The Causal Boundary of Spacetimes Revisited

We present a new development of the causal boundary of spacetimes, originally introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime (or, more generally, a chronological set), we reconsider the GKP ideas to construct a family of completions with a chronology and topology extending the original ones. Many of these completions present undesirable features, like those which appeared in previous approaches by other authors. However, we show that all these deficiencies are due to the attachment of an “excessively big” boundary. In fact, a notion of “completion with minimal boundary” is then introduced in our family such that, when we restrict to these minimal completions, which always exist, all previous objections disappear. The optimal character of our construction is illustrated by a number of satisfactory properties and examples.     

New fungal metabolite geranylgeranyltransferase inhibitors with antifungal activity

Geranylgeranyltransferase I (GGTase I) catalyzes the post-translational transfer of lyophilic diterpenoid geranylgeranyl to the cysteine residue of proteins terminating with a CaaX motif such as Rho1p and Cdc42p. It has been shown that GGTase I activity is essential for viability of Saccharomyces cerevisiae and hence its inhibition is a potential antifungal target. From natural product screening, a number of azaphilones including one novel analog were isolated as broad-spectrum inhibitors of GGTase I. Isolation, structure elucidation, GGTase I inhibitory activities and antifungal activities of these compounds are described.     

Size exclusion chromatographic cleanup for GC/MS determination of organophosphorus pesticide residues in household and vehicle dust

Size exclusion chromatography (SEC) was used as a cleanup method for the analysis of organophosphorus pesticides in household and vehicle dusts. The pesticides investigated were diazinon, methyl parathion, chlorpyrifos, malathion, phosmet, and azinphosmethyl. These compounds are of interest due to their use in agricultural tree fruit production and/or urban pest control. Pesticides were determined via gas chromatography/mass spectrometry with selected-ion monitoring and cool on-column injection. The lower limit of method validation was 0.20 microg/g. Method limits of detection in dust ranged from 0.012-0.055 microg/g. Dust samples were collected with vacuums from the homes and vehicles of people living and working in a rural agricultural region in the central part of Washington State. The analytes were extracted from the dust by sonication in acetone. The extracts were solvent-exchanged to cyclohexane, frozen, thawed, and centrifuged prior to SEC injection. Following SEC, the eluent was split into 2 fractions, concentrated, and injected on-column into the gas chromatograph. This method represents the first complete publication describing the SEC cleanup of organophosphorus pesticides in dusts. Recoveries of pesticides in dusts ranged from 63.5-110.8 +/- 4.9-19.6% over a fortification range of 0.20-10.00 microg/g. This optimized, automated, and reproducible SEC method does not require further treatment or cleanup for trace determination of these organophosphorus pesticides.     

The charge neutrality point in covalent semiconductor surfaces

The electronic surface density of states in the entire energy spectrum is studied for a covalent semiconductor. A one-dimensional model has been firstly analyzed. The results are generalized for the (111)-surface, and it is shown that when an abrupt potential is placed between ions, the only surface band should be half occupied, in agreement with Shockley. However, this no longer holds for a more general situation.     

A quadratic Bolza-type problem in a Riemannian manifold

A classical nonlinear equation on a complete Riemannian manifold is considered. The existence of solutions connecting any two points is studied, i.e., for T>0 the critical points of the functional with x(0)=x₀,x(T)=x₁. When the potential V has a subquadratic growth with respect to x, J_T admits a minimum critical point for any T>0 (infinitely many critical points if the topology of is not trivial). When V has an at most quadratic growth, i.e., , this property does not hold, but an optimal arrival time T(λ)>0 exists such that, if 0<T<T(λ), any pair of points in can be joined by a critical point of the corresponding functional. For the existence and multiplicity results, variational methods and Ljusternik-Schnirelman theory are used. The optimal value is fulfilled by the harmonic oscillator. These ideas work for other related problems.     

