Navier-Stokes equations in 3D thin domains with Navier friction boundary condition

In this article we study the 3D Navier-Stokes equations with Navier friction boundary condition in thin domains. We prove the global existence of strong solutions to the 3D Navier-Stokes equations when the initial data and external forces are in large sets as the thickness of the domain is small. We generalize the techniques developed to study the 3D Navier-Stokes equations in thin domains, see [G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains I: Global attractors and global regularity of solutions, J. Amer. Math. Soc. 6 (1993) 503-568; G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains II: Global regularity of spatially periodic conditions, in: Nonlinear Partial Differential Equations and Their Application, College de France Seminar, vol. XI, Longman, Harlow, 1994, pp. 205-247; R. Temam, M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations 1 (1996) 499-546; R. Temam, M. Ziane, Navier-Stokes equations in thin spherical shells, in: Optimization Methods in Partial Differential Equations, in: Contemp. Math., vol. 209, Amer. Math. Soc., Providence, RI, 1996, pp. 281-314], to the Navier friction boundary condition by introducing a new average operator Mε in the thin direction according to the spectral decomposition of the Stokes operator Aε. Our analysis hinges on the refined investigation of the eigenvalue problem corresponding to the Stokes operator Aε with Navier friction boundary condition.     

Novel optically active 1,3-aminoalcohols derived from D-glucal

A series of ethyl(phenyl) 6-amino-2,3,6-trideoxy-86q584125218852/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-D-glucopyranosides (amino=piperidino (Pip), pyrrolidino (Pyr), azetidino (Az), Bu₂N) have been prepared from tri-O-acetyl-D-glucal to obtain catalysts for asymmetric synthesis and the starting compounds for the syntheses of other bidentate ligands.Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 45–52, January, 2000.     

Electrochemical characteristics of Ce0.8Gd0.2O1.9|La0.6Sr0.4CoO3-δ + Ce0.8Gd0.2O1.9 half-cell

The analysis of the medium temperature half-cell Ce_0.8Gd_0.2O_1.9|70 wt% La_0.6Sr_0.4CoO_{3-86jxww24pk5/xxlarge948.gif" alt="delta" align="BASELINE" BORDER="0">} (LSCO) + 30 wt % Ce_0.8Gd_0.2O_1.9 (CGO) has been made by electrochemical impedance, cyclic voltammetry and chronoamperometry. The shape of complex impedance plots depends on temperature and cathodic polarisation of the electrode. Nyquist (Z86jxww24pk5/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">86jxww24pk5/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">, Z86jxww24pk5/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-) plots were fitted by equivalent circuit taking into account the electrolyte properties (at very high frequencies), charge transfer process at grain boundaries (at high frequencies), and medium and low frequency O₂ reduction process at the cathode surface and inside the porous cathode material. Two different time constants have been obtained for the cathode process, i.e. for electroreduction of oxygen. It was found that the addition of CGO into the cathode material (LSCO) only somewhat decreases the surface catalytic activity but the noticeably higher low-frequency resistance (i.e. mainly diffusion-like mass transfer resistance R_D) values at lower temperatures have been calculated. It was found that the mainly bulk diffusion-limited process at T86jxww24pk5/xxlarge8804.gif" alt="le" align="MIDDLE" BORDER="0">773 K deviates toward the kinetically mixed process (diffusion + charge transfer) with increasing temperature.     

Novel type of heterogenized CuCl2 catalytic systems for oxidative carbonylation of methanol

A novel type of heterogenized CuCl₂ catalysts was designed for the oxidative carbonylation of methanol to dimethyl carbonate (DMC) taking account of the plausible reaction mechanism and intermediates. To prevent severe corrosion of the reaction equipment materials due to Cl^– while keeping the catalytic activity of the homogeneous CuCl₂ catalyst, we adopted, as supports (or ligands) of CuCl₂, four polymers, bearing a 2,286/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-bipyridine (bpy) or pyridine (py) unit, namely, poly(2,286/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-bipyridine-5,586/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-diyl) (Pbpy), poly(pyridine-2,5-diyl) (Ppy), poly(N,N86/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-bisphenylene-2,286/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-bipyridine-4,486/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dicarboxylic amide) (Bpya), and poly(4-methyl-486/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-vinyl-2,286/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-bipyridine) (Pvbpy), together with one chelate compound, 8-quinolinol. The catalytic activity, stability of heterogenized CuCl₂ and their corrosivities to stainless steels were examined in the liquid-phase reaction of the oxidative carbonylation of methanol. These polymer-supported catalysts showed considerable catalytic activity and stability for the DMC synthesis. In particular, the Pbpy-CuCl₂ and Ppy-CuCl₂ catalysts exhibited high DMC yields and selectivity comparable to those of the homogeneous CuCl₂ catalyst. This high activity appears to be associated with the presence of the 86/xxlarge960.gif" alt="pgr" align="BASELINE" BORDER="0">-conjugated system in the polymers, which affect the redox reactions of Cu involved in the catalytic reaction. All of the polymer-supported CuCl₂ catalysts could be easily recycled after filtration, and the initial catalytic activity was maintained after three times of use. The corrosive characters of the catalysts were closely related to CuCl₂ leaching from the supports, which reflects the ability of supports to coordinate Cu. These experimental results suggest that both the electronic structure and the coordination ability of the polymer supports are key factors for the development of an effective catalytic system.     

