Extensions and generalizations of a theorem of Widder and of the theory of symmetric local semigroups

The theory of symmetric local semigroups due to A. Klein and L. Landau (J. Funct. Anal.44 (1981), 121–136) is generalized to semigroups indexed by subsets of $\text{R}$ⁿ for n > 1. The result implies a similar result of A. E. Nussbaum (J. Funct. Anal.48 (1982), 213–223). It is further generalized to semigroups that are symmetric local in some directions and unitary in others. The results are used to give a simple proof of A. Devinatz's (Duke Math. J.22 (1955), 185–192) and N. I. Akhiezer's (“the Classical Moment Problem and Some Related Questions,” Hafner, New York, 1965) generalization of a theorem of Widder concerning the representation of functions as Laplace integrals. This result is extended to the representation as a Laplace integral of a function taking values in $\text{B}$($\text{R}$), the set of bounded linear operators on a Hilbert space $\text{R}$. Also, a theorem is proved encompassing both the result of Devinatz and Akhiezer, and Bochner's theorem on the representation of positive definite functions as Fourier integrals.     

Finding pathways between distant local minima

We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the strategy for choosing successive pairs of local minima that serve as endpoints for the next search. We employ Dijkstra's algorithm [E. W. Dijkstra, Numer. Math. 1, 269 (1959)] to identify the "shortest" path corresponding to missing connections within an evolving database of local minima and the transition states that connect them. The metric employed to determine the shortest missing connection is a function of the minimized Euclidean distance. We present applications to the formation of buckminsterfullerene and to the folding of various biomolecules: the B1 domain of protein G, tryptophan zippers, and the villin headpiece subdomain. The corresponding pathways contain up to 163 transition states and will be used in future discrete path sampling calculations.     

Synthesis of 2-carboxy-4-methylazetidine. A novel isomeric analog of dl-proline

L-Azetidine-2-carboxylic acid is a naturally occurring azetidine currently used in the synthesis of abnormally high molecular weight polypeptides. The synthesis of 2-carboxy-4-methylazetidine is now reported which is a novel isomeric analog of dl -proline. Reaction of α,β-dibromo carbonyl ester with three molar equivalents of benzylamine yields 1-benzyl-2-carbomethoxy-4-methyl-azetidine. Hydrolysis of the latter compound with barium hydroxide yields 1-benzyl-2-carboxyl-4-methylazetidine which, if subjected to catalytic hydrogenation., yields the title compound in practical yield. The cis configuration is tentatively assigned to the title compound on the basis of previously published arguments.     

Improved detection of multi-phosphorylated peptides in the presence of phosphoric acid in liquid chromatography/mass spectrometry

In contrast to lower phosphorylation states (e.g. the tryptic monophosphopeptide FQpSEEQQQTEDELQDK from bovine beta-casein), the specific detection of multi-phosphorylated peptides (e.g. the tetraphosphopeptide RELEELNVPGEIVEpSLpSpSpSEESITR from tryptic digestion of bovine beta-casein) has often been problematic for liquid chromatographic mass spectrometric (LC/MS) analysis owing to their high affinity for adsorption to exposed surfaces. We observed an enhancement in the overall detection of phosphopeptides on addition of phosphoric acid (0.1-1.0%) to the sample solution; a 10-fold increase in sensitivity was determined for the detection of two tryptic phosphopeptides and also a significant improvement in the detection of the tetraphosphopeptide. Using capillary LC with ion trap tandem MS for detection and identification, the achievable detection limits were 50 fmol and 50 pmol for the monophosphopeptide and the tetraphosphopeptide, respectively. Phosphoric acid is believed to act as a blocking agent to available silanol groups on both the silica capillary surface and the C(18)-bonded stationary phase silica surface.     

Matrix-isolation-FTIR spectroscopy with an integrating sphere

The use of an integrating sphere for the measurement of absorption spectra of thin films is described. The thin film (for example a rare gas matrix) is grown directly on the inside surface of the sphere. Multiple reflections inside the integrating sphere lead to significant enhancement of weak absorptions of the film, increasing the sensitivity of such measurements.     

Error bounds for continued fractionsK(1/b n)

Summary A priori truncation error bounds are obtained for continued fractions of the formK(1/b _n),b _n complex. The error bounds are easily applied to the case whenb _n0 asn. A numerical example involving the complex error function is given.     

