PT-Symmetric Quantum Field Theories and the Langevin Equation

Many non-Hermitian but PT-symmetric theories are known to have a real, positive spectrum, and for quantum-mechanical versions of these theories, there exists a consistent probabilistic interpretation. Since the action is complex for these theories, Monte Carlo methods do not apply. In this paper a field-theoretic method for numerical simulations of PT-symmetric Hamiltonians is presented. The method is the complex Langevin equation, which has been used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one-point and two-point Green's functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. This approach may grant insight into the formulation of a probabilistic interpretation for path integrals in PT-symmetric quantum field theories.     

Synthesis and structural characterization of N-para-ferrocenyl benzoyl amino acid ethyl esters and the X-ray crystal structures of the glycyl and (±)-2-aminobutyric acid derivative Fc-C6H4CONHCH(C2H5)CO2Et

A series of N-para-ferrocenyl benzoyl amino acid ethyl esters 1-8 have been prepared by coupling para-ferrocenyl benzoic acid with the amino acid esters using the conventional 1,3-dicyclohexylcarbodiimide (DCC), 1-hydroxybenzotriazole (HOBt) protocol. The amino acids employed in the synthesis were glycine, l-alanine, l-leucine, l-phenylalanine, β-alanine, 4-aminobutyric acid, (±)-2-aminobutyric acid and 2-aminoisobutyric acid. The compounds were fully characterized by a range of spectroscopic techniques such as NMR and mass spectrometry. In addition the X-ray crystal structures of the glycyl 1 and (±)-2-aminobutyrate 7 derivatives have been determined. Analysis of relevant fragments in crystal structures on the Cambridge Structural Database indicates a relative paucity of common fragments such as the α-aminobutyrate group in comparison to the glycyl moiety.     

Electrophoretic separation of protein kinases: altered mobility with different crosslinking agents in the presence of certain detergents

Nondenaturing polyacrylamide gel electrophoresis was used to separate protein kinases in crude extracts and subcellular fractions of murine erythroleukemic cells. The kinases were detected using an in situ phosphorylation assay. The electrophoretic patterns obtained using gel bound to GelBond and prepared with AcrylAide differed from those seen without GelBond and with N,N'-methylenebisacrylamide as cross-linker. In an attempt to improve the resolution of the bands in the membrane fractions, detergent-treated preparations were electrophoresed through gels which contained either 0.1% Triton X-100 or 0.1% Nonidet P-40. The resolution of the bands in this fraction was not, however, improved with the inclusion of the nonionic detergent in the gels. When cytosol was electrophoresed through gels containing detergent, a major band of cAMP-dependent protein kinase activity showed a marked shift in mobility. This may have been the result of a structural change, altering the shape and possibly affecting the charge on the molecule, or the enzyme may have formed aggregates with the detergent.     

Efficient immobilization of a cadmium chemosensor in a thin film: generation of a cadmium sensor prototype

[reaction: see text] The development of an ion-selective chemosensor for Cd(2+) allows generation of a "real-time" sensor. Immobilization of the chemosensor on quartz was achieved in a simple monolayer and in a thin film using a polymer intermediary. As intended, the thin film contains much more chemosensor than the monolayer and provides measurable responses to aqueous Cd(2+) concentrations below 1 microM. Alkali and alkaline earth ions do not interfere with Cd(2+) sensing; Zn(2+) and Cu(2+) are potential interferents.     

Synthetic studies toward longeracemine: a SmI2-mediated spirocyclization and rearrangement cascade to construct the 2-azabicyclo[2.2.1]heptane framework

Longeracemine, a member of the Daphniphyllum family of alkaloids contains a novel carbon framework featuring a highly functionalized 2-azabicyclo[2.2.1]heptane core as part of an overall 5/6/5/5/6/5 skeleton. A synthetic intermediate containing the core of longeracemine has been efficiently prepared by employing a stereoselective SmI₂-mediated cascade reaction to advance a 7-azabicyclo[2.2.1]heptadiene to a 2-azabicyclo[2.2.1]heptene that is functionally poised for conversion to the natural product.

A synthetic intermediate containing the core of longeracemine, that is functionally poised for conversion to the natural product, has been efficiently prepared by employing a stereoselective SmI₂-mediated cascade reaction.     

Synthesis and characterization of peptide-cationic steroid antibiotic conjugates

[reaction: see text] New cationic steroid antibiotics have been prepared by conjugating tripeptides to a triamino analogue of cholic acid. These compounds were synthesized on a solid phase in an indexed library that was screened for antibacterial activity against Gram-negative and Gram-positive bacteria. Selected compounds were synthesized on a larger scale, and minimum inhibition concentrations were measured. These results correlated very well with the screening of the indexed library of antibiotics. The most active antibiotics demonstrate a marked improvement over a related and well characterized cationic steroid antibiotic.     

Some theoretical implications of local optimization

This paper presents some theoretical results concerning the effectiveness of an approximate technique, known as local optimization, as applied to a wide class of problems.First, conditions are described under which the technique ensures exact solutions. Then, in regard to cases in which these conditions cannot be met in practice, a method is presented for estimating the probability that the approximate (locally optimal) solution delivered by such a technique is in fact the exact (globally optimal) solution.This probability may be viewed as a possible criterion of effectiveness in the design of neighborhoods for specific local optimization algorithms.     

Second-harmonic tomography of tissues

A novel noninvasive second-harmonic-generation tomographic method of mapping the structure of animal tissues by use of 100-fs laser pulses at 625nm is described. Subsurface structures were measured with this approach, which is potentially a symmetry-sensitive tool for optical histological reconstruction.