Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

Due to the isotropy $d$-dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. On the $R$-radius hyperboloid model of $d$-dimensional hyperbolic geometry with $R>0$ and $d\ge 2$, we compute azimuthal Fourier expansions for a fundamental solution of Laplace's equation. For $d\ge 2$, we compute a Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace's equation on this negative-constant sectional curvature Riemannian manifold. In three-dimensions, an addition theorem for the azimuthal Fourier coefficients of a fundamental solution for Laplace's equation is obtained through comparison with its corresponding Gegenbauer expansion.Comment: arXiv admin note: substantial text overlap with arXiv:1201.440

An effective one-pot access to polynuclear dispiroheterocyclic structures comprising pyrrolidinyloxindole and imidazothiazolotriazine moieties via a 1,3-dipolar cycloaddition strategy

An effective and highly regio- and diastereoselective one-pot method for the synthesis of new polynuclear dispiroheterocyclic systems with five stereogenic centers (dispiro[imidazo[4,5-e]thiazolo[3,2-b]-1,2,4-triazine-6,3′-pyrrolidine-2′,3′′-indoles]) comprising pyrrolidinyloxindole and imidazo[4,5-e]thiazolo[3,2-b]-1,2,4-triazine moieties has been developed. The method relies on a 1,3-dipolar cycloaddition of azomethine ylides generated in situ from isatin derivatives and sarcosine to 6-benzylideneimidazo[4,5-e]thiazolo[3,2-b]-1,2,4-triazine-2,7-diones

Thioterpenoids as Potential Antithrombotic Drugs: Molecular Docking, Antiaggregant, Anticoagulant and Antioxidant Activities

Natural monoterpenes and their derivatives are widely considered as effective ingredients for the design and production of new biologically active compounds with high antioxidant, antimicrobial and anti-protozoa properties. In this study, we synthesized two series of thiotherpenoids “sulfide-sulfoxide-sulfone”, with different bicyclic monoterpene skeleton (bornane and pinane) structures. The effect of the obtained compounds on platelet aggregation was investigated by using the molecular docking technique. The obtained data revealed that all the synthesized compounds may act as potential inhibitors of platelet aggregation. Moreover, the studied sulfides have shown high antioxidant activity as revealed by lipid peroxidation (LPO) process inhibition in a non-cellular substrate containing animal lipids. The sulfides were able to inhibit erythrocyte oxidative hemolysis, to reduce the accumulation of secondary LPO products in cells and to prevent the oxidation of native oxyhemoglobin. Additionally, the corresponding sulfones and sulfoxides exhibited insignificant antioxidant activity. However, the sulfides were found to exhibit significant antiaggregant and anticoagulant effects. These findings suggest as well that the sulfides could serve as a leader compound for future research and possible practical applications

Design, Spectral Characteristics, Photostability, and Possibilities for Practical Application of BODIPY FL-Labeled Thioterpenoid

This paper presents the design and a comparative analysis of the structural and solvation factors on the spectral and biological properties of the BODIPY biomarker with a thioterpene fragment. Covalent binding of the thioterpene moiety to the butanoic acid residue of meso-substituted BODIPY was carried out to find out the membranotropic effect of conjugate to erythrocytes, and to assess the possibilities of its practical application in bioimaging. The molecular structure of the conjugate was confirmed via X-ray, UV/vis-, NMR-, and MS-spectra. It was found that dye demonstrates high photostability and high fluorescence quantum yield (to ~100%) at 514–519 nm. In addition, the marker was shown to effectively penetrate the erythrocytes membrane in the absence of erythrotoxicity. The conjugation of BODIPY with thioterpenoid is an excellent way to increase affinity dyes to biostructures, including blood components