A supraconvergent scheme for the Korteweg-de Vries equation

Summary A finite-difference method for the integration of the Korteweg-de Vries equation on irregular grids is analyzed. Under periodic boundary conditions, the method is shown to be supraconvergent in the sense that, though being inconsistent, it is second order convergent. However, such a convergence only takes place on grids with an odd number of points per period. When a grid with an even number of points is used, the inconsistency of the method leads to divergence. Numerical results backing the analysis are presented.     

Principal component analysis of the effects of wavefunction modification on the electrostatic potential of indole

The molecular electrostatic potential (MEP) of the indole molecule was calculated in a three‐dimensional grid in which the molecule was centered at the origin. To evaluate the dependence of MEP on the type of calculation, semiempirical, ab initio, and density functional theory methods with different basis sets were employed. The data matrix generated by these calculations was analyzed by principal component analysis (PCA). The appearance of outliers and the effect of wavefunction modifications such as the introduction of electron correlations and diffuse functions were highlighted by the use of PCA. The spatial localization of such effects around the molecule was possible from the loadings values associated with the graphical analysis of the grid points. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Molecular structure and polarity of the C3NH carbene

Ab initio MP 2/4-31G ** calculations indicate that the most stable form of C₃NH is bent and singlet and that the linear structure corresponds to a maximum. The effect of changing the CNH angle on the total energy is slight, but it is quite pronounced on the molecular polarity. The wider angle tends to increase the polarity of C₃NH. MP 2/4-31G ** calculations predict a difference of polarity between linear and bent structures of 0.8 D.     

Unusual and unexpected reactivity of t-butyl dicarbonate (Boc2O) with alcohols in the presence of magnesium perchlorate. A new and general route to t-butyl ethers

[reaction: see text] A new mild method for protecting alcohols as t-butyl ethers is reported. The reaction proceeds with Mg(ClO4)2 and Boc2O and shows general applicability. The deprotection of t-butyl ethers has also been revisited. Preliminary results indicate the CeCl3 x 7H2O/NaI system is a very suitable catalyst for their removal.     

Extended applications of electric cell-substrate impedance sensing for assessment of the structure-function of α2β1 integrin

Electric cell-substrate impedance sensing (ECIS) was applied to assess the structure-function of α2β1 integrin, receptor for collagen and laminin. On collagen-coated gold electrodes, expression of this integrin on human rhabdomyosarcoma (RD) cells (RDX2C2) yielded a five-fold increase in resistance when compared with mock transfected RD (RDpF) cells (34.5±5.2 versus 6.5±0.8 Ω/cell). An intermediate level of 16±2 Ω/cell was measured upon expression of an α2β1 mutant that lacked the α2 cytoplasmic domain (RDX2CO). On laminin, the resistance measured for RDX2C2 cells was also higher but only twice that of RDpF cells at 71±4 and 37±4 Ω/cell, respectively. In comparison, RDX2CO cells (38±4 Ω/cell), exhibiting no enhanced adhesive function, yielded a similar result to that of RDpF cells. On fibronectin, RDX2C2 and RDpF cells, exhibiting comparable levels of adhesion, were similar in resistance measurements at 85±5and 89±7 Ω/cell, respectively. It has been shown that deletion of α2 cytoplasmic domain results in dysregulated recruitment of the α2β1 mutant to focal adhesion complexes that mediate binding of fibronectin. RDX2CO cells on fibronectin, exhibiting reduced adhesive function, was associated with noticeably lower resistance (60±4 Ω/cell). Monitoring electroporation of the RD plasma membrane also indirectly validated cell attachment as reflected by the resistance measured. Results from this study demonstrated the potential of ECIS for study of the structure-function of βl integrin adhesion receptors.     

Synthesis of 2′,3′-dihydrosolanesyl analogues of β-d-arabinofuranosyl-1-monophosphoryldecaprenol with promising antimycobacterial activity

Two new hydrolytically stable analogues of β-d-arabinofuranosyl-1-monophosphoryldecaprenol, the donor substrate for mycobacterial arabinosyltransferase, have been prepared. Biological evaluation of these compounds in vitro against Mycobacterium tuberculosis H₃₇Rv strain revealed a promising activity.     

Superbase-Promoted Acylation of Hindered Alcohols

The commercially available nonionic superbase P(MeNCH(2)CH(2))(3)N (1a) is very useful for the acylation of unreactive hindered alcohols as well as acid-sensitive alcohols. The reactions proceed in high yields using an acid anhydride, and 1a can be regenerated in a single step. The relative rates for benzoylation of (+/-)-menthol in C(6)D(6) using conventional acylation reagents and strong nonionic bases are compared. In general, acetylation with 1a is accelerated in the polar solvent CH(3)CN whereas benzoylation is faster in the nonpolar solvent C(6)H(6). The benzoylation intermediate RC(O)P(MeNCH(2)CH(2))(3)N(+) was found to be in equilibrium with 1a, with lower temperatures favoring the intermediate. The relative stabilities of several known acylating intermediates are compared.     

The Michael addition of indoles to alpha,beta-unsaturated ketones catalyzed by CeCl3.7H2O-NaI combination supported on silica gel

Alkylation of indoles by means of the Michael addition has been the subject of a number of investigation. It is well established that regioselectivity in the additions of indoles to electron-deficient alkenes is strongly controlled by the reaction medium. In a continuation of the work on developing greener and cleaner technologies, the cerium(III) chloride heptahydrate and sodium iodide combination supported on silica gel catalyzes the alkylation of various indoles with alpha,beta-unsaturated ketones giving 3-(3-oxoalkyl)indole derivatives in good yields. The substitution on the indole nucleus occurred exclusively at the 3-position, and N-alkylation products have not been observed.     

Micellar effect on the electron transfer reaction of chromium(V) ion with organic sulfides

The rate of electron transfer from organic sulfides to [Cr^V(ehba)₂]⁻ (ehba-2-ethyl-2-hydroxy butyric acid) decreases with a decrease in the polarity of the medium. The anionic surfactant, SDS and the cationic surfactant, CTAB have different effects on the kinetics of this reaction. The micellar inhibition observed in the presence of SDS is probably due to the decrease in the polarity and the electrostatic repulsion faced by the anionic oxidant from the anionic micelle and the partition of the hydrophobic substrate between the aqueous and micellar phases. The micellar catalysis in the presence of CTAB is attributed to the increase in the concentration of both reactants in the micellar phase. This micellar catalysis is observed to offset the retarding effects of the less polar micellar medium and the unfavorable charge-charge interaction between the + charge developed on S center in the transition state and the cationic micelle. This catalysis is contrary to the enormous micellar inhibition observed with IO₄⁻, HSO₅⁻ and HCO₄⁻ oxidation of organic sulfides.