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.

     

Spacecraft formation flying in the port-Hamiltonian framework

The problem of controlling the relative position and velocity in multi-spacecraft formation flying in the planetary orbits is an enabling technology for current and future research. This paper proposes a family of tracking controllers for different dynamics of Spacecraft Formation Flying (SFF) in the framework of port-Hamiltonian (pH) systems through application of timed Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). The leader–multi-follower architecture is used to address this problem. In this regard, first we model the spacecraft motion in the pH framework in the Earth Centered Inertial frame and then transform it to the Hill frame which is a special local coordinate system. By this technique, we may present a unified structure which encompasses linear/nonlinear dynamics, with/without perturbation. Then, using the timed IDA-PBC method and the contraction analysis, a new method for controlling a family of SFF dynamics is developed. The numerical simulations show the efficiency of the approach in two different cases of missions.

     

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.     

Kinetic determination of silver ion by its perturbation on Belousov-Zhabotinskii oscillating chemical reaction using potentiometric method.

Silver ion can perturb the Belousov-Zhabotinskii (B-Z) oscillating chemical reaction. Therefore, the B-Z oscillating system was applied in the determination of silver ion by using a platinum wire as an indicator electrode in the potentiometric method. The amplitude of the potentiometric oscillation increased linearly in proportion to [Ag+] in the range of 9.42 x 10(-6) M to 2.54 x 10(-4) M, with a correlation coefficient of 0.999 under the optimum conditions. The obtained LOD (2sigma) was 8.85 x 10(-6) M and the relative standard deviation (RSD) for five measurements of 1 x 10(-4) M silver ion was 5%. The influence of some potentially interference was also investigated.     

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.     

Spectrophotometric study of the complexation of iodine with 1,7-diaza-15-crown-5 in chloroform solution

The complex formation reaction between iodine and 1,7-diaza-15-crown-5 (DA15C5) has been studied spectrophotometrically in chloroform at 25°C. The resulting 1:2 (DA15C5:I₂) molecular complex was formulated as (DA15C5...;I⁺)I ₃ ^– . The spectrophotometric results, as well as the conductivity measurements, revealed that the gradual release of triiodide ion from its contact ion paired form in the molecular complex into the solution is the rate determining step of the reaction. The rate constant was calculated ask=(8.8±0.2)×10^–3 min^–1. The formation constant of the molecular complex was evaluated from the computer fitting of the absorbance-mole ratio data as logK _f=6.89±0.09.