On positive strictly singular operators and domination

We study the domination problem by positive strictly singular % operators between Banach lattices. Precisely we show that if E and %F are two Banach lattices such that the norms on E' and F are %order continuous and E satisfies the subsequence splitting property, %and %0S T : E F are two positive operators, then T strictly %singular implies S strictly singular. The special case of %endomorphisms is also considered. Applications to the class of %strictly co-singular (or Pelczynski) operators are given too.     

The sonar beam pattern of a flying bat as it tracks tethered insects

This paper describes measurements of the sonar beam pattern of flying echolocating bats, Eptesicus fuscus, performing various insect capture tasks in a large laboratory flight room. The beam pattern is deduced using the signal intensity across a linear array of microphones. The positions of the bat and insect prey are obtained by stereoscopic reconstruction from two camera views. Results are reported in the form of beam-pattern plots and estimated direction of the beam axis. The bat centers its beam axis on the selected target with a standard deviation (sigma) of 3 degrees. The experimental error is +/- 1.4 degrees. Trials conducted with two targets show that the bat consistently tracks one of the targets with its beam. These findings suggest that the axis of the bat sonar beam is a good index of selective tracking of targets, and in this respect is analogous to gaze in predominantly visual animals.     

Molecular interactions of new pregnenedione derivatives

The in vitro inhibitory activity of five new progesterone derivatives: 17alpha-hydroxy-16beta-methylpregna-1,4,6-triene-3,20-dione 1; 16beta-methyl-17alpha-toluoyloxypregna-1,4,6-triene-3,20-dione 2; 17alpha-hydroxy-6-methylenepregn-4-ene-3,20-dione 3; 6-methylene-17alpha-toluoyloxypregn-4ene-3,20-dione 4 and 17alpha-(p-bromobenzoyloxy)-6-methylenepregn-4-ene-3,20-dione 5 was determined. These compounds were evaluated as 5alpha-reductase inhibitors as well as antagonists for the androgen receptor. Compounds 1, 2, 3, 4 and 5 showed the following inhibitory activity for the 5alpha-reductase enzyme with IC(50) values of: 1 (1.65 microM), 2 (10 microM), 3 (19 nM), 4 (100 nM) and 5 (100 nM). The results of this study also showed the effect of increasing concentrations of the novel steroids upon [(3)H]dihydrotestosterone binding to androgen receptors from male hamster prostate. The K(i) values for compounds 1, 2, 3, 4, 5 and dihydrotestosterone showed the following order of affinity for the androgen receptor: 4>5>dihydrotestosterone>2>3>1. The overall data indicated that all synthesized compounds 1, 2, 3, 4 and 5 are inhibitors of the 5alpha-reductase enzyme present in the hamster prostate. In addition compounds 1, 2, 3, 4 and 5 also presented an affinity for the androgen receptor.     

Characterization of the low-energy electronic excited States of benzoyl-substituted ferrocenes

Resonance Raman spectroscopy has been employed to probe the excited-state distortions associated with the low-energy electronic transition of benzoylferrocene and 1,1'-dibenzoylferrocene. Resonance intensity enhancement of in-plane ligand modes, in general, and the carbonyl stretching mode, in particular, supports the proposal that the excited state populated by this transition contains appreciable metal-to-ligand charge transfer character. The redistribution of charge that occurs upon populating this state weakens the metal-ring bonding and facilitates the loss of a benzoylcyclopentadienide anion. This photochemical reaction has been investigated by an on-line electrospray ionization mass spectrometry technique that allows direct detection of primary and secondary products with solution lifetimes down to the millisecond range.     

Structure-based design of carboxybiphenylindole inhibitors of the ZipA-FtsZ interaction

Structural features of two weak inhibitors of the ZipA-FtsZ protein-protein interaction which were found to bind to overlapping but different areas of the key binding site were combined in one new series of carboxybiphenyl-indoles with improved inhibitory activity.