A proximal point algorithm revisit on the alternating direction method of multipliers

The alternating direction method of multipliers(ADMM)is a benchmark for solving convex programming problems with separable objective functions and linear constraints.In the literature it has been illustrated as an application of the proximal point algorithm(PPA)to the dual problem of the model under consideration.This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter.This primal illustration of ADMM is thus complemental to its dual illustration in the literature.This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily.A worst-case O(1/t)convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas’s generalized ADMM.     

A phase model for point spread function estimation in ground-based astronomy

In ground-based astronomy,images of objects in outer space are acquired via ground-based telescopes.However,the imaging system is generally interfered by atmospheric turbulence and hence images so acquired are blurred with unknown point spread function(PSF).To restore the observed images,aberration of the wavefront at the telescope’s aperture,i.e.,the phase,is utilized to derive the PSF.However,the phase is not readily available.Instead,its gradients can be collected by wavefront sensors.Thus the usual approach is to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase in high accuracy.Here,we develop a model that reconstructs the phase directly.The proposed model uses the tight frame regularization and it can be solved efciently by the Douglas-Rachford alternating direction method of multipliers whose convergence has been well established.Numerical results illustrate that our new model is efcient and gives more accurate estimation for the PSF.     

Some equalities and inequalities of g-continuous frames

In this paper, we derive some equalities and inequalities about g-continuous frames, which are an extension to g-frames and continuous frames. We also discuss the stability of the perturbation of a g-continuous frame.     

Effect of width on the properties of Faraday waves in Hele-Shaw cells

The effect of container geometry on the Faraday waves in Hele-Shaw cells has been investigated. The wave heights increase with the width of the cell and a linear function is selected to express the relation between these data and parameters. The wave lengths also increase with the width and are in good agreement with the dispersion relation. In order to reveal the real nature behind these phenomena, we have developed a gap-averaged model to numerically solve this issue and give an analysis of the result to show how these Faraday waves are formed in a Hele-Shaw cell.     

Synthesis and Crystal Structure of a New Oxovanadium（V） Multicomponent Complex with Acylhydrazone and Benzoylhydrazine

A new oxovanadium（V） complex with the mixed ligand of 2-oxopropionic acid benzoylhydrazone （C10H10N2O3） and benzoylhydrazine （C7H8N2O）, VO（C7H7N2O）（C10H9N2O3）, has been synthesized. Its structure was determined by single crystal X-ray diffraction analysis. The crystal belongs to monoclinic system with space group P21/n and cell parameters： a=1.1136（4） nm, b=0.6217（2） nm, c=2.6038（9） nm, β=97.182（6）°, V= 1.7887（11） nm^3, Z=4, F（000）=836, Mr=407.28, Dc= 1.512 g/cm^3,μ （Mo Kα） =0.592 mm^-1, R1 =0.0445, wR2= 0.1203. Vanadium atom is 6-coordinated by carboxyl and carbonyl O atoms and N atom of one tridentate C10H10N2O3 to form two stable five-membered rings with the same edge, and the other coordinated atoms of N and O come from one bidentate benzoylhydrazine C7H8N2O. The title complex has a six-coordinated V center [VO（N2O3）] with a distorted octahedral arrangement. In the crystal lattice, there are hydrogen bonding interactions between two molecules.     

Theoretical study of the N-H…O red-shifted and blue-shifted hydrogen bonds

Theoretical calculations are performed to study the nature of the hydrogen bonds in complexes HCHO…HNO, HCOOH…HNO, HCHO…NH3, HCOOH…NH3, HCHO…NH2F and HCOOH…NH2F. The geometric structures and vibrational frequencies of these six complexes at the MP2/6-31+G(d,p), MP2/6-311++G(d,p), B3LYP/6-31+G(d,p) and B3LYP/6-311++G(d,p) levels are calculated by standard and counterpoise-corrected methods, respectively. The results indicate that in complexes HCHO…HNO and HCOOH…HNO the N-H bond is strongly contracted and N-H…O blue-shifted hydrogen bonds are observed. While in complexes HCHO…NH3, HCOOH…NH3, HCHO…NH2F and HCOOH…NH2F, the N-H bond is elongated and N-H…O red-shifted hydrogen bonds are found. From the natural bond orbital analysis it can be seen that the X-H bond length in the X-H…Y hydrogen bond is controlled by a balance of four main factors in the opposite directions: hyperconjugation, electron density redistribution, rehybridization and structural reorganization. Among them hyperconjugation has the effect of elongating the X-H bond, and the other three factors belong to the bond shortening effects. In complexes HCHO…HNO and HCOOH…HNO, the shortening effects dominate which lead to the blue shift of the N-H stretching frequencies. In complexes HCHO…NH3, HCOOH…NH3, HCHO…NH2F and HCOOH…NH2F where elongating effects are dominant, the N-H…O hydrogen bonds are red-shifted.     

