THE CAUCHY PROBLEM OF THE HARTREE EQUATION

In this paper, we systematically study the wellposedness, illposedness of the Hartree equation, and obtain the sharp local wellposedness, the global existence in Hs, s≥1 and the small scattering result in Hs for 2 〈γ〈 n and s ≥ 2/γ - 1. In addition, we study the nonexistence of nontrivial asymptotically free solutions of the Hartree equation.     

Corrected equations for susceptibility-induced T2-shortening

Local field gradients created by paramagnetic entities shorten water proton relaxation times, particularly T2. This "novel" relaxation mechanism, now known as susceptibility-induced relaxation, was described twenty years ago by Gueron, and later extended by others to superparamagnetic particles which have a much larger magnetization. Unfortunately, because of subtle but significant errors, those results are valid only in the strict zero-field limit. These errors are corrected in the present article, and new versions of the relaxation equations are presented. The correction is shown to be significant, not only for transverse and longitudinal relaxation in aqueous superparamagnetic colloids, where the "Gueron" effect is known to be important, but even in some cases for transverse paramagnetic relaxation.     

Paramagnetic Proton Nuclear Spin Relaxation Theory of Low-Symmetry Complexes for Electron Spin Quantum NumberS=

A generalization of the modified Solomon–Bloembergen–Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (Δ^ZFS_t) and a static (Δ^ZFS_s) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum numberS= , for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term δ which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spin–lattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua–metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water protonT₁NMRD profiles using both MSBM and the new theory.     

Migration-coalescence of Nanoparticles During Deposition of Au,Ag, Cu,and GaAs on Amorphous SiO2

Nanoparticles formed during the initial period of film growth can migrate, coalesce, and may also melt. Nanoparticles of Au, Ag, Cu, and GaAs ranging from 1 to 15nm in diameter were sputter-deposited on amorphous SiO₂ (a-SiO₂). Transmission electron microscopy was used to analyze the time-dependent change of the dispersion of particles on a thin film. The number density of nanoparticles was nearly constant during the deposition of Ag. For Au, Cu, and GaAs, however, the number density decreased with time during the early deposition period. For example, for Au the number density decreased from 2.8×10¹⁶m^–2 (surface coverage ratio of 0.08) to 1.8×10¹⁶m^–2 (surface coverage ratio of 0.14). The surface coverage increased because the particle size increased as the number density decreased. This decrease suggests that migration followed by coalescence occurred. For Au, although we found evidence of migration of 2-nm particles at 500°C, the migration rate was too slow to account for the results from the deposition experiments. These observations indicate an autocatalytic mechanism that migration followed by coalescence liberates energy by the formation of chemical bonds, heats the coalesced particles, and enhances further migration. The strong dependence of the structure of nanoparticle dispersions on the deposition rate is a direct consequence of the deposition mechanism, which is a nonlinear, kinetically-controlled process.     

The Riemann–Hilbert Problem for Analytic Description of the DM Solitons

A simple exact formula is derived for the profile of the optical pulse propagating over a DM fiber with zero mean dispersion. The dissipation is neglected, and dispersion is assumed to be constant along the adjacent legs of the waveguide, thus providing the applicability of the integrable NLS models within each leg. The formula describes a class of solutions called dispersion-managed solitons (DM solitons), which are periodic along the waveguide and exponentially localized in time. The DM solitons are parameterized by a certain class of spectral data, specified from numerical simulations. Using a related Riemann–Hilbert problem, we reconstruct a profile of the DM soliton from the given spectral data. For sufficiently long legs, the leading term of DM soliton is found in explicit form by asymptotic undressing of the Riemann–Hilbert problem. The analytic results are compared with numerical simulations.     

MoO3表面分散作用对丝光沸石晶体结构的影响

将晶相MoO_3与丝光沸石充分研磨混合后,在一定高温下加热,MoO_3在丝光沸石上自发分散。当分散量较少时,丝光沸石的晶休结构无明显变化,加热时间的延长,MoO_3分散量增加。沸石结晶度降低;当分散量相同时,加热时间延长,沸石结晶度不变。结果表明,丝光沸石晶体结构的破坏,是由于分散的表面层钼与沸石骨架强烈相互作用的结果。MoO_3分散量越多,这种相互作用越强,沸石结晶度越低。     

Al_2（SO_4）_3／γ－Al_2O_3单层分散状态及其对丁烯齐聚反应活性的

用ＸＲＤ、ＴＧ、热重氨吸附法等手段，测定了Ａｌ_２（ＳＯ_４）_３／γ－Ａｌ_２Ｏ_３中单层分散相与Ａｌ_２（ＳＯ_４）_３担载量之间的关系，测定了表面单层最大分散量一阈值。其与用密置单层模型计算所得值接近，这为Ａｌ_２（ＳＯ_４）_３在γ－Ａｌ_２Ｏ_３上单层分散行为提供了证据，且将该催化剂的表面行为与其对丁烯齐聚反应活性进行了关联。     

鼓泡浆液反应器的应用开发研究：Ⅱ液相混合与传热特性

研究了以粉体氧经铝水合物为固相的鼓泡浆液反应器的传热性能和温度分布及沸合特性。结果表明两相和三相体系的传热速度均随表观气速的增大而增大，固相的加入强化了体系的传热效果，但固体浓度大小无明显影响。