Compact High-Order Finite Differences for Interface Problems in One Dimension

This paper is concerned with the construction and analysis ofcompact finite difference approximations to the model linearsource problem –(pu')' + qu = f where the functions p,q, and f can have jump discontinuities at a finite number ofpoints. Explicit formulae that give O(h²) O(h³) and O(h⁴) accuracyare derived, and a procedure for computing three-point schemesof any prescribed order of accuracy is presented. A rigoroustruncation and discretization error analysis is offered. Numericalresults are also given.     

Eigenvalues of the difference and product of projections

There is an isomorphism between the matrices over the Boolean algebra of subsets of a k-element set and the k-tuples of Boolean binary (i.e. zero-one) matrices. This isomorphism allows many problems concerning nonbinary Boolean matrices to the referred to the binary ease. However, there are some features of the general (i.e. nonbinary) case that have not been mentioned, although they differ somewhat from the binary case. We exhibit characterizations of the linear operators that preserve several invariants of matrices over finite Boolean algebras to illustrate the differences and similarities of the general vs. the binary cases. We employ a canonical form that is useful in applying the isomorphism.     

Evolution of a lamellar domain structure for an equilibrating lyotropic liquid crystal

Aerosol OT/water exhibits a lamellar phase over a wide range of concentrations. We show, by magnetic resonance (NMR) and scanning electron microscopy (SEM), that the morphology of the lamellar phase varies significantly across that range and that the rate of equilibration depends strongly on concentration (25, 33, and 50 wt %) with, paradoxically, the faster equilibration at higher surfactant concentrations. We find that the 25 wt % sample exhibits a defect-rich local structure, characteristic of a superposed L(3) character. Further into the lamellar region, at 33 wt %, this defect-rich structure persists heterogeneously, while, at 50 wt %, the lamellar phase domains are highly ordered. The NMR methods used here included (2)H spectroscopy and the two-dimensional NMR method, diffusion-diffusion exchange spectroscopy (DEXSY). The latter was used to obtain quantitative information on the domain sizes and defects within the polydomain lamellar mesophase. Comparison of the NMR with the SEM results suggests that, at 25 wt % AOT, bilayer defects play an important role in influencing the (2)H NMR and DEXSY NMR results.     

Effects of radiation damping on Z-spectra

Radiation damping induced by the strong water magnetization in Z-spectroscopy experiments can be sufficient to perturb significantly the resultant Z-spectrum. With a probe tuned to exact electrical resonance the effects are relatively straightforward, narrowing the central feature of the Z-spectrum. Where, as is commonly the case, the probe is tuned sufficiently well to give optimum signal-to-noise ratio and radiofrequency field strength but is not at exact resonance, radiation damping introduces an unexpected asymmetry into the Z-spectrum. This has the potential to complicate the use of Z-spectrum asymmetry to study chemical exchange, for example in the estimation of pH in vivo.     

Strong Short-Range Cooperativity in Hydrogen-Bond Chains

Chains of hydrogen bonds such as those found in water and proteins are often presumed to be more stable than the sum of the individual H bonds. However, the energetics of cooperativity are complicated by solvent effects and the dynamics of intermolecular interactions, meaning that information on cooperativity typically is derived from theory or indirect structural data. Herein, we present direct measurements of energetic cooperativity in an experimental system in which the geometry and the number of H bonds in a chain were systematically controlled. Strikingly, we found that adding a second H-bond donor to form a chain can almost double the strength of the terminal H bond, while further extensions have little effect. The experimental observations add weight to computations which have suggested that strong, but short-range cooperative effects may occur in H-bond chains.     

Formation of beta-hydroxy histidine in the biosynthesis of nikkomycin antibiotics

Nikkomycins, a group of peptidyl nucleoside antibiotics produced Streptomyces tendae Tü901, are potent competitive inhibitors of chitin synthase. In this study, three nikkomycin biosynthetic enzymes, NikP1, NikQ, and NikP2, were overexpressed, purified, and characterized. The NikP1 activated L-His and transferred it to the carrier protein domain to form L-His-S-NikP1, which served as the beta-hydroxylation substrate of NikQ. The beta-OH-His was then hydrolytically released from NikP1 by NikP2. The results reported here substantiate our earlier proposal that the covalent tethering of an amino acid onto a carrier protein domain prior to downstream modification is a general strategy for diverting a fraction of the amino acid into secondary metabolism.     

Superlattices formed by electrodeposition of silver on iodine-pretreated Pt(111); studies by LEED,Auger spectroscopy and electrochemistry

Reported are studies by LEED and Auger spectroscopy of silver layers electrodeposited on well-characterized Pt(111) surfaces from aqueous solution. Prior to electrodeposition. the Pt(111) surface was treated with I₂ vapor to form the Pt(111) ($\text{7}\text{×}\text{7}$)R19.1°-I superlattice which protected the Pt and Ag surfaces from attack by the electrolyte and residual gases. Electrodeposition of silver occurred in four distinct ranges of electrode potential. Ordered layers having (3 × 3) and (18 × 18) (coincidence lattice) LEED patterns were formed at all coverages from the onset of deposition to the highest coverages studied, about twenty equivalent atomic layers. Formation of ordered Ag layers has therefore been demonstrated, at least for deposits of limited thickness. Auger spectra revealed that for deposits of a few atomic layers. The iodine layer remained attached to the surface during multiple cycles of electrodeposition and dissolution of silver from iodine-free solution. Each peak of the voltammetric current-potential scan produced a change in the LEED pattern.     

Halo- and azidodediazoniation of arenediazonium tetrafluoroborates with trimethylsilyl halides and trimethylsilyl azide and sandmeyer-type bromodediazoniation with Cu(I)Br in [BMIM][PF6] ionic liquid

Reaction of [ArN(2)][BF(4)] salts immobilized in [BMIM][PF(6)] ionic liquid (IL) with TMSX (X = I, Br) and TMSN(3) represents an efficient method for the preparation of iodo-, bromo-, and azido-derivatives via dediazoniation. The reactions can also be effected starting with ArNH(2) by in situ diazotization with [NO][BF(4)] followed by reaction with TMSX or TMSN(3). Depending on the substituents on the benzenediazonium cation, competing fluorodediazoniation (ArF formation) and hydrodediazoniation (ArH formation) were observed. Dediazoniation with TMSN(3) and with TMSI generally gave the highest chemoselectivity toward ArN(3) and ArI formation. The IL was recycled and reused up to 5 times with no appreciable decrease in the conversions. Multinuclear NMR monitoring of the interaction of [ArN(2)][BF(4)]/TMSX, [BMIM][PF6]/TMSX, and [BMIM][PF(6)]/TMSX/[ArN(2)][BF(4)] indicated that TMSF is formed primarily via [ArN(2)][BF(4)]/TMSX, generating [ArN(2)][X] in situ, which gives ArX on dediazoniation. Competing formation of ArF in Sandmeyer-type bromodediazoniation of [ArN(2)][BF(4)] with Cu(I)Br immobilized in the IL points to significant involvement of heterolytic dediazoniation.