同步辐射X射线掠入射衍射实验技术及应用

利用北京同步辐射装置漫散射实验站的五圆衍射仪,建立了掠入射X射线衍射实验方法.对Si表面生长的Ge/Si量子点及其在Si表层产生的应变进行了成功测量,表明此方法可以有效地提取表面层的微弱信号.实验结果表明,Ge/Si量子点的形成除了在Si衬底表层形成了晶格具有横向膨胀应变的区域之外,还在Si衬底中形成了具有横向压缩应变的区域.     

Visible frequency broadband dielectric metahologram by random Fourier phase-only encoding

In recent years,metasurfaces that enable the flexible wavefront modulation at sub-wavelength scale have been widely used into holographic display,due to its prominent advantages in polarization degrees of freedom,viewing angle,and achromaticity in comparison with traditional holographic devices.In holography,the computational complexity of hologram,imaging sharpness,energy utilization,reproduction rate,and system indirection are all determined by the encoding method.Here,we propose a visible frequency broadband dielectric metahologram based on the random Fourier phase-only encoding method.Using this simple and convenient method,we design and fabricate a transmission-type geometric phase all-dielectric metahologram,which can realize holographic display with high quality in the visible frequency range.This method encodes the amplitude information into the phase function only once,eliminating the cumbersome iterations,which greatly simplifies the calculation process,and may facilitate the preparation of large area nanoprint-holograms.     

Photosensitivity and grating development in trans-4-stilbenemethanol-doped poly(methyl methacrylate) materials

This paper reports the photosensitivity of poly(methyl methacrylate) (PMMA) and its copolymer doped with trans-4-stilbenemethanol. UV irradiation of the doped-PMMA at 325 nm induced the trans- to cis-isomerization of the dopant. This process was confirmed by ¹H NMR spectra of trans-4-stilbenemethanol in CDCL₃ solvent before and after irradiation. The isomerization can be initiated by the irradiation with an intensity of 0.62 mW/cm². Photo-induced refractive index change of −0.0024 was obtained when a PMMA copolymer film doped with 5.1 wt% dopant was exposed to 325 nm light. Lorentz-Lorenz equation was used to estimate the refractive index of a trans-4-stilbenemethanol-PMMA composite and a trans-4-stilbenemethanol-PMMA copolymer composite from the mole refraction and van der Waals volume of each component. A slight elevation of molecular packing coefficient (K) for PMMA and its copolymer containing the dopant implies a denser aggregation as compared to the polymer without the dopant. Long period gratings were created in doped-PMMA films and doped-PMMA copolymer fibers using amplitude mask technique. Gratings were confirmed by microscopic observation and diffraction patterns.     

Application of l-thiazolidine-4-carboxylic acid monolayer in electrochemical determination of copper(II)

L-Thiazolidine-4-carboxylic acid monolayer was prepared on gold electrodes through the self-assembly approach. Such novel thioether-based monolayer could efficiently preconcentrate Cu²⁺, which provided a simple, stable and reproducible method for the determination of Cu²⁺. The modified electrodes were stable enough to be continuously used for one week (more than 30 times regeneration) with lower than 10% decrease in the response. They retained their initial activity for more than one month if used once a day. The calibration curve was linear for Cu²⁺ from 0.6 to 158.8 μg L^?1 with a detection limit of 0.38 μg L^?1. The relative standard deviation was 3.2% for a series of six successive measurements. The proposed method was applied in the determination of Cu²⁺ in mineral water and human hair samples.