Analysis of Corrugated Long-Period Gratings in Planar Waveguides and Their Polarization Dependence

We present a theoretical analysis of corrugated long-period gratings in planar waveguides. In particular, we calculate the transmission spectra for both the TE and TM polarizations and highlight the polarization-independence conditions.     

Effect of ionic environments on the adsorption and diffusion characteristics of serine alkaline protease enzyme in polyethersulfone ultrafiltration membranes

Static adsorption of serine alkaline protease (SAP) enzyme on hydrophobic polyether sulfone (PES) ultrafiltration membranes in different ionic environments was investigated. The amount of SAP adsorbed on membranes was the lowest at its isoelectric point (IEP) where the maximum adsorption was obtained below the IEP of the enzyme. The extent of SAP adsorption in the phosphate buffer solutions including different salts followed the order: (NH4)2HPO4 > KH2PO4 > Na2HPO4-NaH2PO4 (buffer) > CaCl2 > ((NH4)2HPO4 + H2PO4 + CaCl2), which was consistent with the Hofmeister series. The zeta potentials of membranes contacted with the ionic species were calculated by streaming potential measurements and found that the increase in ionic strength decreased the electrical double layer thickness leading to a decrease in adsorption. A model based on mass balance was developed to calculate the diffusion coefficient of SAP in PES membranes. Employing experimental data evaluated in a diffusion cell along with the data of adsorption isotherms, diffusion coefficients of SAP in PES membranes in the presence of different ionic species were calculated. To detect the structural changes occurred, membrane surfaces were analysed by Fourier transform infrared-attenuated total reflectance (FTIR-ATR) measurements.     

多自由度Maxwell阻尼器减震结构(Ⅱ)——等效阻尼

对多自由度带支撑Maxwell阻尼器减震结构的等效阻尼比进行了系统研究。构建了耗能结构一般微分和积分混合地震响应方程组;基于与多自由度随机平均法分析完全相同的等效准则,建立了耗能结构各振型等效阻尼比的一般解析计算式。与一些典型问题的模态应变能法的计算精度进行对比分析,结果显示:本文方法的计算结果在特定条件下与精确解完全相同;在一个二自由度系统中相对位移响应方差的误差分别为0.99%和0.45%,优于应变能法的8%和5.4%,表明了本文方法的有效性。从而为建立此类耗能结构等效阻尼分析的完备解析解法、直接应用反应谱法进行实际工程设计提供了依据。     

Self-Concordant Barriers for Convex Approximations of Structured Convex Sets

We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the approximation is moderate) self-concordant barriers. This approach extends the reach of the modern theory of interior-point methods, and lays the foundation for new ways to treat structured convex optimization problems with a very large number of constraints. Moreover, our approach provides a strong connection from the theory of self-concordant barriers to the combinatorial optimization literature on solving packing and covering problems.     

Reviving Pólya's “Look Back” in a Singapore school

This study is based on the stance that Pólya's “Look Back,” though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project, we focus on a redesign of a teacher development programme that is targeted to help teachers realize Pólya's original vision of Look Back in the classroom. We report the cases of two teachers who have participated in the teacher development programme: their thinking about Look Back (through interview records) and their interpretation of Look Back in their classroom practice (through video records). By bringing these two spheres of data together, we discuss their degree of ‘buy-in’ to Look Back in the overall problem solving enterprise.     

Visible-Light-Induced Heptacene Generation under Ambient Conditions: Utilization of Single-crystal Interior as an Isolated Reaction Site

The photo-induced generation of unstable molecules generally requires stringent conditions to prevent oxidation and the concomitant decomposition of the products. The visible-light-induced conversion of two heptacene precursors to heptacene was studied. Single crystals of bis- and mono-α-diketone-type heptacene precursors ( 7-DK2 and 7-DK1 , respectively), were prepared to investigate the effect of precursor structure on reactivity. The photoirradiation of a 7-DK2 single crystal cleaved only one α-diketone group, forming an intermediate bearing a pentacene subunit, while that of a 7-DK1 single crystal gave rise to characteristic absorption peaks of heptacene and their increase in intensity with photoirradiation time, indicating the generation of heptacene without decomposition. Heptacene production was not observed when the precursors were photoirradiated in solution, implying that the single crystal interior provided isolation from the external environment, thus preventing heptacene oxidation.     

Extracting the low-energy constant ${L}_{0}^{r}$ at three flavors from pion-kaon scattering

Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the only free low-energy constant at ${ \mathcal O }({p}^{4})$, known as ${L}_{0}^{r}$, in SU (4∣1) Partially-Quenched Chiral Perturbation theory using the data from the Extended Twisted Mass collaboration, ${L}_{0}^{r}(\mu ={M}_{\rho })=0.77(20)(25)(7)(7)(2)\cdot {10}^{-3}$. The theory uncertainties originate from the unphysical scattering length, the physical low-energy constants, the higher-order chiral corrections, the (lattice) meson masses and the pion decay constant, respectively.     

Studies on frequency and gate voltage effects on the dielectric properties of Au/n-Si (110) structure with PVA–nickel acetate composite film interfacial layer

The admittance technique was used in order to investigate the frequency dependence of dielectric constant (????), dielectric loss (????), dielectric loss tangent (tan??), the ac electrical conductivity (?? _ac), and the electric modulus of PVA (Ni-doped) structure. Experimental results revealed that the values of ???? , ????, (tan??), ?? _ac and the electric modulus show fairly large frequency and gate bias dispersion due to the interface charges and polarization. The ?? _ac is found to increase with both increasing frequency and voltage. It can be concluded that the interface charges and interfacial polarization have strong influence on the dielectric properties of metal?Cpolymer?Csemiconductor (MIS) structures especially at low frequencies and in depletion and accumulation regions. The results of this study indicate that the ???? values of Au/PVA/n-Si with Nickel-doped PVA interfacial layer are quite higher compared to those with pure and other dopant/mixture??s of PVA.