Criticality of the exponential rate of decay for the largest nearest-neighbor link in random geometric graphs

Let n points be placed independently in d-dimensional space according to the density f(x) = A(d)e(-lambda parallel to x parallel to alpha), lambda, alpha > 0, x is an element of R-d, d >= 2. Let d(n) be the longest edge length of the nearest-neighbor graph on these points. We show that (lambda(-1) log n)(1-1/alpha) d(n) - b(n) converges weakly to the Gumbel distribution, where b(n) similar to ((d - 1)/lambda alpha) log log n. We also prove the following strong law for the normalized nearest-neighbor distance (d) over tilde (n) = (lambda(-1) log n)(1-1/alpha) d(n)/log log n: (d - 1)/alpha lambda <= lim inf(n ->infinity) (d) over tilde (n) <= lim sup(n ->infinity) (d) over tilde (n) <= d/alpha lambda almost surely. Thus, the exponential rate of decay alpha = 1 is critical, in the sense that, for alpha > 1, d(n) -> 0, whereas, for alpha <= 1, d(n) -> infinity almost surely as n -> infinity.

Infinite dimensional slow modulations in a well known delayed model for cutting tool vibrations

We apply the method of multiple scales (MMS) to a well-known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the timescale of typical cutting tool oscillations. The MMS up to second order, recently developed for such systems, is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than the first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy in that plotted solutions of moderate amplitudes are visually near-indistinguishable. The advantages of the present analysis are that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space; lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS; the strong sensitivity of the slow modulation dynamics to small changes in parameter values, peculiar to such systems with large delays, is seen clearly; and though certain parameters are treated as small (or, reciprocally, large), the analysis is not restricted to infinitesimal distances from the Hopf bifurcation.

Sodium-alginate-based proton-exchange membranes as electrolytes for DMFCs

Novel mixed-matrix membranes prepared by blending sodium alginate (NaAlg) with polyvinyl alcohol (PVA) and certain heteropolyacids (HPAs), such as phosphomolybdic acid (PMoA), phosphotungstic acid (PWA) and silicotungstic acid (SWA), followed by ex-situ cross-linking with glutaraldehyde (GA) to achieve the desired mechanical and chemical stability, are reported for use as electrolytes in direct methanol fuel cells (DMFCs). NaAlg-PVA-HPA mixed matrices possess a polymeric network with micro-domains that restrict methanol cross-over. The mixed-matrix membranes are characterised for their mechanical and thermal properties. Methanol cross-over rates across NaAlg-PVA and NaAlg-PVA-HPA mixed-matrix membranes are studied by measuring the mass balance of methanol using a density meter. The DMFC using NaAlg-PVA-SWA exhibits a peak power-density of 68 mW cm(-2) at a load current-density of 225 mA cm(-2), while operating at 343 K. The rheological properties of NaAlg and NaAlg-PVA-SWA viscous solutions are studied and their behaviour validated by a non-Newtonian power-law.

Synthesis Of (+/-)-Beta-Cuparenone Via 3-Oxa-Beta-Cuparenone

Grignard reaction followed by ozonolysis, or ozonolysis followed by Grignard reaction on the pentenoate 8, generates the diol 9. Cyclodehydration of 9 leads to the 3-oxacuparene (6), whereas PCC oxidation furnishes the 3-oxa-beta-cuparenone (7). Methanesulfonic acid-P2O5 transforms 7 into cyclopentenones 4, 5, known precursors to beta-cuparenone (3), and the naphthalenone 14.

The effects of beta-mercaptoethanol and sodium dodecyl sulfate on the Humicola insolens beta-glucosidase

Hydrolysis of p-nitrophenyl-beta-D-glucoside by the beta-glucosidase of a thermophilic and cellulolytic fungus, Humicola insolens was stimulated by two-fold in the presence of high concentrations of beta-mercaptoethanol. This enzyme did not have any free sulfhydryl groups and high concentrations of beta-mercaptoethanol (5% v/v) reduced all of the three disulfide bonds present in the enzyme. In contrast, the hydrolysis of cellobiose and cellulose polymers was inhibited by 50% under the same conditions. Sodium dodecyl sulfate (1% w/v) even in combination with beta-mercaptoethanol did not show any significant effects on this enzyme. These unusual properties suggest that this enzyme may be of significant importance for understanding the structure of the enzyme.