Simultaneous hydrogen and peroxide production by photocatalytic water splitting

Photocatalytic oxidation of water is a promising method to realize large-scale H₂O₂ production without a hazardous and energy-intensive process. In this study, we introduce a Pt/TiO₂(anatase) photocatalyst to construct a simple and environmentally friendly system to achieve simultaneous H₂ and H₂O₂ production. Both H₂ and H₂O₂ are high-value chemicals, and their separation is automatic. Even without the assistance of a sacrificial agent, the system can reach an efficiency of 7410 and 5096 μmol g^–1 h^–1 (first 1 h) for H₂ and H₂O₂, respectively, which is much higher than that of a commercial Pt/TiO₂(anatase) system that has a similar morphology. This exceptional activity is attributed to the more favorable two-electron oxidation of water to H₂O₂, compared with the four-electron oxidation of water to O₂.     

On the maximal length of two sequences of integers in arithmetic progressions with the same prime divisors

In this paper we consider an analogue of the problem of Erds and Woods for arithmetic progressions. A positive answer follows from theabc conjecture. Partial results are obtained unconditionally.     

A large deviation principle for (r,p)-capacities on the Wiener space

Summary We formulate and prove a large deviation principle for the (r, p)-capacity on an abstract Wiener space. As an application, we obtain a sharpening of Strassen's law of the iterated logarithm in terms of the capacity.     

The regioselectivity of the formation of 2-pyrazolylthiazoles and their precursors from the reaction of 2-hydrazinothiazoles with 4,4,4-trifluoro-1-hetaryl-1,3-butanediones

Reaction of 2-hydrazinothiazoles 1 with 1-thienyl- and 1-furyl-1,3-butanediones 2a,b in methanol in the presence of hydrochloric acid mainly leads to a mixture of pyrazoles 3 and pyrazolines 4 or pyrazoles 3 and 5 in strong acidic conditions. Isomeric hydrazones 6 and pyrazolines 4 were formed and isolated in these reactions in the absence of hydrochloric acid. It has been shown that the regioselectivity in the reaction of diketones 2 with hydrazine 1 is governed by both the concentration of acid and the nature of substituents in the 1,3-diketones 2. Cyclization of hydrazones 6 is shown to occur under milder conditions than dehydration for pyrazolines 4. The new heterocyclic compounds were prepared and fully characterized by NMR spectra and by X-ray analysis for 3c.     

Synthesis and crystal structure ofN,N′-DicyclohexylpiperazineN,N′-dioxide octahydrate

N,N86/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-DicyclohexylpiperazineN,N86/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dioxide octahydrate, C₁₆H₄₆N₂O₁₀,M _r=426.55, monoclinic, space groupC2/m (No. 12),a=12.961(4),b=11.533(4),c=7.907(1) Å, 86/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">=98.37(2)^o,V=1169.3(6) ų,Z=2. The structure was solved by the direct method and refined toR=0.045 for 1192 observed MoK _{86/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">} reflections. TheN,N86/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dioxide molecule occupies a site of symmetry 2/m. The piperazine ring takes the chair form with the two N–O bonds oriented axially in atrans configuration. Hydrogen bonding between the water molecules, as well as between theN-oxide groups and water molecules, gives rise to a puckered layer composed of edge-sharing four-membered, five-membered, six-membered, and eight-membered rings. Adjacent layers are cross-linked by theN,N86/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dicyclohexylpiperazine moieties lying between them, thereby generating a 86/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">sandwich86/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> structure consolidated by covalent and hydrogen bonding. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82062 (8 pages).     

X-H (X = C, N, O, Si, P, S) 键离解能计算的密度泛函方法研究

使用了不同密度泛函方法计算X-H (X = C, N, O, Si, P, S) 键离解能，并分析不同密度泛函方法的计算精度。研究发现大多数密度泛函方法包括B3LYP, B3P86, B3PW91, G96LYP, PBE1PBE，和BH&HLYP都明显低估键离解能13-25 kJ/mol。该现象与是否使用无限基组无关，因为即使使用无限基组键离解能仍然被低估。因此密度泛函方法不适合用于键离解能的估算。其中B3P86方法的偏差最小。进一步分析表明，使用限制性开壳层计算并无任何优势，在大多数情况下非限制性开壳层计算实际上比限制性开壳层计算要好。最后，我们发现了密度泛函方法对键离解能的低估是系统的，因此建议利用校准后的UDFT/6-311++G(d, p)方法计算化学键离解能。