Convergence of the Structure Function of a Multifractal Random Walk in a Mixed Asymptotic Setting

Some asymptotic properties of a Brownian motion in multifractal time, also called multifractal random walk, are established. We show the almost sure and L ¹ convergence of its structure function. This is an issue directly connected to the scale invariance and multifractal property of the sample paths. We place ourselves in a mixed asymptotic setting where both the observation length and the sampling frequency may go together to infinity at different rates. The results we obtain are similar to the ones that were given by Ossiander and Waymire [19 Ossiander , M. , and Waymire , E.C. 2000 . Statistical estimation for multiplicative cascades . Ann. Stat. 28 : 1533 – 1560 .[Crossref], [Web of Science ®] , [Google Scholar]] and Bacry et al. [1 Bacry , E. , Gloter , A. , Hoffmann , M. , and Muzy , J.F. Multifractal analysis in a mixed asymptotic framework . Ann. Appl. Prob. (to appear) . [Google Scholar]] in the simpler framework of Mandelbrot cascades.     

New large deviation results for some super-Brownian processes

We give large deviation results for the super-Brownian excursion conditioned to have unit mass or unit extinction time and for super-Brownian motion with constant non-positive drift. We use a representation of these processes by a path-valued process, the so-called Brownian snake for which we state large deviation principles.     

A Unique Tryptophan C‐Prenyltransferase from the Kawaguchipeptin Biosynthetic Pathway

Cyanobactins are a rapidly growing family of linear and cyclic peptides produced by cyanobacteria. Kawaguchipeptins A and B, two macrocyclic undecapeptides reported earlier from Microcystis aeruginosa NIES‐88, are shown to be products of the cyanobactin biosynthetic pathway. The 9 kb kawaguchipeptin (kgp) gene cluster was identified in a 5.26 Mb draft genome of Microcystis aeruginosa NIES‐88. We verified that this gene cluster is responsible for the production of the kawaguchipeptins through heterologous expression of the kgp gene cluster in Escherichia coli. The KgpF prenyltransferase was overexpressed and was shown to prenylate C‐3 of Trp residues in both linear and cyclic peptides in vitro. Our findings serve to further enhance the structural diversity of cyanobactins to include tryptophan‐prenylated cyclic peptides.     

MAS-NMR study of lithium zinc silicate glasses and glass-ceramics with various ZnO content

Lithium zinc silicate glasses of composition (mol%): 17.5Li₂O-(72−x)SiO₂-xZnO−5.1Na₂O−1.3P₂O₅−4.1B₂O₃, 5.5?x?17.7, were prepared by conventional melt-quenched technique and converted to glass-ceramic by controlled crystallization process. ²⁹Si and ³¹P MAS-NMR was used to characterize the structure of both glass and glass-ceramic samples. Despite the complex glass composition, Q², Q³ and Q⁴ sites are identified from ²⁹Si MAS-NMR, which relative intensities are found to vary with the ZnO content, indicating a network depolymerization by ZnO. Moreover, well separated Q³ and Q⁴ resonances for low ZnO content indicates the occurrence of phase separation. From ³¹P MAS-NMR, it is seen that phosphorus is mainly present in the form of ortho-(Q⁰) and pyro-phosphate (Q¹) structural units and variation of ZnO content did not have much effect on these resonances, which provides an additional evidence for phase separation in the glass. On conversion to glass-ceramics, lithium disilicate (Li₂Si₂O₅), lithium zinc ortho-silicate (Li₃Zn_0.5SiO₄), tridymite (SiO₂) and cristobalite (SiO₂) were identified as major silicate crystalline phases. Using ²⁹Si MAS-NMR, quantification of these silicate crystalline phases is carried out and correlated with the ZnO content in the glass-ceramics samples. In addition, ³¹P spectra unambiguously revealed the presence of crystalline Li₃PO₄ and (Na,Li)₃PO₄ in the glass-ceramics.     

17O solid-state NMR and first-principles calculations of sodium trimetaphosphate (Na3P3O9), tripolyphosphate (Na5P3O10), and pyrophosphate (Na4P2O7)

The assignment of high-field (18.8 T) (17)O MAS and 3QMAS spectra has been completed by use of first-principles calculations for three crystalline sodium phosphates, Na 3P 3O 9, Na 5P 3O 10, and Na 4P 2O 7. In Na 3P 3O 9, the calculated parameters, quadrupolar constant ( C Q), quadrupolar asymmetry (eta Q), and the isotropic chemical shift (delta cs) correspond to those deduced experimentally, and the calculation is mandatory to achieve a complete assignment. For the sodium tripolyphosphate Na 5P 3O 10, the situation is more complex because of the free rotation of the end-chain phosphate groups. The assignment obtained with ab initio calculations can however be confirmed by the (17)O{ (31)P} MAS-J-HMQC spectrum. Na 4P 2O 7 (17)O MAS and 3QMAS spectra show a complex pattern in agreement with the computed NMR parameters, which indicate that all of the oxygens exhibit very similar values. These results are related to structural data to better understand the influence of the oxygen environment on the NMR parameters. The findings are used to interpret those results observed on a binary sodium phosphate glass.     