Planar electrochromatography

Recent developments in planar electrochromatography (PEC) in both the normal-phase and the reversed-phase modes, and at both atmospheric and elevated pressure, are reviewed. Other forced-flow techniques in planar chromatography are also briefly covered. Mobile phase migration in PEC is primarily due to electroosmotic flow, which is controlled by the applied electric field. Capillary mediated flow is an important secondary contributor to migration, and occurs because the layer is unsaturated as a consequence of liquid evaporating from the layer due to Joule heating. The magnitude of the electric field and the concentration of ions in solution are important variables that control both electroosmotic flow and Joule heating. Separations are faster and more efficient than those obtained by conventional planar chromatography, provided appropriate experimental conditions are selected. With inappropriate conditions, either mobile phase accumulates on the surface of the sorbent layer, or Joule heating causes excessive evaporation. The former results in poor spot shape, and the latter can cause the layer to dry. Good separations are obtained when there is a balance between these two effects. The problems associated with mobile phase accumulating on the surface of the sorbent layer, and with excessive evaporation of mobile phase, do not occur with pressurized planar electrochromatography. This technique is performed at high pressure, under conditions that allow heat to be removed form the sorbent layer. This allows the use of a substantially higher electric field than in PEC, and results in a high mobile phase flow rate.     

Intermolecular interactions in pi-stacked conjugated molecules. Synthesis,structure, and spectral characterization of alkyl bithiazole oligomers

Syntheses are reported of new 4,4'-dialkyl-2,2'-bithiazole oligomers that have alkenoxy side chains that are capable of easy conversion to oligomers with functionalized side chains, e.g., terminally substituted hydroxy chains. The crystal structures of two representative oligomers (4,4',4' ',4' "-tetra-(2-propenoxymethyl)-2,2',5',5' ',2' ',2' "-quaterthiazole (3P2) and 4,4',4' ',4' "-tetra-(3-hydroxypropyloxymethyl)-2,2',5',5' ',2' ',2' "-quaterthiazole (3H2)) were determined; 3P2 crystallizes in a pi-stacked motif with two molecules per unit cell, whereas 3H2 forms pi-stacks that are linked with hydrogen bonds to form infinite two-dimensional sheets with one molecule per unit cell. A comparison of the UV-vis spectra of the compounds in solution and in the solid state provides unequivocal evidence for the presence of a Davydov splitting, W(D) approximately 0.2 eV, in solid 3P2. The spectra are interpreted in the framework of molecular exciton theory to extract a value of the intermolecular transfer integral, J approximately 0.2 eV, for a total exciton bandwidth of ca. 0.8 eV. Monte Carlo calculations were used to determine the density of states of the exciton band and the absorption and emission line shapes of the 0 <-- 0 transition. It is suggested that the "three-humped" absorption profile typical of partially crystalline, regioregular polymers is the "optical signature" of pi-stacking.     

Photoinduced electron transfer at liquid|liquid interfaces. Part VII. Correlation between self-organisation and structure of water-soluble photoactive species

The self-organisation of a variety of dyes at the water|1,2-dichloroethane interface was studied by admittance measurements, photocurrent–potential curves and light polarisation anisotropy of the photocurrent. The heterogeneous photo-oxidation of ferrocene was studied at interfaces sensitised by Sn(IV) meso-tetra-(4-carboxyphenyl) porphyrin dichloride (SnTPPC), chlorin e-6, protoporphyrin IX (protoIX) and Fe(III) protoporphyrin IX chloride (Fe-protoIX). Cyclic voltammograms and capacitance voltage curves exhibit different features associated with the self-assembly of the dye species at the liquid|liquid boundary. In the case of SnTPPC, the capacitance curves displayed the characteristic responses commonly associated with the specific adsorption of ionic species. On the other hand, chlorin e-6, protoIX and Fe-protoIX show rather complex behaviour suggesting not only changes in the excess charge but also in the dielectric permittivity of the interface. Differences in the photocurrent efficiency were also observed under the same experimental conditions. The relative magnitude of the photocurrent responses were rationalised in terms of the phenomenological electron transfer rate constant, the photon capture cross-sections and the lifetime of the triplet state as obtained from nanosecond flash photolysis. Finally, the average molecular orientation of the adsorbed photoactive species was estimated from the photocurrent dependence on the angle of light polarisation in total internal reflection. The results show a clear correlation between the orientation of the transition dipole and the distribution of the peripheral carboxyl groups responsible for the hydrophilic nature of the dyes.     

Forbidden matrix proton spin flip satellites in trapped electron EPR spectra

Observation of the 35 GHz EPR spectrum of γ-irradiated 10 M NaOH/H₂O and 10 M NaOD/D₂O glassy ices at 77°K has revealed proton spin flip satellites associated with the trapped elctron EPR line. This suggests that forbidden satellite transitions contribute to the lineshape of the trapped electron line in the 9 GHz spectrum which has commonly been studied.