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.     

连续波锁模Pr3+:YLF激光器

本文报导了采用氩离子激光器来泵浦Pr³⁺:YLF晶体,应用声光调制器实现了主动锁模;同时应用振动─高反射平面镜也实现了被动锁模,两种锁模均得到了ps光脉冲.据作者了解这是这种晶体材料的第一次锁模运转.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

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.