An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Soulamarin, a new coumarin from stem bark of Calophyllum soulattri

The extracts of the stem bark of Calophyllum soulattri gave a new pyranocoumarin, soulamarin (1), together with five other xanthones caloxanthone B (2), caloxanthone C (3), macluraxanthone (4), trapezifolixanthone (5) and brasixanthone B (6) one common triterpene, friedelin (7), and the steroidal triterpene stigmasterol (8). The structures of these compounds were established based on spectral evidence (1D and 2D NMR).     

<em>Mesua beccariana </em>(Clusiaceae), A Source of Potential Anti-cancer Lead Compounds in Drug Discovery

An investigation on biologically active secondary metabolites from the stem bark of Mesua beccariana was carried out. A new cyclodione, mesuadione (1), along with several known constituents which are beccamarin (2), 2,5-dihydroxy-1,3,4-trimethoxy anthraquinone (3), 4-methoxy-1,3,5-trihydroxyanthraquinone (4), betulinic acid (5) and stigmasterol (6) were obtained from this ongoing research. Structures of these compounds were elucidated by extensive spectroscopic methods, including 1D and 2D-NMR, GC-MS, IR and UV techniques. Preliminary tests of the in vitro cytotoxic activities of all the isolated metabolites against a panel of human cancer cell lines Raji (lymphoma), SNU-1 (gastric carcinoma), K562 (erythroleukemia cells), LS-174T (colorectal adenocarcinoma), HeLa (cervical cells), SK-MEL-28 (malignant melanoma cells), NCI-H23 (lung adenocarcinoma), IMR-32 (neuroblastoma) and Hep-G2 (hepatocellular liver carcinoma) were carried out using an MTT assay. Mesuadione (1), beccamarin (2), betulinic acid (5) and stigmasterol (6) displayed strong inhibition of Raji cell proliferation, while the proliferation rate of SK-MEL-28 and HeLa were strongly inhibited by stigmasterol (6) and beccamarin (2), indicating these secondary metabolites could be anti-cancer lead compounds in drug discovery.     

Isolation and structural modifications of ananixanthone from Calophyllum teysmannii and their cytotoxic activities

Two naturally occurring xanthones, ananixanthone (1) and β-mangostin (2), were isolated using column chromatographic method from the n-hexane and methanol extracts of Calophyllum teysmannii, respectively. The major constituent, ananixanthone (1), was subjected to structural modifications via acetylation, methylation and benzylation yielding four new xanthone derivatives, ananixanthone monoacetate (3), ananixanthone diacetate (4), 5-methoxyananixanthone (5) and 5-O-benzylananixanthone (6). Compound 1 together with its four new derivatives were subjected to MTT assay against three cancer cell lines; SNU-1, K562 and LS174T. The results indicated that the parent compound has greater cytotoxicity capabilities against SNU-1 and K562 cell lines with IC₅₀ values of 8.97 ± 0.11 and 2.96 ± 0.06 μg/mL, respectively. Compound 5 on the other hand exhibited better cytotoxicity against LS174T cell line with an IC₅₀ value of 5.76 ± 1.07 μg/mL.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.