Regularity of minimizers of non-isotropic integrals of the calculus of variations

The regularity of the minimizers of a special type of non-isotropic variational minimization problem is studied. The particularity of the potential of energy is that it has different growth rate with respect to different parts of the derivatives of the function. In particular, the model treated in this paper can be described as $$\Phi (Du) = |\partial _1 u|^2 + |\partial _2 u|^2 + |\partial _3 u|^2 + |\partial _3 u - |^p .$$ By using a result of P.Marcellini (cf. [4]) and perturbation method, it is proved that the minimizer of the Dirichlet boundary value problem is a function of W _loc ^{1, ∞} .     

Highly regioselective rearrangement of 2-substituted vinylepoxides catalyzed by gallium(III) triflate

Gallium(III) triflate catalyzed the rearrangement of 2-substituted vinylepoxides into beta,gamma-unsaturated carbonyl compounds with high regio- and chemoselectivity (>97/3) in low catalyst loading (1-5 mol %). The alkyl-substituted trimethylsilylvinyl epoxides gave beta,gamma-unsaturated ketone, but aryl-substituted vinylepoxides gave the aldehydes instead.     

Novel one-dimensional tubelike and two-dimensional polycatenated metal-organic frameworks

Two novel metal-organic frameworks (MOFs) [Zn(TITMB)(OAc)](OH).8.5H(2)O (1) and [Ag(TITMB)N(3)].H(2)O (2) [TITMB = 1,3,5-tris(imidazol-1-ylmethyl)-2,4,6-trimethylbenzene, OAc = acetate anion] were synthesized and their structures were determined by X-ray crystallography. Complex 1 crystallizes in tetragonal space group P(-)4 with a = 23.2664(7) and c = 11.9890(3) A and Z = 8. 1 has a one-dimensional tubelike structure with large inner pore size of approximately 17 A. Complex 2 crystallizes in monoclinic space group C2 with a = 20.7193(10), b = 11.5677(8), and c = 12.2944(6) A, beta = 125.5770(10) degrees, and Z = 4. 2 consists of two-dimensional honeycomb networks that interpenetrate each other to generate a polycatenated structure. In these two complexes, both zinc(II) and silver(I) atoms are four-coordinated with the same tetrahedral coordination geometry. The topologies of 1 and 2 are predominated by the conformations of TITMB, which are cis, trans, trans in 1 and cis, cis, cis in 2, respectively.     

Use of p-dimethylaminobenzalhyde as a colored reagent for determination of procaine hydrochloride by spectrophotometry

Spectrophotometric determination of procaine hydrochloride is described. The procaine hydrochloride reacts with p-dimethylaminobenzalhyde in glacial acetic acid to form an Schiff base which is a yellow compound, and its maximum absorption wavelength is at 455nm, ₄₅₅=3.46×10⁴. The absorbance for procaine hydrochloride from 0.2 to 15 μg ml⁻¹ obeys Beer's law. The linear regression equation of the calibration graph is C=5.866A−0.02, with a linear regression correlative coefficient is 0.9994 and relative standard deviation (RSD) of 1.7%; the detection limit is 0.1 μg ml⁻¹; recovery is from 92.0 to 110.0%. Effects of reaction medium, temperature, gentamycin, beneylpenicillin, kanamycin, streptomycin, foreign ions, and stand for time on the determination of procaine hydrochloride have been examined. The results obtained by this method agreed with those by the official method (dead-stop titration). This method is rapid and simple, and can be used for the determination of procaine hydrochloride in injection solution of procaine hydrochloride.     

Simultaneous quantification of budesonide and its two metabolites, 6beta-hydroxybudesonide and 16alpha-hydroxyprednisolone,in human plasma by liquid chromatography negative electrospray ionization tandem mass spectrometry

A sensitive, rapid and selective liquid chromatography negative electrospray ionization tandem mass spectrometry [LC-(-)ESI-MS-MS] method has been developed and validated for the simultaneous quantification of budesonide (BUD) and its major metabolites, 6beta-hydroxybudesonide (OH-BUD) and 16alpha-hydroxyprednisolone (OH-PRED) in human plasma. The method was validated over a linear range from 0.1 to 10 ng/mL for all three analytes using a solid-phase extraction procedure with 9-fluoro-hydrocortisone as the internal standard. The between-day and within-day coefficients of variation for all compounds were < or =20% at the concentrations of lower limit of quantification and < or =15% at other quality control concentrations. The utility of this assay was demonstrated by monitoring BUD, OH-BUD and OH-PRED plasma concentrations in one healthy subject for 24 h following a 3 mg oral dose of budesonide, administered as a pH modified release capsule (Budenofalk) to healthy volunteers.