The identification of 14 alpha,17 beta-dihydroxyandrost-4-en-3-one monohydrate and 14 alpha,17 beta-dihydroxyandrosta-1,4-dien-3-one monohydrate, metabolites of androstenedione in Mucor piriformis

The microorganism Mucor piriformis transforms androst-4-ene-3,17-dione into a major and several minor metabolites. X-ray crystallographic analysis of two of these metabolites was undertaken to determine unambiguously their composition and chirality. Crystals belong to the orthorhombic space-group P2(1)2(1)2(1), with a = 7.199(4) angstrom and a = 6.023(3) angstrom, b = 11.719(3) angstrom and b = 13.455(4) angstrom, c = 20.409(3) angstrom and c = 20.702(4) angstrom for the two title compounds, respectively. The structures have been refined to final R values of 0.060 and 0.040, respectively.

Ability of human chorionic gonadotropin beta-subunit to inhibit the steroidogenic response to lutropin.

Ability of the beta-subunit of human chorionic gonadotropin to inhibit the response to lutropin (luteinizing hormone, LH) was tested in the immature rat ovarian system and pregnant-mare-serum-gonadotropin-primed rat ovarian system with progesterone production being used as the response. Human chorionic gonadotropin beta-subunit was found to inhibit human and ovine lutropin-stimulated progesterone production. At a constant dose of lutropin, inhibition was dependent on the concentration of beta-subunit. When concentration of the beta-subunit was kept constant at 5.0 microgram/ml and the concentration of lutropin was varied, the inhibition was maximum at the saturating concentration of the native hormone. The alpha-subunit of the human chorionic gonadotropin did not inhibit the response to lutropin. The lutropin/beta-subunit ratio required to produce an inhibition of response was much lower than that required to bring about an observable inhibition of binding.

Biochemical and structural characterization of recombinant hyoscyamine 6 beta-hydroxylase from Datura metel L.

Hyoscyamine 6 beta-hydroxylase (H6H; EC 1.14.11.11), an important enzyme in the biosynthesis of tropane alkaloids, catalyzes the hydroxylation of hyoscyamine to give 6 beta-hydroxyhyoscyamine and its epoxidation in the biosynthetic pathway leading to scopolamine. Datura metel produces scopolamine as the predominant tropane alkaloid. The cDNA encoding H6H from D. mete! (DmH6H) was cloned, heterologously expressed and biochemically characterized. The purified recombinant His-tagged H6H from D. mete! (DmrH6H) was capable of converting hyoscyamine to scopolamine. The functionally expressed DmrH6H was confirmed by HPLC and ESI-MS verification of the products, 6 beta-hydroxyhyoscyamine and its derivative, scopolamine; the DmrH6H epoxidase activity was low compared to the hydroxylase activity. The K-m values for both the substrates, hyoscyamine and 2-oxoglutarate, were 50 mu M each. The CD (circular dichroism) spectrum of the DmrH6H indicated a preponderance of alpha-helicity in the secondary structure. From the fluorescence studies, Stern-Volmer constants for hyoscyamine and 2-oxoglutarate were found to be 0.14 M-1 and 0.56 M-1, respectively. These data suggested that the binding of the substrates, hyoscyamine and 2-oxoglutarate, to the enzyme induced significant conformational changes. (C) 2010 Elsevier Masson SAS. All rights reserved.

Time-Resolved Resonance Raman Studies on Proton-Induced Electron-Transfer Reaction from Triplet Excited State of 2-Methoxynaphthalene to Decafluorobenzophenone

In this paper time-resolved resonance Raman (TR3) spectra of intermediates generated by proton induced electron-transfer reaction between triplet 2-methoxynaphthalene ((ROMe)-R-3) and decafluorobenzophenone (DFBP) are presented The TR3 vibrational spectra and structure of 2-methoxynaphthalene cation radical (ROMe+) have been analyzed by density functional theory (DFT) calculation It is observed that the structure of naphthalene ring of ROMe+ deviates from the structure of cation radical of naphthalene