The Numerical Solution of Laplace's Equation on a Wedge

Laplace's equation is considered on regions in the plane, withthe boundary having corners; and the double-layer potentialis used to derive a solution. The essential difficulties, boththeoretically and numerically, are reduced to the case in whichthe boundary is a simple open wedge. The theoretical behaviourof the double layer integral equation is studied explicitly,and then piecewise linear and piecewise quadratic collocationmethods are applied to the numerical solution of the equation.The major question of interest is the stability of the inversesof the approximating equations. The behaviour of the numericalmethods is somewhat surprising, and it is much better than pastanalyses would have led one to expect.     

拟桶式空间的强对偶空间值的向量测度

证明了在某种紧性条件下拟桶式空间的强对偶空间值的向量测度的唯一存在性。     

Comparison of isoscalar and isovector (e,e′) M1 form factors at high momentum transfer

Electron scattering M1 form factors have been measured for the ground state and for the 2.313 MeV M1 transition in ¹⁴N. Whereas the ground-state form factor is in good accord with 1p-shell models, the data for the 2.313 MeV transition show an unexplained enhancement at high momentum transfers.     

Ab initio study of possible intermediates in the no(4Π) catalyzed geometric isomerizations of olefins

The geometries of acyclic and three-membered ring (nitroxide) H₄C₂NO radicals in their ground ²Π electronic states have been optimized completely at ab initio UHF and ROHF theoretical levels with the STO-3G and the 6-31G** basis sets. The optimizations favour the cyclic nitroxide structure energetically. However ΔE(acyclic - cyclic) at the UHF and ROHF/6-31G** levels are only 3.2 and 1.9 kcal mol^-1, respectively. Incomplete MP2/6-311G** optimizations support these results. The zero-point energy computed at the ROHF/6-31G** level for the nitroxide radical is 2.5 kcal mol^-1 higher than that for the acyclic structure, thus reversing the relative energies by 0.6 kcal mol^-1. The energies of the two radical structures, relative to the sum of those for ethylene and NO, are very close to literature values of the activation energies for the thermal, NO catalyzed geometrical isomerizations of olefins. Thus cyclic nitroxide intermediates may play a role not only in the Hg 6(³P₁) photosensitized, but also in the thermal, NO-catalyzed geometric isomerizations of olefins. Paper dedicated to Professor Otto P. Strausz; presented in part at the 75th Canadian Chemical Congress and Exhibition, Edmonton, May 31 – June 4, 1992.     

Microscale correlation between surface chemistry, texture, and the adhesive strength of Staphylococcus epidermidis

Staphylococcus epidermidis is among the most commonly isolated microbes from medical implant infections, particularly in the colonization of blood-contacting devices. We explored the relationships between surface wettability and root-mean-square roughness (Rq) on microbial adhesive strength to a substrate. Molecular-level interactions between S. epidermidis and a variety of chemically and texturally distinct model substrata were characterized using a cellular probe and atomic force microscopy (AFM). Substrata included gold, aliphatic and aromatic self-assembled monolayers, and polymeric and proteinaceous materials. Substrate hydrophobicity, described in terms of the water contact angle, was an insufficient parameter to explain the adhesive force of the bacterium for any of the surfaces. Correlations between adhesion forces and Rq showed weak relationships for most surfaces. We used an alternate methodology to characterize the texture of the surface that is based on a fractal tiling algorithm applied to images of each surface. The relative area as a function of the scale of observation was calculated. The discrete bonding model (DBM) was applied, which describes the area available for bonding interactions over the full range of observational scales contained in the measured substrate texture. Weak negative correlations were obtained between the adhesion forces and the area available for interaction, suggesting that increased roughness decreases bacterial adhesion when nano- to micrometer scales are considered. We suggest that modification of the DBM is needed in order to include discontinuous bonding. The adhesive strength is still related to the area available for bonding on a particular scale, but on some very fine scales, the bacteria may not be able to conform to the valleys or pits of the substrate. Therefore, the bonding between the bacterium and substrate becomes discontinuous, occurring only on the tops of ridges or asperities.     

Decarboxylative Cyclization of Allylic Cyclic Carbamates: Mechanism Studies and Applications to the Synthesis of Natural Products

The mechanism of decarboxylative cyclization of allylic cyclic carbamates 1 leading to 2-substituted △~3-piperidines and-pyrrolidines, as well as its applications to the total synthesis of (--)codonopsine, are described.     

Cis-UROCANIC ACID DOWN-REGULATES THE INDUCTION OF ADENOSINE 3'', 5''-CYCLIC MONOPHOSPHATE BY EITHER trans-UROCANIC ACID OR HISTAMINE IN HUMAN DERMAL FIBROBLASTS in vitro

It has been demonstrated that UVB radiation (290-320 nm) suppresses mammalian cell-mediated immunity by effecting the trans to cis isomerization of urocanic acid (UCA) in the stratum corneum, the uppermost layer of the skin. Trans-urocanic acid has been shown to be the photoreceptor for UVB-induced immune suppression and the cis-isomer has been demonstrated to be immunosuppressive. Little is known, however, about how the isomerization of UCA may affect the proximal or distal cells of the skin or the immune system. We report here that trans-UCA is biologically active in vitro in human dermal fibroblasts, inducing adenyl cyclase as measured by cAMP (adenosine 3',5'-cyclic monophosphate) formation in a dose-dependent manner similar to the action of histamine. Trans-UCA and histamine stimulate 50% of maximum activity at concentrations of 3.3 microM and 13.8 microM respectively. Cis-UCA does not increase cAMP in these human fibroblasts but actively down regulates the increase of cAMP induced by either histamine or trans-UCA. Cis-UCA down regulated the histamine response by 75% and the trans-UCA response by 60% at a concentration range of 1 mM to 1 nM. The trans-UCA induction of cAMP can also be downregulated with an H2 histamine receptor antagonist cimetidine. These results support the hypothesis that a cellular target for cis-UCA is the dermal fibroblast and the effects reported here may represent the initial biochemical and cellular event for UVB-induced immune suppression i.e. the immediate step following the isomerization of trans to cis-UCA is the down regulation of cAMP by cis-UCA. Regulation of such an important second messenger such as cAMP could then allow cascading signals to occur, leading to immune suppression.