Coefficient rings of numerical semigroup algebras

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show that arithmetic and set-theoretic properties of a numerical semigroup ring are properties of an equi-gcd numerical semigroup algebra.

     

An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given.     

Asphaltene self-association and water-in-hydrocarbon emulsions

The configuration of asphaltenes on the water-oil interface was evaluated from a combination of molar mass, interfacial tension, drop size distribution, and gravimetric measurements of model emulsions consisting of asphaltenes, toluene, heptane, and water. Molar mass measurements were required because asphaltenes self-associate and the level of self-association varies with asphaltene concentration, the resin content, solvent type, and temperature. Plots of interfacial tension versus the log of asphaltene molar concentration were employed to determine the average interfacial area of asphaltene molecules on the interface. The moles of asphaltenes per area of emulsion interface were determined from the molar mass data as well as drop size distributions and gravimetric measurements of the model emulsions. The results indicate that asphaltenes form monolayers on the interface even at concentrations as high as 40 kg/m(3). As well, large aggregates with molar masses exceeding approximately 10,000 g/mol did not appear to adsorb at the interface. The area occupied by the asphaltenes on the interface was constant indicating that self-associated asphaltenes simply extend further into the continuous phase than nonassociated asphaltenes. The thickness of the monolayer ranged from 2 to 9 nm.     

Heteropoly acids, their salts and polyoxometalates as heterogenous, efficient and eco-friendly catalysts in organic reactions: Some recent advances

In this review article, some recent advances of applying heteropoly acids and polyoxometalates as heterogeneous, reusable and eco-friendly catalysts in organic synthesis are discussed.     

An efficient and chemoselective method for protection of thiols catalyzed by aluminumdodecatungstophosphate (AlPW12O40), as a highly water tolerant Lewis acid catalyst

Protection of various thiols with diphenylmethanol was achieved in high yields at room temperature using catalytic amounts of AlPW₁₂O₄₀ in CH₂Cl₂. In the presence of this catalyst, protection of SH versus OH was achieved with high chemoselectivity and yields. The catalyst can be easily recovered and reused. Deprotection of DPM thioethers was also achieved using molecular iodine at reflux in CH₂Cl₂ in high yields.     

Facile protection of carbonyl compounds as oxathiolanes and transoxathioacetalization of oxyacetals promoted by iron(III) trifluoroacetate or trifluoromethanesulfonate as chemoselective and recyclable catalysts

Oxathioacetalization of carbonyl compounds and transoxathioacetalization of O,O-acetals/ketals are reported under nearly neutral conditions promoted by iron(III) trifluoroacetate [Fe(CF₃CO₂)₃] or trifluoromethanesulfonate [Fe(CF₃SO₃)₃] as recyclable and highly efficient Lewis acid catalysts.