Free groups in a normal subgroup of the field of fractions of a skew polynomial ring

Let k(t) be the field of rational functions over the field k, let σ be a k-automorphism of K = k(t), let D = K(X;σ) be the ring of fractions of the skew polynomial ring K[X;σ], and let D^? be the multiplicative group of D. We show that if N is a noncentral normal subgroup of D^?, then N contains a free subgroup. We also prove that when k is algebraically closed and σ has infinite order, there exists a specialization from D to a quaternion algebra. This allows us to explicitly present free subgroups in D^?.     

Semilattice transversals of regular bands I

Every regular band can be isomorphically embedded into a regular band which has a semilattice transversal. The latter constitute the variety of regular split bands, whose subvariety lattice is isomorphic to the lattice of regular band varieties.     

Structure of relatively free dimonoids

Loday introduced the notion of a dimonoid and constructed the free dimonoid. The paper concerns the variety theory of dimonoids. We recall and summarize the results obtained by Loday, the author as well as others on the structure of some relatively free dimonoids. This part of the paper should be viewed as a survey, however we include some new ideas in the last sections. Namely, we construct a free (?z;rs)-dimonoid, a free (rs;rz)-dimonoid, a free rs-dimonoid, a free (rb;rs)-dimonoid, a free (rs;rb)-dimonoid and characterize the least (?z;rs)-congruence, the least (rs;rz)-congruence, the least rs-congruence, the least (rb;rs)-congruence and the least (rs;rb)-congruence on the free dimonoid. We also establish that the automorphism groups of constructed free algebras are isomorphic to the symmetric group and the semigroups of the free rs-dimonoid are anti-isomorphic.     

Automorphisms of the endomorphism semigroup of a free commutative dimonoid

We determine all isomorphisms between the endomorphism semigroups of free commutative dimonoids and prove that all automorphisms of the endomorphism semigroup of a free commutative dimonoid are quasi-inner. In particular, we answer a question of B. I. Plotkin.     

A free boundary problem arising from DCIS mathematical model

Ductal carcinoma in situ – a special cancer – is confined within the breast ductal only. We derive the mathematical ductal carcinoma in situ model in a form of a nonlinear parabolic equation with initial, boundary, and free boundary conditions. Existence, uniqueness, and stability of problem are proved. Algorithm and illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2016 John Wiley & Sons, Ltd.     

Monolayer 1T and 1T′ MoSO as Promising Electrocatalyst for Hydrogen Evolution based on First Principle Calculations

Molybdenum disulfide (MoS₂) has been regarded as one of the most promising candidates for replacing Pt group noble metals as an efficient electrocatalyst to enhance the hydrogen evolution reaction (HER) in consideration of its relatively high earth abundance. Recent studies show that the catalytic efficiency of MoS₂ for HER can be promoted by the presence of 1T-phase MoS₂. It is hard to precisely control the formation of 1T-MoS₂, however, due to its metastability relative to 2H-MoS₂. Elevating the stability of 1T phase allotrope is therefore of great importance and could be realized by replacing divalent S with monovalent elements or groups according to crystal field theory, which has been demonstrated through our first-principles density functional theory (DFT) calculation results. Differential Gibbs free energy analysis for hydrogen adsorption (ΔG_H*) suggest that 1T and 1T′ MoSO (O doped MoS₂) might be taken as potential candidate catalysts for HER process with better performance than 1T and 1T′ MoS₂. We also propose a probable approach to synthesize 1T and 1T′ MoSO under oxidation circumstance environment of graphene oxide.     

Melatonin in Wine and Beer: Beneficial Effects

Melatonin is a hormone secreted in the pineal gland with several functions, especially regulation of circadian sleep cycle and the biological processes related to it. This review evaluates the bioavailability of melatonin and resulting metabolites, the presence of melatonin in wine and beer and factors that influence it, and finally the different benefits related to treatment with melatonin. When administered orally, melatonin is mainly absorbed in the rectum and the ileum; it has a half-life of about 0.45–1 h and is extensively inactivated in the liver by phase 2 enzymes. Melatonin (MEL) concentration varies from picograms to ng/mL in fermented beverages such as wine and beer, depending on the fermentation process. These low quantities, within a dietary intake, are enough to reach significant plasma concentrations of melatonin, and are thus able to exert beneficial effects. Melatonin has demonstrated antioxidant, anticarcinogenic, immunomodulatory and neuroprotective actions. These benefits are related to its free radical scavenging properties as well and the direct interaction with melatonin receptors, which are involved in complex intracellular signaling pathways, including inhibition of angiogenesis and cell proliferation, among others. In the present review, the current evidence on the effects of melatonin on different pathophysiological conditions is also discussed.     

Color Stabilization of Apulian Red Wines through the Sequential Inoculation of Starmerella bacillaris and Saccharomyces cerevisiae

Mixed fermentation using Starmerella bacillaris and Saccharomyces cerevisiae has gained attention in recent years due to their ability to modulate the qualitative parameters of enological interest, such as the color intensity and stability of wine. In this study, three of the most important red Apulian varieties were fermented through two pure inoculations of Saccharomyces cerevisiae strains or the sequential inoculation of Saccharomyces cerevisiae after 48 h from Starmerella bacillaris. The evolution of anthocyanin profiles and chromatic characteristics were determined in the produced wines at draining off and after 18 months of bottle aging in order to assess the impact of the different fermentation protocols on the potential color stabilization and shelf-life. The chemical composition analysis showed titratable acidity and ethanol content exhibiting marked differences among wines after fermentation and aging. The 48 h inoculation delay produced wines with higher values of color intensity and color stability. This was ascribed to the increased presence of compounds, such as stable A-type vitisins and reddish/violet ethylidene-bridge flavonol-anthocyanin adducts, in the mixed fermentation. Our results proved that the sequential fermentation of Starmerella bacillaris and Saccharomyces cerevisiae could enhance the chromatic profile as well as the stability of the red wines, thus improving their organoleptic quality.