Young＇s modulus surface and Poisson＇s ratio curve for tetragonal crystals

This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E（hkl） and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [001^-], [100], [001^-], [101^-] and [112^-] equals v（100, θ）, v（001, θ）, v（110,θ）, v（101,θ） and v（111, θ） respectively, are constructed for nine tetragonal crystals （ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon）. The characteristics of them are analysed in detail.     

Two weight commutators in the Dirichlet and Neumann Laplacian settings

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian ${\mathrm{\Delta }}_{N_{+}}$ on the upper half space ${\mathbb{R}}_{+}^n$ and the reflection Neumann Laplacian ${\mathrm{\Delta }}_N$ on ${\mathbb{R}}^n$ with respect to the weights associated to ${\mathrm{\Delta }}_{N_{+}}$ and ${\mathrm{\Delta }}_N$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to ${\mathrm{\Delta }}_N$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on ${\mathbb{R}}^n$ and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt $A^p$ weights with $p\in (1,2]$ while the previously known related results cover only $p\in (1,\frac{n+1}{n}]$. We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian ${\mathrm{\Delta }}_{D_{+}}$ on ${\mathbb{R}}_{+}^n$.     

The non-covalent bindings of CF2Cl2 with NO and SO2

Ab initio calculations have been performed on the complexes of CF₂Cl₂ with NO and SO₂, and a set of stable configurations for CF₂Cl₂–NO and CF₂Cl₂–SO₂ were found with no imaginary frequencies by the MP2 method. In addition, the binding energy and the NBO analysis were used to evaluate the relative stability of the complexes. The calculated results indicate that the weak interactions in the CF₂Cl₂–NO and CF₂Cl₂–SO₂ systems involved are enhanced with the increase of the number of non-covalent bonds. Further studies predict that the CF₂Cl₂–SO₂ system may play a more important role than the CF₂Cl₂–NO system in environmental problem because the former offers a stronger interaction than the latter. Furthermore, the non-covalent binding interactions of Cl···N and Cl···O for CF₂Cl₂–NO system, Cl···O, Cl···S and F···S for CF₂Cl₂–SO₂ system, are the dominant forces, which seem to be very significant as a driving force influencing the arrangement of molecules, especially in CF₂Cl₂–SO₂ system.     

THE ROLE OF INTERFACIAL INTERACTIONS IN THE PARTICLE/BUBBLE ATTACHMENT

The Van Oss surface thermodynamic theory of polar and apolar interfacial interactions was extended to the interaction between mineral surfaces and bubbles across liquid media. The acid base (polar) interfacial interactions are supposed to be responsible for the hydration repulsion between a hydrophilic mineral and a bubble as well as for the hydrophobic attraction between a hydrophobic mineral and the bubble.     

Dispersion Mechanism of Superfine SiC Particles in the Different Condition Liquid

SiC@A1(OH)₃-Y(OH)₃ core-shell composite particles are synthesized by co-precipitation method for strengthening the antioxidation of SiC at high temperature. To reach better A1(OH)₃-Y(OH)₃ composite shell and higher coating ratio on the SiC particles surfaces, SiC particles must be adequately dispersed in the SiC suspension during the coating process. The dispersion mechanism of SiC particles is investigated by the sedimentation method. Through test and analysis, the optimum conditions of the dispersion of SiC particles in the SiC suspension are sedimentating for 10 minutes, ultrasonic dispersion for 10 minutes, the lower SiC concentration, pH = 9, the dispersant content for the 2% volume of SiC suspension and using the polyelectrolyte dispersant, respectively.     

Concurrent synthesis of vanillin and isovanillin

A method for concurrent synthesis of vanillin and isovanillin has been developed by a nonregioselective Vilsmeier–Haack reaction of O-alkyl guaiacols. O-Alkylation of guaiacol provided the corresponding O-alkyl guaiacol (1), which was then formylated with N-methylformanilide/phosphorus oxychloride to give a mixture of 4-alkoxy-3-methoxy-benzaldehyde (2) and 3-alkoxy-4-methoxybenzaldehyde (3). Finally, the obtained mixture underwent a selective dealkylation by anhydrous aluminium trichloride, while leaving methyl groups intact to simultaneously achieve the significant fine chemicals vanillin and isovanillin.