determination of microamounts niobium in silicate rock,when niobiumcontent is at the level of 8×10~(-3)%,with the relative standard deviationof about 3%.     

用θ-2θ型衍射仪测定溶液结构的新方法

叙述了用θ－２θ型Ｘ射线衍射仪精确测定电解质溶液结构的新实验技术。设计制作了具有恒温功能的超厚液体样品池，并建立了样品池窗口强度的校正方法。优化了液体Ｘ射线衍射数据和结构参数精细化的计算机程序，获得了非常令人满意的实验结果。由θ－２θ型Ｘ射线衍射仪精确测定的径向分布函数与θ－θ型衍射仪自由散射比较，表明ＤＲＦ分辨率有所提高。     

Influence of crystallization conditions on the crystalline transformation behavior of nylon 10 14

Three kinds of nylon 10 14 crystals with different perfections were prepared under various crystallization conditions. The Brill transition behavior of these nylon 10 14 crystals was investigated by variable-temperature X-ray diffraction. It was found that the crystallization conditions influence the Brill transition temperature greatly. The Brill transition temperature of the lamellar crystals grown from dilute solution is so high that no Brill transition temperature can be observed before melting. However, for crystals postannealed at 125 °C, the Brill transition temperature is as low as 130 °C. The results show that the Brill transition behavior of nylons is strongly dependent on the crystallization conditions, for example, the perfections of the crystals.     

Immunosuppressive ent‐Kaurene Diterpenoids from Isodon serra

Three new enmein‐type ent‐kaurenoids, i.e., the two pairs 1 and 2 of 20‐epimers and the (20R)‐isomer 3 , besides the seven known diterpenoids 4 – 10 , were isolated from the aerial parts of Isodon serra. Their structures were elucidated by spectroscopic techniques and X‐ray diffraction. The immunosuppressive effect for T‐lymphocytes proliferation induced by Con A in BALB/c mouse was evaluated for the isolates 1 – 10 . They all displayed a remarkable inhibitory effect, with multi‐glycosides of Tripterygium wilfordii as positive reference substance (Table 3).