Tenth Peregrine breather solution to the NLS equation

In this paper we construct a particularly important solution to the focusing NLS equation, namely a Peregrine breather of the rank 10 which we call, P₁₀$P_{10}$ breather. The related explicit formula is given by the ratio of two polynomials of degree 110 with integer coefficients times trivial exponential factor. This formula drastically simplifies for the “initial values” namely for t=0$t=0$ or x=0$x=0$. This formula confirms a general conjecture saying that between all quasi-rational solutions of the rank N$N$ fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x=0,t=0)$(x=0,t=0)$, the P_N$P_N$ breather is distinguished by the fact that P_N(0,0)=2N+1$P_N(0,0)=2N+1$ and, in the aforementioned class of quasi-rational solutions, it is an absolute maximum. At the end we also make a few remarks concerning the rational deformations of P₁₀$P_{10}$ breather involving 2N−2$2N-2$ free real parameters chosen in a way that P_N$P_N$ breather itself corresponds to the zero values of these parameters although we have no intention to discuss the properties of these deformations here.     

A New Chemical Method to Desulfenylate Indol-3-yl Sulfides

Abstract

Desulfenylation of indol-3-yl sulfides liberates the most reactive position of the ring for further transformations. The usual procedure, utilizing Raney Nickel (P. G. Gassman, et. al., J. Am. Chem. SOC. 1974,96, 5495) offers a limited scope due to incompatibility of a number of functional groups towards the reducing agent. Based on our recent mechanistic studies of the acid-catalysed rearrangement of indol-3-yl sulfides to indol-2-yl sulfides (P. Hamel, et. al., Chem. Commun. 1989, 63; J. Org. Chem. 1992, 57, 2694), we have developed a novel, non-reductive desulfenylation method which permits easy access to 3-unsubstituted indoles bearing a wide array of substituents. Thus, 3-indolyl sulfides, readily obtained from appropriate phenylhydrazines (via Fischer indolization) or anilines (Gassman method, vide infra) are smoothly desulfenylated in good yields in trifluoroacetic acid in the presence of an appropriate nucleophilic trapping agent. Thiols proved to be very effective trapping agents and thiosalicylic acid (TSA) is a thiol of choice, being non-volatile and easily separable from reaction products.     

Preparation of the N-(2-Bromo-2-Nitroethenyl) Benzenamine: The First One-Pot Synthesis of a β-Halo-β-Nitroenamine

Bromonitromethane, triethyl orthoformate and aniline react together, in a one-flask procedure, to afford the title compound.     

Mode-I interlaminar fracture behaviour of nanoparticle modified epoxy/basalt fibre-reinforced laminates

The effect of nano-reinforcements on fracture behaviour of bulk epoxy nanocomposites and mode-I interlaminar fracture toughness of filament-wound basalt fibre-reinforced laminates was studied. Fracture energy of the bulk epoxy nanocomposites significantly increased with acrylic tri-block-copolymer addition but remained unchanged with incorporation of nanoclay. Delamination fracture toughness was not influenced by the presence of nanoparticles in the matrix. Decreasing fibre volume fraction, on the other hand, significantly improved interlaminar fracture energy. Rigid fibres in these composites constrict the stress field ahead of the crack-tip. Hence, increasing resin content enhanced composite delamination energy by increasing the capacity for matrix deformation. Interlaminar crack propagation through the composite was observed to occur mainly by interfacial failure and matrix cracking.     

Screening of Wood/Forest and Vine By-Products as Sources of New Drugs for Sustainable Strategies to Control Fusarium graminearum and the Production of Mycotoxins

Fusarium graminearum is a fungal pathogen that can colonize small-grain cereals and maize and secrete type B trichothecene (TCTB) mycotoxins. The development of environmental-friendly strategies guaranteeing the safety of food and feed is a key challenge facing agriculture today. One of these strategies lies on the promising capacity of products issued from natural sources to counteract crop pests. In this work, the in vitro efficiency of sixteen extracts obtained from eight natural sources using subcritical water extraction at two temperatures was assessed against fungal growth and TCTB production by F. graminearum. Maritime pine sawdust extract was shown to be extremely efficient, leading to a significant inhibition of up to 89% of the fungal growth and up to 65% reduction of the mycotoxin production by F. graminearum. Liquid chromatography/mass spectrometry analysis of this active extract revealed the presence of three families of phenolics with a predominance of methylated compounds and suggested that the abundance of methylated structures, and therefore of hydrophobic compounds, could be a primary factor underpinning the activity of the maritime pine sawdust extract. Altogether, our data support that wood/forest by-products could be promising sources of bioactive compounds for controlling F. graminearum and its production of mycotoxins.     

Ultraviolet properties of maximal supergravity

We argue that recent results in string perturbation theory indicate that the four-graviton amplitude of four-dimensional N=8 supergravity might be ultraviolet finite up to eight loops. We similarly argue that the h-loop M-graviton amplitude might be finite for h<7+M/2.     

CORSICA: correction of structured noise in fMRI by automatic identification of ICA components

When applied to functional magnetic resonance imaging (fMRI) data, spatial independent component analysis (sICA), a data-driven technique that addresses the blind source separation problem, seems able to extract components specifically related to physiological noise and brain movements. These components should be removed from the data to achieve structured noise reduction and improve any subsequent detection and analysis of signal fluctuations related to neural activity. We propose a new automatic method called CORSICA (CORrection of Structured noise using spatial Independent Component Analysis) to identify the components related to physiological noise, using prior information on the spatial localization of the main physiological fluctuations in fMRI data. As opposed to existing spectral priors, which may be subject to aliasing effects for long-TR data sets (typically acquired with TR >1 s), such spatial priors can be applied to fMRI data, regardless of the TR of the acquisitions. By comparing the proposed automatic selection to a manual selection performed visually by a human operator, we first show that CORSICA is able to identify the noise-related components for long-TR data with a high sensitivity and a specificity of 1. On short-TR data sets, we validate that the proposed method of noise reduction allows a substantial improvement of the signal-to-noise ratio evaluated at the cardiac and respiratory frequencies, even in the gray matter, while preserving the main fluctuations related to neural activity.