Enhanced Karush–Kuhn–Tucker condition and weaker constraint qualifications

In this paper we study necessary optimality conditions for nonsmooth optimization problems with equality, inequality and abstract set constraints. We derive the enhanced Fritz John condition which contains some new information even in the smooth case than the classical enhanced Fritz John condition. From this enhanced Fritz John condition we derive the enhanced Karush–Kuhn–Tucker condition and introduce the associated pseudonormality and quasinormality condition. We prove that either pseudonormality or quasinormality with regularity on the constraint functions and the set constraint implies the existence of a local error bound. Finally we give a tighter upper estimate for the Fréchet subdifferential and the limiting subdifferential of the value function in terms of quasinormal multipliers which is usually a smaller set than the set of classical normal multipliers. In particular we show that the value function of a perturbed problem is Lipschitz continuous under the perturbed quasinormality condition which is much weaker than the classical normality condition.     

Hydrothermal preparation and photoluminescence of bundle-like structure of ZnWO4 nanorods

ZnWO₄ nanorods with a bundle-like structure were synthesized at 180°C for 12 h by a hydrothermal technology from Na₂WO₄⋅2H₂O and ZnSO₄⋅7H₂O in the presence of sodium dodecyl sulfate (SDS). The as-synthesized bundle-like structure of ZnWO₄ nanorods was characterized by various techniques: TEM, XRD and EDS. The luminescence properties of the bundle-like structure of the ZnWO₄ nanorods were investigated by photoluminescence (PL) spectroscopy.     

Generation of Multiple-Atom Entangled States with Weak Cross-Kerr Nonlinearity

We propose a scheme to generate multiple-atom entangled states in separate cavities. In our scheme, only weak cross-Kerr mediums, homodyne measurement, and some linear elements are employed. With the help of homodyne measurement, four-atom GHZ state can be obtained with high probability and fidelity, and the proposal can be easily scaled to prepare multiple-atom GHZ state. Under ideal conditions, the success probability will not be affected by atomic numbers.     

Oscillatory and anti-oscillatory motifs in genetic regulatory networks

Recently,self-sustained oscillatory genetic regulatory networks(GRNs) have attracted significant attention in the biological field.Given a GRN,it is important to anticipate whether the network could generate oscillation with proper parameters,and what the key ingredients for the oscillation are.In this paper the ranges of some function-related parameters which are favorable to sustained oscillations are considered.In particular,some oscillatory motifs appearing with high-frequency in most of the oscillatory GRNs are observed.Moreover,there are some anti-oscillatory motifs which have a strong oscillation repressing effect.Some conclusions analyzing these motif effects and constructing oscillatory GRNs are provided.     

Multichannel and omnidirectional transparency in periodic metamaterial layers

Multichannel and omnidirectional transmission can be realized in one-dimensional periodic metamaterial layers, where double-negative materials and single-negative materials are alternately stacked. The proposed structures can produce as many resonance transmission modes as desired by adjusting the number of the periods. Such transmission modes with perfect transmission are robust against incident angles and polarizations. The frequencies and frequency intervals of these modes can be tuned by changing the thicknesses of the metamaterial layers. Composite right/left-handed transmission lines with lumped elements (capacitors and inductors) were used to verify the characteristics of the considered system. Our findings provide an efficient way to select useful multiple channel signals from all directions, and it is useful in optoelectronic device applications.     

毛细管电泳法分离联萘酚对映体

利用新的手性选择剂苄基氯化辛可宁，在非水相中成功地分离了联萘酚的对映体，并对分离的机理作了初步地探讨。     

Flow injection kinetic spectrophotometric determination of ascorbic acid based on an inhibiting effect

A rapid and sensitive flow-injection kinetic spectrophotometric method is proposed for the determination of ascorbic acid. The procedure is based on the inhibiting effect of ascorbic acid on the enhancing effect of oxalate on the potassium dichromate-potassium iodide/rhodamine 6G system. The detection limit and linear ranges are 0.08 and 0.10-4.00 microg/ml, respectively. The relative standard deviation of 11 replicate measurements is less than 2.0%. This method has been successfully used to determine ascorbic acid in pharmaceuticals, tomatoes and oranges.     

Influence of anodizing voltage mode on the nanostructure of TiO2 nanotubes

The nanostructure of self-ordered porous anodic TiO₂ nanotubes (PATNTs) has extraordinary influence on their physical and chemical properties. For this reason, extensive attention has been paid on pulse anodization to regulate the nanostructure of PATNT. However, the relationships between the nanostructures and current curves still remain unclear. Based on the traditional potentiostatic and pulse anodizations, five different modes (i.e., potentiostatic, pulse, triangle wave, decrease, and increase step by step) of applied voltage and their influences on the nanostructures of PATNT have been investigated in detail. The growing rates of the nanotubes anodized under five different modes were compared for the first time. The results show that the growing rate of pulse voltage anodization is the fastest, reaching 116.4 nm min^?1. The slowest is triangle wave voltage anodization, only 59.3 nm min^?1. When the applied voltage decreases step-by-step, branched nanotubes can be formed in the bottom of PATNT. Yet, when the applied voltage increases step-by-step, triple-layer nanotubes with different diameters are formed, and the forming mechanism of this special nanostructure is discussed. The present results may be helpful to understand the mechanism of PATNT and facilitate the assembling diverse nanostructures for extensive applications in photocatalysis, dye-sensitized solar cells, and biomedical devices.     

Synthesis of dendritic polyamide with protected amino functional groups in the periphery

A homologous series of first-to third-generation dendritic polyamides 2a, 3, and 5 with tris(aminoethyl) amine (TREA) as the core and the protected amino functional groups at the periphery were synthesized via active ester route from “Schlüter” type dendron 1a. Their structures were characterized by ¹H-NMR and mass spectra. Based on the efficient synthesis of the first generation dendrimer 2a (yield 75%), the synthesis of second-generation dendrimer 3 was found to be more efficient via the convergent method (yield 69%), while the mixed strategy was applied efficiently for the synthesis of the higher generation dendrimer 5 (yield 37%). The overall yield for the third generation dendrimer 5 from Schlüter dendron is 12%. __________ Translated from Huaxue Tongbao (Chemistry), 2005, 68(12) (in Chinese)