Antioxidant,Antibacterial and Dyeing Potential of Crude Pigment Extract of Gonatophragmium triuniae and Its Chemical Characterization

Filamentous fungi synthesize natural products as an ecological function. In this study, an interesting indigenous fungus producing orange pigment exogenously was investigated in detail as it possesses additional attributes along with colouring properties. An interesting fungus was isolated from a dicot plant, Maytenus rothiana. After a detailed study, the fungal isolate turned out to be a species of Gonatophragmium belonging to the family Acrospermaceae. Based on the morphological, cultural, and sequence-based phylogenetic analysis, the identity of this fungus was confirmed as Gonatophragmium triuniae. Although this fungus grows moderately, it produces good amounts of pigment on an agar medium. The fermented crude extract isolated from G. triuniae has shown antioxidant activity with an IC₅₀ value of 0.99 mg/mL and antibacterial activity against Gram-positive bacteria (with MIC of 3.91 μg/mL against Bacillus subtilis, and 15.6 μg/mL and 31.25 μg/mL for Staphylococcus aureus and Micrococcus luteus, respectively). Dyeing of cotton fabric mordanted with FeSO₄ using crude pigment was found to be satisfactory based on visual observation, suggesting its possible use in the textile industry. The orange pigment was purified from the crude extract by preparative HP-TLC. In addition, UV-Vis, FTIR, HRMS and NMR (¹H NMR, ¹³C NMR), COSY, and DEPT analyses revealed the orange pigment to be “1,2-dimethoxy-3H-phenoxazin-3-one” (C₁₄H₁₁NO₄, m/z 257). To our understanding, the present study is the first comprehensive report on Gonatophragmium triuniae as a potential pigment producer, reporting “1,2-dimethoxy-3H-phenoxazin-3-one” as the main pigment from the crude hexane extract. Moreover, this is the first study reporting antioxidant, antibacterial, and dyeing potential of crude extract of G. triuniae, suggesting possible potential applications of pigments and other bioactive secondary metabolites of the G. triuniae in textile and pharmaceutical industry.     

New insights into the polymerization of methyl methacrylate initiated by rare-earth borohydride complexes: a combined experimental and computational approach

Polymerization of methyl methacrylate (MMA) initiated by the rare-earth borohydride complexes [Ln(BH(4))(3)(thf)(3)] (Ln=Nd, Sm) or [Sm(BH(4))(Cp*)(2)(thf)] (Cp*=eta-C(5)Me(5)) proceeds at ambient temperature to give rather syndiotactic poly(methyl methacrylate) (PMMA) with molar masses M(n) higher than expected and quite broad molar mass distributions, which is consistent with a poor initiation efficiency. The polymerization of MMA was investigated by performing density functional theory (DFT) calculations on an eta-C(5)H(5) model metallocene and showed that in the reaction of [Eu(BH(4))(Cp)(2)] with MMA the borate [Eu(Cp)(2){(OBH(3))(OMe)C=C(Me)(2)}] (e-2) complex, which forms via the enolate [Eu(Cp)(2){O(OMe)C=C(Me)(2)}] (e), is calculated to be exergonic and is the most likely of all of the possible products. This product is favored because the reaction that leads to the formation of carboxylate [Eu(Cp)(2){OOC-C(Me)(=CH(2))}] (f) is thermodynamically favorable, but kinetically disfavored, and both of the potential products from a Markovnikov [Eu(Cp)(2){O(OMe)C-CH(Me)(CH(2)BH(3))}] (g) or anti-Markovnikov [Eu(Cp)(2){O(OMe)C-C(Me(2))(BH(3))}] (h) hydroboration reaction are also kinetically inaccessible. Similar computational results were obtained for the reaction of [Eu(BH(4))(3)] and MMA with all of the products showing extra stabilization. The DFT calculations performed by using [Eu(Cp)(2)(H)] to model the mechanism previously reported for the polymerization of MMA initiated by [Sm(Cp*)(2)(H)](2) confirmed the favorable exergonic formation of the intermediate [Eu(Cp)(2){O(OMe)C=C(Me)(2)}] (e') as the kinetic product, this enolate species ultimately leads to the formation of PMMA as experimentally observed. Replacing H by BH(4) thus prevents the 1,4-addition of the [Eu(BH(4))(Cp)(2)] borohydride ligand to the first incoming MMA molecule and instead favors the formation of the borate complex e-2. This intermediate is the somewhat active species in the polymerization of MMA initiated by the borohydride precursors [Ln(BH(4))(3)(thf)(3)] or [Sm(BH(4))(Cp*)(2)(thf)].     

Effect of concentrate solution pH and mineral composition of a whey protein diluate solution on membrane fouling formation during conventional electrodialysis

The aim of this work was to study the effect of the concentrate solution pH and the composition in calcium, carbonate and protein of the diluate solution to be treated by conventional electrodialysis on the fouling of ion-exchange membranes. Conductivity, system resistance, pH of the diluate and cation migration were monitored to follow the evolution of the demineralization. Total cation migration was similar for all conditions although different forms of fouling were identified after three consecutive 100 min electrodialysis treatments. The nature of fouling and the membrane surface fouled depended on the concentrate pH value, the diluate mineral composition and the intrinsic composition of the whey isolate. Once conditions leading to membrane fouling were identified, an alternative configuration for our electrodialysis stack is proposed to prevent fouling onset.