Elliptic equations with BMO coefficients in Reifenberg domains

The inhomogeneous Dirichlet problems concerning divergence form elliptic equations are studied. Optimal regularity requirements on the coefficients and domains for the W^1,p theory, 1 < p < ∞, are obtained. The principal coefficients are supposed to be in the John‐Nirenberg space with small BMO seminorms. The domain is a Reifenberg domain. These conditions for the W^1,p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains. In fact, these domains might have fractal dimensions. © 2004 Wiley Periodicals, Inc.     

Synthesis,structure, spectroscopic and magnetic properties of a novel two-dimensional copper(II) complex Na2[Cu(pba)] · 6H2O [pba = 1,3-propylenebis(oxamato)]

The copper(II) complex Na₂[Cu(pba)] · 6H₂O has been synthesized and its structure determined. It consists of a novel two-dimensional network of [Cu(pba)]^2– anions connected to each other through the sodium ion as a bridge. Spectroscopic and magnetic properties have been measured and a spin distribution calculation has been carried out with the GAUSSIAN-94. Theoretical calculations indicate the rather larger spin density on nitrogen atoms should be responsible for the satellite lines appearing beside the main hyperfine coupling signs of copper(II). The antiferromagnetic interaction may be due to the intermolecular interaction and/or different copper(II) ions through the Na⁺ bridge in the same layer.     

"单摆"课程小结

课程小结是教学的重要环节，画龙点晴的课程小结可起到梳理要点，迁移知识，归纳总结的作用．课程小结重在概括精炼，条理清晰，有利学生理性认识的形成．现以单摆为例，浅谈一下教学的课程小结，小结可在学生归纳总结的基础上，由教师再做系统的总结．     

A method to collect an infrared spectrum in solution.

Herein we report a new method to collect a qualified infrared spectrum of a solute in solution by two solvent cells with different thickness during background single-beam spectrum scanning. By collecting the background spectrum with two cells (two stages), we successfully achieved accurate solvent compensation between a sample and a reference, namely, the solvent amounts in the sample and background measurements could become congruent. Therefore, the solvent bands were thoroughly suppressed in the infrared spectrum and a qualified spectrum of the solute was obtained.     

Mono-dispersed cross-linked polystyrene micro-spheres prepared by seed swelling polymerization method

A two-step swelling procedure was adopted to synthesize mono-dispersed and highly cross-linked poly (St-divinylbenzene) particles with PSt micro-spheres (1.80 μm in diameter). The PSt micro-spheres were prepared by a dispersion polymerization method and used as seeds. The effects of monomer concentration, ratio of ethanol to water, swelling reagents, crosslinking reagents, swelling temperature and agitation speed on particle size were investigated in detail. The morphologies and size distributions of these micro-spheres were examined by SEM and particle size analysis (PSA). The T _g of the micro-spheres was measured by DSC. The results indicate that the particles (6.20 μm in diameter) exhibit excellent mono dispersed property and high crosslinking degree when the concentration of the swelling reagent was 25%, the concentration of the crosslinking reagents was 23%, the swelling temperature was 30°C and the stirring speed was 150 r/min. __________ Translated from Chinese Journal of Applied Chemistry, 2007, 24(11): 1289–1294     

Multi-layer thin films/substrate system subjected to non-uniform misfit strains

Current methodologies used for the inference of thin film stress through curvature measurement are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to a single layer of thin film deposited on a substrate subjected to the non-uniform misfit strain in the thin film. Such methodologies are further extended to multi-layer thin films deposited on a substrate in the present study. Each thin film may have its own non-uniform misfit strain. We derive relations between the stresses in each thin film and the change of system curvatures due to the deposition of each thin film. The interface shear stresses between the adjacent films and between the thin film and the substrate are also obtained from the system curvatures. This provides the basis for the experimental determination of thin film stresses in multi-layer thin films on a substrate.     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

Miscibility and phase structure of binary blends of polylactide and poly(methyl methacrylate)

Blends of amorphous poly(DL‐lactide) (DL‐PLA) and crystalline poly(L‐lactide) (PLLA) with poly(methyl methacrylate) (PMMA) were prepared by both solution/precipitation and solution‐casting film methods. The miscibility, crystallization behavior, and component interaction of these blends were examined by differential scanning calorimetry. Only one glass‐transition temperature (T_g) was found in the DL‐PLA/PMMA solution/precipitation blends, indicating miscibility in this system. Two isolated T_g's appeared in the DL‐PLA/PMMA solution‐casting film blends, suggesting two segregated phases in the blend system, but evidence showed that two components were partially miscible. In the PLLA/PMMA blend, the crystallization of PLLA was greatly restricted by amorphous PMMA. Once the thermal history of the blend was destroyed, PLLA and PMMA were miscible. The T_g composition relationship for both DL‐PLA/PMMA and PLLA/PMMA miscible systems obeyed the Gordon–Taylor equation. Experiment results indicated that there is no more favorable trend of DL‐PLA to form miscible blends with PMMA than PLLA when PLLA is in the amorphous state. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 23–30, 2003     

An Additive Problem with Primes in Arithmetic Progressions

In this paper, we extend a classical result of Hua to arithmetic progressions with large moduli. The result implies the Linnik Theorem on the least prime in an arithmetic progression.     

Synthesis of molecular imprinted organic-inorganic hybrid polymer binding caffeine

Random copolymers of poly{(methacrylamide)-co-(vinyl trimethoxysilane)} and poly{(methacrylic acid)-co-(vinyl trimethoxysilane)} were synthesized via a free radical polymerization reaction. Acid catalyzed sol-gel process of tetraethylorthosilicate (TEOS) with aforementioned polymers in the presence of methyl xanthine class of alkaloid like caffeine resulted in the formation of highly transparent monoliths. Solvent extraction of the template leaves behind the recognition sites intact with high selectivity towards the print molecule. The ionic and non-specific adsorptions, which are considered to be the main disadvantages of the molecularly imprinted polymers (MIP), are prevented to a considerable extent by the end capping of surface silanol groups. The template binding efficiencies of MIP were determined by HPLC analysis.