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.     

Use of high-molecular-mass polyacrylamides as matrices for microchip electrophoresis of DNA fragments

DNA fragment analysis requires the use of polymer solutions as sieving matrices. Generally, such matrices are constituted of high-molar-weight polymers employed at a concentration higher than their entanglement threshold concentration. These polymer solutions are highly viscous and difficult to use in the narrow channels of a microchip. Ultralarge polyacrylamides synthesized via a nonconventional method, being the low-temperature plasma-induced polymerization (PIP), were used as DNA sieving matrices for microchip electrophoresis. The distinctive features of these polymers (ultralarge molecular mass and linearity) allow their use at a dilute concentration. Dilute PIP polyacrylamides revealed a constant value of resolution in a broad range of DNA fragment sizes (123 bp-1353 bp), thus proving to be effective in common genotyping applications. Moreover, the low viscosity of the dilute solutions enable it to be easier and faster in filling the channel between runs, thus enhancing the throughput of the microchip devices.     

The impedance behavior of the cell Au/HClO4 · 5.5 H2O/Au in the temperature range 4.2–300 K

The impedance of the cell Au/HClO₄-5.5 H₂O/Au was investigated in the frequency range 1 to 10⁵ Hz between 4.2 and 300 K. The analysis of the data enables an evaluation of important electrolyte properties such as conductivity and dielectric constant in a wide range of temperatures, predominantly in the solid state of the electrolyte HClO₄-5.5 H₂O (T_f = 228 K). The double layer capacity of the gold electrodes was also determined; it shows a qualitatively similar result compared with previous measurements. In the solid state, the ionic conductivity exhibits two distinct activation energies of 0.37 and 0.54 eV corresponding to the two phases present in HClO₄-5.5 H₂O above and below 170 K. Below 120 K the activation energy becomes very small and tends to zero around 80 K indicating possible tunneling processes in the rigid H₂O structure. At about the same temperature the dielectric constant reaches its low temperature limit with a value _∞ ≈ 11 which is considerably higher than the value of pure ice of _∞ ≈ 3.     

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.