Nonlinear compression of optical solitons

In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single field in a fiber medium with phase modulation and fibre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modified NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.     

On an evolution operator connecting Lagrangian and Hamiltonian formalisms

The unambiguous evolution operator K was recently introduced in the theory of constrained systems. By viewing K as a vector field over the Legendre transformation, we give an intrinsic characterization of it through simple and intuitive properties. Some immediate consequences are explored.     

Reductive coupling of α,β-enones I: Reduction of methyl-vinyl ketone and mesityl oxide.

Reductive coupling of methyl-vinyl ketone with TiCl₄-Mg gives pinacol $\text{1}$ (25%). According to the reducing agents, mesityl oxide yields 2,4,5,7-tetramethyl-octa-2,4,6-triene $\text{3}$ (with 4TiCl₃-LialH₄), triene $\text{3}$ or 2,4,5,7-tetramethyl-octa-2,6-dien-4,5-diol $\text{5}$ (with TiCl₄-Mg), pinacol $\text{5}$ (with VCl₃-Mg), and 2-acetyl-1,3,3,4,4-pentamethyl-cyclopentane $\text{7}$ (with CrCl₃-Mg or FeCl₃-Mg or ZrCl₄ or ZrCl₄-Mg) as major products.     

Dihydrogen complexes of electrophilic metal centers: observation of Cr(CO)5(H2), W(CO)5(H2) and [Re(CO)5(H2)]+

Photolysis of dichloromethane solutions of M(CO)6 (M = Cr, W) at low temperature in the presence of hydrogen gas affords W(CO)5(H2) (1) and Cr(CO)5(H2) (2). Complexes 1 and 2 are characterized as dihydrogen complexes based on short T1 values for the hydride resonances and a large HD coupling of 35.3 Hz (W) and 35.8 Hz (Cr) in the HD derivatives. A cationic analogue, [Re(CO)5(H2)]+ (3), was prepared by reaction of Re(CO)5Cl with [Et3Si][B(C6F5)4] in fluorobenzene under hydrogen. Complex 3-d1 exhibits JHD = 33.9 Hz. Complex 3 is strongly acidic, with complete deprotonation by diethyl ether; complexes 1 and 2 are moderately acidic. Deprotonation of 1 is complete in the presence of one equivalent of triethylamine.     

Evaluation of multiple solid-phase microextraction as a technique to remove the matrix effect in packaging analysis for determination of volatile organic compounds

Multiple solid-phase microextraction (SPME) is an useful technique for the direct quantification of solid samples removing any matrix effect. The volatile organic compounds formed in the extrusion-coating process of multilayer packaging materials have already been quantified by multiple HS-SPME coupled to gas chromatography (GC)-mass spectrometry (MS) using volatile organic compound (VOC) solutions in hexadecane for calibration. In this article, water is proposed as solvent to prepare the calibration solutions because it provides a shorter calibration time, better linearity, better reproducibility, and lower detection limits than hexadecane. Besides, the extraction of VOCs from aqueous solutions is exhaustive and avoids the extrapolations needed to calculate the total peak areas, as they can be calculated as the sum of the individual areas of each extraction. Finally, it is checked whether the two solvents provide the same mean values for the total peak areas.     

LINGO, an efficient holographic text based method to calculate biophysical properties and intermolecular similarities

SMILES strings are the most compact text based molecular representations. Implicitly they contain the information needed to compute all kinds of molecular structures and, thus, molecular properties derived from these structures. We show that this implicit information can be accessed directly at SMILES string level without the need to apply explicit time-consuming conversion of the SMILES strings into molecular graphs or 3D structures with subsequent 2D or 3D QSPR calculations. Our method is based on the fragmentation of SMILES strings into overlapping substrings of a defined size that we call LINGOs. The integral set of LINGOs derived from a given SMILES string, the LINGO profile, is a hologram of the SMILES representation of the molecule described. LINGO profiles provide input for QSPR models and the calculation of intermolecular similarities at very low computational cost. The octanol/water partition coefficient (LlogP) QSPR model achieved a correlation coefficient R2=0.93, a root-mean-square error RRMS=0.49 log units, a goodness of prediction correlation coefficient Q2=0.89 and a QRMS=0.61 log units. The intrinsic aqueous solubility (LlogS) QSPR model achieved correlation coefficient values of R2=0.91, Q2=0.82, and RRMS=0.60 and QRMS=0.89 log units. Integral Tanimoto coefficients computed from LINGO profiles provided sharp discrimination between random and bioisoster pairs extracted from Accelrys Bioster Database. Average similarities (LINGOsim) were 0.07 for the random pairs and 0.36 for the bioisosteric pairs.     

Saturated resins or stress of the resin

Although the solid-phase mode is an excellent strategy for the preparation of both biomolecules and small molecules, the synthesis of polyproline-based dendrimers has provided evidence that the capacity of the bead is limited. This phenomenon, which can be interpreted as saturation or stress of the resin, can lead to a complete breakdown of the bead structure.     

Silylketenes under Kulinkovich conditions: alkene/ketene exchange versus nucleophilic addition. Application to the stereoselective preparation of vinylcyclopropanols

Silylketenes react under Kulinkovich conditions through two competitive pathways: alkene/ketene exchange versus nucleophilic addition. In both cases, the organotitanium intermediate reacts with an aldehyde to yield an adduct which can undergo an elimination to yield a vinylcyclopropanol or an α,β-unsaturated carbonyl compound.     

Symplectic supercuspidal representations and related problems

In this paper, we summarize the basic structures and properties of irreducible symplectic supercuspidal representations of GLn(F) over a p-adic local field F with characteristic zero, and explore possible topics for further investigation.