半定矩阵秩极小的非凸精确松弛

本文主要研究半定矩阵秩极小问题(P)的非凸精确松弛及其性质.首先,为求解问题(P),我们引入其Schatten p-范数(0＜p＜1)松弛,记为(Sp).其次,通过定义半定限制等距常数和半定限制正交常数,我们给出了问题(P)有唯—解的充分条件.最后,利用半定限制等距性质,我们给出了问题(P)和(Sp)有相同唯一解的充分条件.特别地,对任意0＜p＜1,我们还得到—个一致的精确恢复条件.     

Comment on “On the Neumann function and the method of images in spherical and ellipsoidal geometry”

In this note, we point out two errors in the article “On the Neumann function and the method of images in spherical and ellipsoidal geometry” by Dassios and Sten. Two corrections are then proposed.     

Multi-Residue Analysis by Liquid Chromatography-Mass Spectrometry Coupling. Application to Drinking and River Waters

Abstract

The coupling between liquid chromatography and mass spectrometry with an APCI or ESI interface (in positive or negative mode) is used here for multi-residue analyses in natural waters, covering basic and neutral pesticides as well as acid pesticides. The methods developed are applied to drinking and, river waters after the samples are concentrated by liquid-liquid extraction or solid phase extraction on C18 cartridges. Comparisons are made between UV detection and mass spectrometry and between two chromatographic methods for acid substances. The quantitation limits range from 0.01 to 0.1 μg/l according to the substance.     

A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation

We consider a shallow water equation of the Camassa–Holm type, which contains nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L ^p setting.     

Nonlinear dynamics for proper ferroelastic transitions for which the landau condition is violated

On the basis of a lattice model the domain structure for ferroelastic transformations is examined. The model accounts for both strongly nonlinear and competing interactions which allow for, in some situations, the propagation of nonlinear excitations. The model can be mostly applied to proper ferroelastic transformations of which In-Tl, Ti-Ni, etc.… are good prototypes. The phonon dispersion of the transverse acoustic waves obtained in the linearized case is discussed and the results show first a phonon softening at nonzero wave-number and next an upwards convexity of the phonon branch near the long-wavelength limit. This can be seen as pre-transitional effects. In a fully nonlinear case we consider vanishing dilatation transformations and the continuum approximation is applied to the one-dimensional version. Then, we investigate nonlinear excitations; three main classes of solution are found: i) quasi-harmonic solutions corresponding to periodically modulated structures in space which is a precursor effect of the elastic transformation, ii) an array of solitons made of periodic arrangements of parent-elastic domains and iii) a moving strain soliton. All the significant results are numerically illustrated by means of the microscopic model. Finally, the similarity to martensitic transformations and some extensions of the model are outlined.     

An efficient stereoselective synthesis of aminocyclohexenes from 7-azanorbornenes via LiAlH4 mediated tandem double bond migration-ring opening sequence

hNav1.7 had received great interest in the past decade owing to its attractive mechanism of actions in pain processing pathway. More recently, we developed a series of efficacious hNav1.7 inhibitors for analgesic, which were characterized with a novel aminocyclohexene as pharmacophore. Herein, we reported our synthetic efforts to construct the unique scaffold, which can be rapidly accessed from readily available 7-azanorbornenes via an unexpected catalyst-free, LiAlH₄ mediated tandem double bond migration-ring opening sequence. A probable mechanism was proposed to illuminate the good regio- and stereoselectivity.     

信息化条件下我国资产证券化研究

资产证券化凭借其独特的交易机制，已经成为发达国家资本市场的主流融资手段，更是全球领域最重要的金融创新之一。它不但为市场机制作用的发挥奠定了基础，而且充分体现了金融市场一体化的客观要求。信息化条件下，资产证券化快速渗透到社会经济领域的各个层面，对经济运行效率能够产生深远的影响。     

Application of a biological‐based nanomagnetic catalyst in the synthesis of bis‐pyrazols and pyrano[3,2‐c]pyrazoles

{Fe₃O₄@SiO₂@(CH₂)₃‐thiourea dioxide‐SO₃H/HCl}, a newly reported nanomagnetic core–shell supported solid acid catalyst, was successfully employed in the preparation of 4,4′‐(arylmethylene)bis(1H –pyrazol‐5‐ol) and pyrano[3,2‐c ]pyrazole derivatives. The presented methods are very efficient and high‐yielding. Also, the catalyst exhibited powerful potential for reusability in both types of reactions.     

Coupling influence on the refractive index sensitivity of photonic wire ring resonator

By taking the coupling effect into consideration, we study the resonance condition of a photonic wire microring resonator (PWRR) sensor and compare our results with the previous work. Simulation results show that the resonant wavelength and sensitivity strongly depend on the coupling strength. The difference caused by the coupling effect can be up to tens of nanometers for the resonant peak position and tens of nm/RIU for the sensitivity in a silicon-on-insulator (SOI) PWRR. Such a giant influence from coupling effect cannot be disregarded and should be considered seriously for the design and application of PWRRs. It also shows an alternative tuning technique by controlling the coupling strength.     

Two optimal Dai–Liao conjugate gradient methods

Two adaptive choices for the parameter of Dai–Liao conjugate gradient (CG) method are suggested. One of which is obtained by minimizing the distance between search directions of Dai–Liao method and a three-term CG method proposed by Zhang et al. and the other one is obtained by minimizing Frobenius condition number of the search direction matrix. Global convergence analyses are made briefly. Numerical results are reported; they demonstrate effectiveness of the suggested adaptive choices.