The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

Chemical constituents from leaves and trunk bark of Rinorea oblongifolia (Violaceae)

Abstract

Two new coruleoellagic acid derivatives, 3,4′,5,5′,-tetramethylcoruleoellagic acid (1); 3′,4,4′,5,5′-pentamethylcoruleoellagic acid (2) and a new friedelane-type triterpene derivative rinol (5), were isolated from leaves and trunk bark of Rinorea oblongifolia (Violaceae) along with seven known compounds including 3,3′,4,4′,5′-pentamethylcoruleoellagic acid (3), hexamethylcoruleoellagic acid (4), 28-hydroxyfriedelin (6), friedelin (7), friedelan-3-ol (8), scopoletin (9) and β-sitosterol-3-O-β-D-glucopyranoside (10). Their structures were elucidated by means of spectroscopic methods including IR, 1D and 2D NMR in conjunction with mass spectrometry. Crude extracts of leaves and trunk bark as well as compounds 1–4 were evaluated for their antibacterial activities against 7 pathogenic bacterial strains (Streptococcus pneumoniae ATCC49619, Staphylococcus aureus ATCC 43300, Klepsiella pneumoniae ATCC 700603, Haemophilus influenza ATCC 49247, Escherichia coli ATCC 25922, Pseudomonas aeruginosa HM601, Staphylococcus aureus BAA 977). Compound (3) displayed noteworthy activity against Haemophilus influenza with MIC value of 9.38?µg/mL.     

Antimicrobial and antileishmanial xanthones from the stem bark of <Emphasis Type="Italic">Allanblackia gabonensis</Emphasis>

The phytochemical study of the stem bark of Allanblackia gabonensis has resulted in the isolation and characterization of one new xanthone derivative, named allanxanthone D, together with ten known compounds, including six xanthone derivatives, allanxanthone A, 1,5-dihydroxyxanthone, 1,7-dihydroxyxanthone and 1,3,6,7-tetrahydroxy-2-(3-methylbut-2-enyl)xanthone, forbexanthone, 6-deoxyisojacareubin, one polyisoprenylated benzophenone, guttiferone F, one flavanol, epicathechin, two phytosterols, β-sitosterol, and campesterol. The structures of these compounds were established on the basis of one- and two-dimensional NMR homo- and heteronuclear evidence. These compounds were evaluated for their activity against Leishmania amazonensis in vitro and antimicrobial activities against a range of Gram-negative and Gram-positive bacteria. Published in Khimiya Prirodnykh Soedinenii, No. 5, pp. 471–475, September-October, 2008.     

Antimicrobial and antileishmanial xanthones from the stem bark of Allanblackia gabonensis (Guttiferae)

The phytochemical study of stem bark of Allanblackia gabonensis has resulted in the isolation and characterisation of one new xanthone derivative, named allanxanthone D, together with 10 known compounds, including 6 xanthones derivatives, allanxanthone A, 1,5-dihydroxyxanthone, 1,7-dihydroxyxanthone and 1,3,6,7-tetrahydroxy-2-(3-methylbut-2-enyl)xanthone, forbexanthone, 6-deoxyisojacareubin, one polyisoprenylated benzophenone, guttiferone F, one flavanol, epicathechin, two phytosterols, beta-sitosterol and campesterol. The structures of these compounds were established on the basis of one- and two-dimensional NMR homo- and hetero-nuclear evidence. These compounds were evaluated for their activity against Leishmania amazonensis in vitro and antimicrobial activities against a range of Gram negative and Gram positive bacteria.