数值模拟孤立波通过水下孤立方柱的粘性流动

本文用完整二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和ＶＯＦ方法，研究孤立波通过淹没水下孤立直立方柱水域时的波形变化和粘性流场运动。本文对孤立波通过水下 孤立直方柱的情形进行了实例计算。给出了波形随时间的演化图，可以看到反射波、前传波和跟随的振荡型小波列的生成及涡流场的运动演化，并与势流计算结果进行了比较。     

A generalization of Rayleigh's theorem for the infinite harmonic crystal

We show that if one replacesN masses in an infinite harmonic, perfect-dimensional crystal byN ₁ lighter andN ₂ heavier ones such thatN ₁+ N₂ =N is finite, then one introduces at most vN₁ (isolated) bound states. This can be considered as an extension of the results of Romerio and Wreszinski.Supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).     

A parametrization method for solving nonlinear two-point boundary value problems

A sharper version of the local Hadamard theorem on the solvability of nonlinear equations is proved. Additional parameters are introduced, and a two-parameter family of algorithms for solving nonlinear two-point boundary value problems is proposed. Conditions for the convergence of these algorithms are given in terms of the initial data. Using the right-hand side of the system of differential equations and the boundary conditions, equations are constructed from which initial approximations to the unknown parameters can be found. A criterion is established for the existence of an isolated solution to a nonlinear two-point boundary value problem. This solution is shown to be a continuous function of the data specifying the problem.     

Vanishing of the top local cohomology modules over Noetherian rings

Let R be a (not necessarily local) Noetherian ring and M a finitely generated R-module of finite dimension d. Let be an ideal of R and denote the intersection of all prime ideals . It is shown that

Synthesis, Structure and Photo- luminescence of Cu[（PPh3）2]（acac） （PPh3 = Triphenylphosphine, acac = Acetylacetone）

A novel complex Cu(PPh3)2(acac) 1 (PPh3 = triphenylphosphine, acac = acetylacetone) was obtained by a solution reaction and structurally characterized by X-ray diffraction. The crystal belongs to monoclinic, space group P21/n with a = 13.7361(8), b = 12.8204(7), c = 19.7638(13) , β = 95.946(2)°, C41H37CuO2P2, Mr = 687.19, V = 3461.7(4) 3, Z = 4, Dc = 1.319 g/cm3, S = 1.067, μ(MoKα) = 0.758 mm–1, F(000) = 1432, R = 0.0403 and wR = 0.0990. Complex 1 is characterized by an isolated structure. X-ray structure analysis of 1 shows that acac behaves as a chelating ligand and PPh3 coordinates as a monodentate ligand to the Cu(I) atoms. Photoluminescent investigation reveals that the title complex displays a strong green-light emission.     

Characterizations and Catalytic Properties of Transition Metal Ions Incorporated in Mesoporous Materials

Mesoporous materials typified by MCM-41 possess well-ordered mesoporous channels with controllable pore sizes from 2-30 nm, and are expected as desirable materials for catalysis.However, silicious mesoporous materials generally do not have sufficient intrinsic catalytic activities.Thus many studies have focused on introducing catalytically active sites. It is expected that different synthetic methods would result in different coordination structures of metal cations introduced in MCM-41, and thus different catalytic properties in catalytic reactions. The author's group has used two methods, i.e., direct hydrothermal synthesis (DHT) and template-ion exchange (TIE), for the syntheses of V-, Fe-, and Cr-MCM-41 and applied them as catalysts to selective oxidations of hydrocarbons. This paper highlights the characterizations of the coordination structures of these metal cations introduced into MCM-41 by the DHT and the TIE methods, and the structural-property relationships of these metal ion-containing MCM-41 materials in selective oxidation reactions.MCM-41 was prepared by hydrothermal synthesis using hexadecyltrimethylammonium bromide and sodium silicate as the sources of template and silicon, respectively. In the DHT method, metal cations were directly added into the synthesis gel before hydrothermal synthesis, while the exchanging of metal ions in ethanolic solutions with the template cations contained in the uncalcined MCM-41 was performed in the TIE method. XRD and N2-adsorption measurements showed that the mesoporous regularity was not destroyed with both synthetic methods for all the metal ion-containing MCM-41 with appropriate contents of metal cations.For V-MCM-41, the characterizations with mainly EXAFS suggested that V5+ cations were in tetrahedral coordination and mainly incorporated inside the framework of MCM-41 to substitute Si4+in the samples by the DHT method. Tetrahedrally coordinated Vanadyl species were also obtained by the TIE method, but the VO4 was dispersed on the wall surface of MCM-41. The V-MCM-41-DHT showed higher selectivity in the partial oxidations of C3H8 and i-C4H10 to alkenes and acrolein and methacrolein, but the V-MCM-41-TIE exhibited better catalytic activities in the partial oxidation of CH4 to HCHO and the oxidative dehydrogenation of C2H6.For Fe-MCM-41, EXAFS studies indicated that the DHT method also resulted in Fe3+ cations incorporated inside the framework of MCM-41 if iron content was lower than ca. 1 wt%. However,aggregated iron oxides with iron in octahedral coordination were mainly observed in the calcined Fe-MCM-41 by the TIE method. In the partial oxidation of CH4 to HCHO with O2 and the epoxidation of styrene with H2O2, the Fe-MCM-41 by the DHT method exhibits remarkably higher catalytic performances than that by the TIE method.Chromium could not be incorporated inside the framework of MCM-41 to substitute Si4+, and both synthetic methods led to surface chromate species. However, the DHT method resulted in only monochromate species on the wall surface of MCM-41 while polychromate species existed over the sample by the TIE method as indicated by the UV-Raman spectroscopic studies. The two types of Cr-MCM-41 exhibited distinctly different catalytic behaviors in the partial oxidation of CH4 with O2.The Cr-MCM-41-DHT was remarkably more selective towards HCHO formation.