Efficient synthesis of enantiomerically pure alpha-alkyl cyclopropanecarbonitrile derivatives from pyrazolines

[reaction: see text] Thermolysis of enantiopure sulfonyl pyrazolines 4 and 5, easily obtained from (Z)-3-p-tolylsulfinylacrylonitriles (1), afforded sulfonyl cyclopropanes (6, 7) in a completely stereoselective manner in almost quantitative yields. Both cyclopropanes and alkylidenecyclopropanes, containing one or two chiral carbon atoms, one of them being quaternary, were obtained by hydrogenolysis of the C-S bonding and under the conditions reported by Julia, respectively. The highly stereoselective extrusion of nitrogen suggests a concerted mechanism.     

N-(phenylthio)-epsilon-caprolactam: a new promoter for the activation of thioglycosides

N-(phenylthio)-epsilon-caprolactam (1) has been applied as a new promoter for the activation of thioglycosides. This proceeds by the reaction of 1 with trifluoromethansulfonic anhydride, which subsequently activates the thioglycoside for glycosidic bond formation. Notably, the reaction proceeds efficiently at room temperature and is adaptable to our reactivity-based one-pot oligosaccharide synthesis. [reaction: see text]     

On the Almost Intersections of Transient Brownian Motions

Let {B ₁ ^d (t)} and {B ^d ₂(t)} be independent Brownian motions in R ^d starting from 0 and nx respectively, and let w ^d _i (a,b) ={xR ^d : B ^d _i (t)=x for some t(a,b)}, i=1,2. Asymptotic expressions as n for the probability of dist(w ^d ₁(n ² t ₁, n ² t ₂), w ₂ ^d (0,n ² t ₃))1 with d4, respectively for the probability of dist(w ₁ ⁴(n ² t ₁,n ² t ₂),w ₂ ⁴(0,n ² t ₃))1 are obtained. As an application, an improvement of a result due to M. Aizenman concerning the intersections of Wiener sausages in R ⁴ is presented.     

Generalized phase diversity for wave-front sensing

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.     

Does the Schulman's titration of microemulsions really provide meaningful parameters?

In 1955, Bowcott and Schulman coined the term microemulsions and, in passing, proposed a cosurfactant titration of interfaces tailored for water-in-oil systems (Bowcott, J. E.; Schulman, J. H. Z. Elektrochem. 1955, 59, 283). This procedure, elegant and inexpensive, is accomplished by dilution with both oil and cosurfactant up to the onset of microemulsion formation. The rationale they proposed for this method should furnish, with high accuracy, the composition of reverse micelles and continuous bulk in the presence of cosurfactant partition. The present paper demonstrates, by means of pulsed gradient spin-echo NMR, that the Schulman's titration quantitatively describes the cosurfactant partition and that the titration path really corresponds to a dilution path for reverse micelles (at constant composition) dispersed in a continuous bulk (at constant composition).     

Supermassive Black Holes May Be Limited by the Holographic Bound

Supermassive Black Holes are the most entropic objects found in the universe. The Holographic Bound (HB) to the entropy is used to constrain their formation time with initial masses 10^6–8 M , as inferred from observations. We find that the entropy considerations are more limiting than causality for this direct formation. Later we analyze the possibility of SMBHs growing from seed black holes. The growth of the initial mass is studied in the case of accretion of pure radiation and quintessence fields, and we find that there is a class of models that may allow this metamorphosis. Our analysis generalizes recent work for some models of quintessence capable of producing a substantial growth in a short time, while simultaneously obeying the causal and Holographic Bound limits.     

Power-law time distribution of large earthquakes

We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.     

Intersection Local Times of Independent Brownian Motions as Generalized White Noise Functionals

A 'chaos expansion' of the intersection local time functional of two independent Brownian motions in R ^d is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their L ^p -properties are discussed. An important tool for deriving the chaos expansion is a computation of the 'S-transform' of the corresponding regularized intersection local times and a control about their singular limit.