A convenient synthesis of 3-aryl-5-methylidene-2-thiohydantoins

3-Aryl-5-methylidene-2-thiohydantoins were constructed in one-pot reaction of aryl isothiocyanates and 3-morpholino- alanine in alkaline medium with the subsequent treatment with boiling hydrochloric acid.     

Highly diastereoselective multicomponent synthesis of polysubstituted 2-hydroxy-2-trifluoromethylpiperidineswith four and five stereogenic centers

The Michael–Mannich cascade cyclization of cyano olefins, ethyl 4,4,4-trifluoro-3-oxobutanoate, aromatic aldehydes and ammonium acetate provides convenient stereoselective formation of ethyl 5,5-dicyano-4,6-diaryl-2-hydroxy-2-(trifluoromethyl)piperidine-3-carboxylates with fourstereogenic centers and dialkyl 4,6-diaryl-5-cyano-2-hydroxy-2-(trifluoromethyl)piperidine-3,5-dicarboxylates with five stereogenic centers. Ammonium acetate plays dual role, acting as a base and as a nitrogen source.     

Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.     

Direct Transformation of Arenols Based on C—O Activation

In the view of substrate availability, atomic efficiency and cost, directly using arenols as coupling partners in cross‐coupling, would be one of the most attractive goals. Up to date, many efforts have been made to activate the C—O bond of phenols with different strategies, for example, through in‐situ formed intermediates, through a catalytic reductive dearomatization‐condensation‐rearomatization sequence or catalytic deoxygenation. In this review, we summarized recent advances in cross‐couplings of arenols as the electrophiles via C—O activation.     

Metabolomics techniques applied in the investigation of phenolic acids from the agro-industrial by-product of Carapa guianensis Aubl

Processing of Carapa guianensis seeds to obtain oil on an industrial scale generates a significant amount of by-product, approximately 66% w/w, which is called cake and is a potential source of biomolecules, including simple phenolic structures. For this reason, studies were carried out on the chemical profiles of hydrolyzed extract from this agro-industrial by-product through High Performance Thin-Layer Chromatography (HPTLC) and Gas Chromatography coupled to Mass Spectrometry (GC–MS). These techniques were used to detect metabolic classes and/or groups, and to identify, for the first time, thirteen simple phenolic acids in this by-product. The sample antioxidant capacity was determined by methods of 2,2-diphenyl-1-picrylhydrazyl (DPPH)and 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt (ABTS⁺) radicals direct sequestration. The hydrolyzed fraction showed a total of 63.47% in the relative abundance of the total of compounds, standing out: p-hydroxybenzoic acid (39.19%) and protocatechuic acid (3,4-dihydroxybenzoic acid) (5.62%), both from hydroxybenzoic acids and 3-(3,4-dihydroxyphenyl)lactic acid, (7.76%) hydroxycinnamic acids derivatives. In these results, the fraction rich in simple phenolic acids was obtained, attributing the prominent behavior of this matrix antioxidant activity, expressed by (IC₅₀: of 16.42 µg/mL and 6.52 µg/mL for DPPH and ABTS⁺ radicals, respectively). The research demonstrated an alternative to applicability that involves sustainability from agro-industrial. These techniques were used to detect metabolic classes and/or groups, and to identify, for the first time, thirteen simple phenolic acids in this by-product, generating a process capable of converting biomass into a bioproduct, consisting of bioactive compounds, in addition to adding value to the industrial chain.     

A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi-Hamiltonian structures

For the orthosymplectic Lie superalgebra $\text{◂⋅▸}OSP(2,2)$, we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures.