Time integration of the non-linear Galerkin method

e-mail: bosco{at}mac.cie.uva.es, frutos@mac.cie.uva.es Numerical tests are presented that, for the Kuramoto-Sivashinskyand a reaction-diffusion equation, compare the non-linear Galerkinmethod with standard pseudospectral and pure spectral Galerkindiscretizations. The results show that, for these problems,the non-linear Galerkin method is not competitive with eitherpure spectral Galerkin or pseudospectral discretizations.     

Exponential stability for a contact problem in thermoelasticity

We consider the unilateral problem for the thermoelastic equationand we show that the solution decays exponentially to zero astime goes to infinity; that is, denoting by E(t) the first-orderenergy of the system, we show that positive constants C and exist which satisfy E(t)CE(0)e^–$$$.     

Dynamic equilibria in the products of intramolecular Buchner additions of diazoketones to aryl rings bearing methoxy substituents

Rhodium carboxylate catalyzed aromatic addition reactions of a range of diazoketones bearing methoxy-substituted aryl rings have been explored. While the existence of norcaradiene-cycloheptatriene equilibria in related compounds is well established, the aromatic addition products in this study display more complex dynamic equilibria due to conjugation with the methoxy group; the experimental evidence for this is discussed in detail. In the azulenone products 21-26 derived from p-methoxy-substituted diazoketones 14-16, the diastereomers interconvert via a spiro intermediate 39. A related mechanistic process in the azulenones 43-46 derived from the o-methoxy-substituted diazoketones 17, 18 interconverts regioisomers, explaining the conflicting reports for the regioselectivity of the cyclization of diazoketone 1. With the m-methoxy-substituted diazoketone 19, involvement of the methoxy group through a different pathway results in fragmentation of the azulenone to form the tetralone 47. With the azulenones 21-26 exclusive trapping of the norcaradiene associated with the less thermodynamically stable diastereomers in a cycloadduct with N-phenylmaleimide is observed. Due to the presence of the activating methoxy substituent on the aromatic ring, the aromatic addition reactions of the diazoketones studied were not very sensitive to the nature of the rhodium catalyst.     

Complexes of the heavier alkaline Earth metals Ca, Sr, and Ba with O-functionalized phosphanide ligands

Metathesis reactions between either SrI(2) or BaI(2) and 2 equiv of the potassium phosphanide [[(Me(3)Si)(2)CH]-(C(6)H(4)-2-OMe)P]K yield, after recrystallization, the complexes [[([Me(3)Si](2)CH)(C(6)H(4)-2-OMe)P](2)M(THF)(n)] [M = Sr, n = 2 (5); Ba, n = 3 (6)]. Similar metathesis reactions between MI(2) and 2 equiv of the more sterically demanding potassium phosphanide [[(Me(3)Si)(2)CH](C(6)H(3)-2-OMe-3-Me)P]K yield the chemically isostructural complexes [[([Me(3)Si](2)CH)(C(6)H(3)-2-OMe-3-Me)P](2)M(THF)(2)] [M = Ca (9), Sr (7), Ba (8)]. Compounds 5-9 have been characterized by multi-element NMR spectroscopy and X-ray crystallography. Complex 9 is thermally unstable and decomposes at room temperature to give the tertiary phosphane [(Me(3)Si)(2)CH](C(6)H(3)-2-OMe-3-Me)P(Me) and an unidentified Ca-containing product. Compounds 5 and 6 also decompose at elevated temperatures to give the corresponding tertiary phosphane [(Me(3)Si)(2)CH](C(6)H(4)-2-OMe)P(Me) and intractable metal-containing products. The decomposition of 5, 6, and 9 suggests that these compounds undergo an intramolecular methyl migration from the O atom in one phosphanide ligand to the P atom of an adjacent phosphanide ligand to give species containing dianionic alkoxo-phosphanide ligands.     

New 1- and 2-dimensional polymeric structures of cyanopyridine complexes of Ag(I) and Cu(I)

Polymeric transition metal chalcogenides have attracted much attention because of their possible unusual properties directly derived from their extended structures. The molecules n-cyanopyridine (n = 2, 3, and 4) and pyridine-3,4-dicarbonitrile are found to function as bidentate or monodentate (only pyridine nitrogen donor atom) ligands in the coordination of silver(I) and copper(I) ions, respectively. The mode of coordination depends on the anion and the crystallization conditions and has been elucidated in all cases by single-crystal X-ray crystallography. We report here the syntheses, structural characterization, and electrical properties of six new polymers, [Ag(2)(2-cyanopyridine)(2)(NO(3))(2)](n)(1), [Ag(4)(3-cyanopyridine)(8)(SiF(6))(2)(H(2)O)(2)](n) (2), [Ag(3-cyanopyridine)(2)(NO(3))](n)(3), [Ag(pyridine-3,4-dicarbonitrile)(2)(NO(3))](n)(4), [Cu(I)(4-cyanopyridine)(2)(SCN)](n)(5), and [Cu(I)(pyridine-3,4-dicarbonitrile)(2)(SCN)](n)(6). Compounds 1 and 2 exhibit novel two-dimensional networks, while 3-6 have one-dimensional chain structures, in which 3 is a single-stranded helix. Room-temperature conductivities of 1, 2, 4, and 6 have been measured and are 3.1 x 10(-)(7), 2.7 x 10(-)(7), 7.4 x 10(-)(6), and 4.3 x 10(-)(5) S.cm(-)(1), respectively. The effect of temperature on the conductivities has been investigated.     

龙爪芦荟和库拉索芦荟中微量锗的测定与红外光谱区别

采用吸光光度法对龙爪芦荟和库拉索芦荟中的微量锗进行了测定,并探讨了两种芦荟的红外光谱的区别。结果表明,龙爪芦荟中含锗量在26.1～28.6μg·g-1,回收率为91.6%～97 5%。库拉索芦荟中含锗量在16.8～20.0μg·g-1,回收率为87.1%～94.5%。两种芦荟的FT IR光谱图在2100cm-1处有明显差异,由此可区别两种芦荟。     

Development of an enantioselective synthetic route to neocarzinostatin chromophore and its use for multiple radioisotopic incorporation

A convergent, enantioselective synthetic route to the natural product neocarzinostatin chromophore (1) is described. Synthesis of the chromophore aglycon (2) was targeted initially. Chemistry previously developed for the synthesis of a neocarzinostatin core model (4) failed in the requisite 1,3-transposition of an allylic silyl ether when applied toward the preparation of 2 with use of the more highly oxygenated substrates 27 and 54. An alternative synthetic plan was therefore developed, based upon a proposed reduction of the epoxy alcohol 58 to form the aglycon 2, a transformation that was achieved in a novel manner, using a combination of the reagents triphenylphosphine, iodine, and imidazole. The successful route to 1 and 2 began with the convergent coupling of the epoxydiyne 15, obtained in 9 steps (43% overall yield) from D-glyceraldehyde acetonide, and the cyclopentenone (+)-14, prepared in one step (75-85% yield) from the prostaglandin intermediate (+)-16, affording the alcohol 22 in 80% yield and with > or =20:1 diastereoselectivity. The alcohol 22 was then converted into the epoxy alcohol 58 in 17 steps with an average yield of 92% and an overall yield of 22%. Key features of this sequence include the diastereoselective Sharpless asymmetric epoxidation of allylic alcohol 81 (98% yield); intramolecular acetylide addition within the epoxy aldehyde 82, using Masamune's lithium diphenyltetramethyldisilazide base (85% yield); selective esterification of the diol 84 with the naphthoic acid 13 followed by selective cleavage of the chloroacetate protective group in situ to furnish the naphthoic acid ester 85 in 80% yield; and elimination of the tertiary hydroxyl group within intermediate 88 using the Martin sulfurane reagent (79% yield). Reductive transposition of the product epoxy alcohol (58) then formed neocarzinostatin chromophore aglycon (2, 71% yield). Studies directed toward the glycosylation of 2 focused initially on the preparation of the N-methylamino --> hydroxyl replacement analogue 3, an alpha-D-fucose derivative of neocarzinostatin chromophore, formed in 42% yield by a two-step Schmidt glycosylation-deprotection sequence. For the synthesis of 1, an extensive search for a suitable 2'-N-methylfucosamine glycosyl donor led to the discovery that the reaction of 2 with the trichloroacetimidate 108, containing a free N-methylamino group, formed the alpha-glycoside 114 selectively in the presence of boron trifluoride diethyl etherate. Subsequent deprotection of 114 under mildly acidic conditions then furnished the labile chromophore (1). The synthetic route was readily modified for the preparation of singly and doubly (3)H- and (14)C-labeled 1, compounds unavailable by other means, for studies of the mechanism of action of neocarzinostatin in vivo.     

Statistical validation of classification and calibration models using bootstrapped Latin partitions

Unbiased evaluation of classification and calibration methods is important, especially as these methods are applied to increasingly complex data sets that are under-determined. Precision bounds, such as confidence intervals, are required for interpreting any experimental result. Using bootstrapped Latin partitions to evaluate classification and calibration models, bounds on the average predictions were obtained. These bounds characterize sources of variation attributed to building the model and the composition of the training set with respect to the test set. Furthermore, precision bounds on the average of the model-variable loadings allow the significance of characteristic features to be estimated. The procedure for bootstrapped Latin partitions is given and demonstrated with synthetic data sets for classification using linear discriminant analysis and fuzzy rule-building expert systems, and for calibration using partial least squares regression with one and three properties. All analyses were implemented on a personal computer with the longest evaluation requiring 6-h processing time. Analysis of variance and matched sample t-tests were also used to demonstrate the statistical power of these tests.