Exact Solutions of Covariant Wave Equations with a Multipole Source Term on Curved Spacetimes

A formalism is presented for calculating exactsolutions of covariant inhomogeneous scalar and tensorwave equations whose source terms are arbitrary ordermultipoles on a curved background spacetime. The developed formalism is based on the theory ofthe higher-order fundamental solutions for wave equationwhich are the distributions that satisfy theinhomogeneous wave equation with the corresponding order covariant derivatives of the Dirac deltafunction on the right-hand side. Like the classicalGreen's function for a scalar wave equation, thehigher-order fundamental solutions contain a direct termwhich has support on the light cone as well as a tailterm which has support inside the light cone. Knowinghow to compute the fundamental solutions of arbitraryorder, one can find exact multipole solutions of wave equations on curved spacetimes. Wepresent complete recurrent algorithms for calculatingthe arbitrary-order fundamental solutions and the exactmultipole solutions in a form convenient for practical computations. As an example we apply thealgorithm to a massless scalar wave field on aparticular Robertson-Walker spacetime.     

Synthesis of diversely functionalized hexahydropyrrolo[2,3-b]indoles using domino reactions, olefination, isomerization and Claisen rearrangement followed by reductive cyclization

Hexahydropyrrolo[2,3-b]indoles 6 were synthesized in five steps from indolin-3-one 8 by a general and efficient method, in which elements of molecular diversity were readily added onto the 3a-position of the pyrrolo[2,3-b]indole ring system. Horner-Wadsworth-Emmons reaction of 2-allyloxyindolin-3-ones 7, derived from indolin-3-one 8 and a variety of allylic alcohols, smoothly proceeded with successive Claisen rearrangement to give the corresponding 3-allyl-3-cyanomethylindolin-2-ones 15. Indolin-2-ones 15 were converted into pyrrolo[2,3-b]indoles 6 using partial hydrolysis followed by reductive cyclization with LiAlH(4). Synthesis of N-methylated pyrrolo[2,3-b]indole derivatives 23 and 26 is also described.     

Topological investigations of binary and ternary mixtures: excess isentropic compressibilities

The speed of sound, U_ij 1,3-dioxolane (D) in binary mixtures (ij) with benzene, cyclohexane, n-hexane or n-heptane and U_ijk for 1,3-dioxolane in ternary mixtures (ijk) with the same hydrocarbons have been measured as a function of composition at 298.15 K. The observed data have been utilised to evaluate excess isentropic compressibility of binary, (κ_s^E)_ij and ternary (κ_s^E)_ijk mixtures using density and speed of sound values of the binary and ternary mixtures. The Moelyn-Huggins concept of interaction between the molecular surfaces of the components of a binary mixture [Polymer 12 (1971) 389] has been extended to evaluate excess isentropic compressibility of the studied binary and ternary mixtures. It has been observed that κ_s^E values predicted by a graph-theoretical approach using connectivities of third degree for binary mixtures compare reasonably well with their corresponding experimental values and κ_s^E for ternary mixtures are of the same sign and order of magnitude.     

On some estimates and Carleson type measure for multifunctional holomorphic spaces in the unit ball

The aim of this paper is to obtain some new estimates for multifunctional holomorphic expressions by using properties of Bergman metric ball. Also we obtain some characterizations of Carleson type measure for some multifunctional holomorphic spaces defined with Bergman metric ball.     

On some new sharp estimates in analytic Herz-type function spaces in tubular domains over symmetric cones

We obtain new sharp embedding theorems for mixed-norm Herz-type analytic spaces in tubular domains over symmetric cones. These results enlarge the list of recent sharp theorems in analytic spaces obtained by Nana and Sehba (2015).     

Impact of Peels Extracts from an Italian Ancient Tomato Variety Grown under Drought Stress Conditions on Vascular Related Dysfunction

Background: Tomato by-products contain a great variety of biologically active substances and represent a significant source of natural antioxidant supplements of the human diet. The aim of the work was to compare the antioxidant properties of a by-product from an ancient Tuscan tomato variety, Rosso di Pitigliano (RED), obtained by growing plants in normal conditions (-Ctr) or in drought stress conditions (-Ds) for their beneficial effects on vascular related dysfunction. Methods: The antioxidant activity and total polyphenol content (TPC) were measured. The identification of bioactive compounds of tomato peel was performed by HPLC. HUVEC were pre-treated with different TPC of RED-Ctr or RED-Ds, then stressed with H₂O₂. Cell viability, ROS production and CAT, SOD and GPx activities were evaluated. Permeation of antioxidant molecules contained in RED across excised rat intestine was also studied. Results: RED-Ds tomato peel extract possessed higher TPC than compared to RED-Ctr (361.32 ± 7.204 mg vs. 152.46 ± 1.568 mg GAE/100 g fresh weight). All extracts were non-cytotoxic. Two hour pre-treatment with 5 µg GAE/mL from RED-Ctr or RED-Ds showed protection from H₂O₂-induced oxidative stress and significantly reduced ROS production raising SOD and CAT activity (* p < 0.05 and ** p < 0.005 vs. H₂O₂, respectively). The permeation of antioxidant molecules contained in RED-Ctr or RED-Ds across excised rat intestine was high with non-significant difference between the two RED types (41.9 ± 9.6% vs. 26.6 ± 7.8%). Conclusions: RED-Ds tomato peel extract represents a good source of bioactive molecules, which protects HUVECs from oxidative stress at low concentration.     

Total synthesis of (+/-)-flustramines A and C, (+/-)-flustramide A, and (-)- and (+)-debromoflustramines A

Here we describe the efficient total synthesis of the three title hexahydropyrrolo[2,3-b]indole alkaloids and debromo derivative from readily available indolin-3-ones using key domino reactions, olefination-isomerization-Claisen rearrangement (OIC), and reductive cyclization (RC). (+/-)-Flustramine C (5) was synthesized in five steps from 6-bromoindolin-3-one 9 via a key intermediate 13a. (+/-)-Flustramine A (1) has been obtained by reduction of flustramide A (6), which has been prepared in five steps from 13a. (+/-)-Debromoflustramine A (19) was provided in a similar manner from 13b. The (-)- and (+)-enantiomers of 19 were synthesized through optical resolution of (+/-)-carboxylic acid 17b using (R)-4-phenyloxazolidin-2-one.     

On some new sharp embedding theorems in minimal and pseudoconvex domains

We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in Cⁿ. Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are heavily based on nice properties of the r-lattice. Some results of this paper can be also obtained in some unbounded domains, namely tubular domains over symmetric cones.