The obstacle problem for a fractional Monge–Ampère equation

Abstract

We study the obstacle problem for a nonlocal, degenerate elliptic Monge–Ampère equation. We show existence and regularity of a unique classical solution to the problem and regularity of the free boundary.     

Synthesis and structural elucidation of some new heterocyclic β-diketone derivatives of boron

Some new β-diketone derivatives of boron having the general formula B₂O(OAc)_4?n[OC(R)$\text{C:CON(Ph)N:C}$ CH₃]_n (where n = 1 or 2; R = CH₃, C₂H₅, C₆H₅ and p-ClC₆H₄) have been synthesised by the reactions of oxy-bis(diacetatoborane) and substituted pyrazolones, such as 4-acyl-3-methyl-1-phenyl-2-pyrazolin-5-ones (acyl = acetyl, propionyl, benzoyl and p-chlorobenzoyl) in dry toluene solution in 1:1 and 1:2 molar ratios. These derivatives have been characterised by elemental analysis, molecular weight measurements. Structures have been proposed on the basis of chemical reactions, IR, ¹H and ¹¹B NMR spectral studies.In the derivatives B₂O(OAc)₃[OC(R)$\text{C:CON(Ph)N:C}$ CH₃] two of the three acetate groups are unidentate and the third is bridged between two boron atoms along with BOB linkage. Whereas the derivatives B₂O(OAc)₂[OC(R)$\text{C:CON(Ph)N:C}$ CH₃]₂ are the mixture of geometrical isomers.     

Partial molar volumes of gases dissolved in liquids. Part I. Selected literature data and some estimation techniques

Experimental data, of precision better than 3%, available in the literature for the partial molar volumes of gases at infinite dilution in nonaqueous polar and nonpolar solvents are reviewed. Various empirical and semiempirical techniques for estimating this property are summarized and their usefulness is examined. Several graphical correlations provide useful rough estimates (within 10%). Values derived from corresponding-states and scaled-particle treatments vary considerably, and more-accurate experimental results are needed to establish the utility of these approaches.     

Thermodynamics of aqueous mixtures of nonelectrolytes. IV. Excess volumes of water-acetonitrile mixtures from 15 to 35°C

Excess volumes of water-acetonitrile mixtures were obtained from measurements of density over the entire mole fraction range and at 5 degree intervals from 15 to 35°C. Partial molar excess volumes at the five temperatures, excess coefficients of thermal expansion at 25°C and partial molar excess expansibilities at 25°C were derived from the results. The values of the various volumetric properties are compared with data from the literature.Issued as NRCC No. 19500     

先进蛋黄-蛋壳结构能源转化纳米反应器

蛋黄-蛋壳结构独特的纳米结构及特性,使其在很多领域中具有潜在的应用价值,因此近年来受到了广泛关注.本综述总结了使用蛋黄-蛋壳纳米结构作为纳米反应器的研究进展.从合成策略出发,主要强调最近五年合成蛋黄-蛋壳纳米结构的最新研究进展.通过光催化,甲烷重整和电催化等反应作为典型的反应过程,重点讨论蛋黄-蛋壳结构纳米反应器在催化领域的应用,并对该领域未来的发展进行了展望.     

ZnO-AuxCu1−x Alloy and ZnO-AuxAl1−x Alloy Vertically Aligned Nanocomposites for Low-Loss Plasmonic Metamaterials

Hyperbolic metamaterials are a class of materials exhibiting anisotropic dielectric function owing to the morphology of the nanostructures. In these structures, one direction behaves as a metal, and the orthogonal direction behaves as a dielectric material. Applications include subdiffraction imaging and hyperlenses. However, key limiting factors include energy losses of noble metals and challenging fabrication methods. In this work, self-assembled plasmonic metamaterials consisting of anisotropic nanoalloy pillars embedded into the ZnO matrix are developed using a seed-layer approach. Alloys of Au_xAl_1−x or Au_xCu_1−x are explored due to their lower losses and higher stability. Optical and microstructural properties were explored. The ZnO-Au_xCu_1−x system demonstrated excellent epitaxial quality and optical properties compared with the ZnO-Au_xAl_1−x system. Both nanocomposite systems demonstrate plasmonic resonance, hyperbolic dispersion, low losses, and epsilon-near-zero permittivity, making them promising candidates towards direct photonic integration.     

Estimation of pure component properties. Part 4: Estimation of the saturated liquid viscosity of non-electrolyte organic compounds via group contributions and group interactions

A new group contribution method for the prediction of pure component saturated liquid viscosity has been developed. The method is an extension of the pure component property estimation techniques that we have developed for normal boiling points, critical property data, and vapour pressures. Predictions can be made from simply having knowledge of the molecular structure of the compound. In addition, the structural group definitions for the method are identical to those proposed for estimation of saturated vapour pressures. Structural groups were defined in a standardized form and fragmentation of the molecular structures was performed by an automatic procedure to eliminate any arbitrary assumptions. The new method is based on liquid viscosity data for more than 1600 components. Results of the new method are compared to several other estimation methods published in literature and are found to be significantly better. A relative mean deviation in viscosity of 15.3% was observed for 813 components (12,139 data points). By comparison, the Van Velzen method, the best literature method in our benchmarking exercise produced a relative mean deviation of 92.8% for 670 components (11,115 data points). Estimation results at the normal boiling temperature were also tested against an empirical rule for more than 4000 components. The range of the method is usually from the triple or melting point to a reduced temperature of 0.75–0.8. Larger than average deviations were observed in the case of molecules with higher rotational symmetry, but no specific correction of this effect was included in this method.