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.

     

Definition and detection of data-based uniqueness in evaluating bilinear (two-way) chemical measurements

Multivariate curve resolution methods, frequently used in analyzing bilinear data sets, result in ambiguous decomposition in general. Implementing the adequate constraints may lead to reduce the so-called rotational ambiguity drastically, and in the most favorable cases to the unique solution. However, in some special cases, non-negativity constraint as minimal information of the system is a sufficient condition to resolve profiles uniquely. Although, several studies on exploring the uniqueness of the bilinear non-negatively constrained multivariate curve resolution methods have been made in the literature, it has still remained a mysterious question. In 1995, Manne published his profile-based theorems giving the necessary and sufficient conditions of the unique resolution. In this study, a new term, i.e., data-based uniqueness is defined and investigated in details, and a general procedure is suggested for detection of uniquely recovered profile(s) on the basis of data set structure in the abstract space. Close inspection of Borgen plots of these data sets leads to realize the comprehensive information of local rank, and these argumentations furnish a basis for data-based uniqueness theorem. The reported phenomenon and its exploration is a new stage (it can be said fundament) in understanding and describing the bilinear (matrix-type) chemical data in general.     

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.     

Thermal behavior of holo- and hemicellulose obtained from rice straw and bagasse

Thermal gravimetric analysis, and differential thermal behavior of holo- and hemicelluloses obtained from rice straw and bagasse were investigated. Degradation was found to be of first order reaction. The activation energy values and the rate constants were calculated from the kinetic of weight loss. Hemicellulose was found to be less stable than holocellulose, and the stability of the samples was arranged in the order, rice straw holo- > bagasse holo- > rice straw hemi- > bagasse hemicellulose. Degradation of rice straw (holo- as well as hemicellulose) was performed via two exothermic processes, whereas bagasse hemicellulose combustion was completed through three exothermic processes. The magnitude and the shape of the exotherms depend, mainly, on the chemical composition of the sample.     

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.     

Structure–retardation factor relationship of natural amino acids in two different mobile phases of RP-TLC

Abstract

Separation of amino acids (AAs) and their simple and inexpensive determination/identification is an interesting topic in biological and protein science, different food industries, and drug factories. Also, the presentation of the chromatographic behavior of compounds in a predictive model can be effective to estimate the structural/chemical properties of analyte and mobile phases. In this work for the first time, retardation factor (R_F) of 42 AAs in reversed-phase thin layer chromatography (RP-TLC) was modeled. Acetonitrile-sodium azide solution and 1,2 dioxane-sodium azide solution were two mobile phases which have been studied in this work. Results showed that the values of R_F are correlated with the structural properties of AAs and these properties had some similarities and differences in two noted mobile phases. For the TLC data in two mobile phases, five parametric linear models were suggested (R²_train = 0.93 and 0.97; R²_test = 0.93 and 0.99). The models were also evaluated with different statistical approaches. It was shown that increasing the sum of geometrical distances between N and O in AAs causes decreasing their R_F in RP-TLC using both mobile phases. Other structural effects of AAs on their separation in the desired RP-TLC system were also discussed.