The use of polarization modulation and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement

A novel common-path polarization modulation and amplitude-sensitive optical heterodyne polarimeter is setup in order to characterize a phase retardation plate (PRP) in real time. The phase retardation ΔΦ and fast-axis angle β of the linear birefringence parameters (LBP) of a PRP are measured simultaneously. Meanwhile, the dynamic ranges of 0° < ΔΦ < 180° and 0° < β < 180° are demonstrated experimentally. In order to measure LBP in real time, a polarization modulation is introduced by continuously rotating the tested PRP such that ΔΦ and β are able to be obtained in terms of the ratio of the amplitudes of S polarization and the ratio of P polarization of the heterodyne signals, respectively. Consequently, this novel method, which combines optical heterodyne interferometry with a polarization modulation technique, not only improves the detection sensitivity, but also provides a real time capability to measure LBP. In addition, the error in the LBP measurement is derived and analyzed.     

Deposition of lead iodide films on Rh(1 0 0) electrodes from colloidal solutions––the effect of an iodine adlayer

The growth of PbI₂ precipitates on single crystal substrates from colloidal solutions has been investigated with in air scanning tunneling microscopy and synchrotron-based X-ray photoelectron spectroscopy. The PbI₂ growth on Rh(1 0 0) results in nano-clusters with lateral dimensions between 30 and 60 Å, consistent with earlier reports. However, the growth of PbI₂ on a well-ordered iodinated Rh(1 0 0), denoted as (√2×√2)R45°-I, leads to atomically smooth PbI₂ films having a hexagonal symmetry with lattice constant identical to the bulk value of 4.5 Å. The heteroepitaxy is believed to be effected by the atomic iodine monolayer that helps to accommodate large lattice mismatch between PbI₂ and Rh surface with short-range van der Waals interaction.     

Characterization of isolated homogeneous hypersurface singularities in ?4

Let V be a hypersurface with an isolated singularity at the origin in ℂ ⁿ⁺¹. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface signularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau’s theorem remains true for singularities with geometric genus equal to zero. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Complex geometry: Its brief history and its future

This paper reviews the brief history of complex geometry and looks into its future.     

Enhanced cycling stability of o-LiMnO2 cathode modified by lithium boron oxide coating for lithium-ion batteries

The effect of lithium boron oxide (LBO) coating on the electrochemical performance of orthorhombic LiMnO₂ (o-LiMnO₂) cathode for lithium-ion batteries is investigated. o-LiMnO₂ synthesized via solid state synthesis technique is modified with LBO addition. The presence of LBO is identified via Fourier transform infrared spectroscopy analysis. o-LiMnO₂ is observed to transform to a spinel-like phase during cycling which undergoes capacity fading. Studies indicate that the presence of 1–2 wt% LBO results in an improved capacity and better capacity retention with cycling. The pristine sample reveals a maximum specific capacity of 172 mAhg^?1, whereas the LBO-modified samples display about 189.1 mAhg^?1 in the cycling tests conducted at a rate of 50 mAg^?1 in the voltage range of 2–4.5 V. After 70 cycles, the LBO-modified LiMnO₂ displayed higher capacity retention of 175 mAhg^?1 as compared to the pristine sample that exhibited 130 mAhg^?1. By analyzing the charge–discharge behavior, it is observed that the capacity obtained from lithium insertion into the tetrahedral sites of the spinel structure is more or less constant throughout the cycling and that the bulk of the capacity loss is resulting when lithium is inserted into the octahedral sites of the spinel structure. Impedance measurement reveals a reduced charge-transfer resistance for the LBO-modified samples suggesting that the presence of LBO is countering capacity loss arising from insertion of lithium into the octahedral sites thus contributing to the overall cycling stability.     

Comparative Research of Chemical Profiling in Different Parts of Fissistigma oldhamii by Ultra-High-Performance Liquid Chromatography Coupled with Hybrid Quadrupole-Orbitrap Mass Spectrometry

The roots of Fissistigma oldhamii (FO) are widely used as medicine with the effect of dispelling wind and dampness, promoting blood circulation and relieving pains, and its fruits are considered delicious. However, Hakka people always utilize its above-ground parts as a famous folk medicine, Xiangteng, with significant differences from literatures. Studies of chemical composition showed there were multiple aristolactams that possessed high nephrotoxicity, pending evaluation research about their distribution in FO. In this study, a sensitive, selective, rapid and reliable method was established to comparatively perform qualitative and semi-quantitative analysis of the constituents in roots, stems, leaves, fruits and insect galls, using an Ultra-High-Performance Liquid Chromatography coupled with Hybrid Quadrupole Orbitrap Mass Spectrometry (UPLC-Q-Exactive Orbitrap MS, or Q-Exactive for short). To make more accurate identification and comparison of FO chemicals, all MS data were aligned and screened by XCMS, then their structures were elucidated according to MSⁿ ion fragments between the detected and standards, published ones or these generated by MS fragmenter. A total of 79 compounds were identified, including 33 alkaloids, 29 flavonoids, 11 phenylpropanoids, etc. There were 54 common components in all five parts, while another 25 components were just detected in some parts. Six toxic aristolactams were detected in this experiment, including aristolactam AII, AIIIa, BII, BIII, FI and FII, of which the relative contents in above-ground stems were much higher than roots. Meanwhile, multivariate statistical analysis was performed and showed significant differences both in type and content of the ingredients within all FO parts. The results implied that above-ground FO parts should be carefully valued for oral administration and eating fruits. This study demonstrated that the high-resolution mass spectrometry coupled with multivariate statistical methods was a powerful tool in compound analysis of complicated herbal extracts, and the results provide the basis for its further application, scientific development of quality standard and utilization.     

Gauss–Manin Connection in Disguise: Calabi–Yau Threefolds

We describe a Lie Algebra on the moduli space of non-rigid compact Calabi–Yau threefolds enhanced with differential forms and its relation to the Bershadsky–Cecotti–Ooguri–Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions \({{\bf F}_{g}^{\rm alg}, g \geq 1}\), which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck’s algebraic de Rham cohomology and on the algebraic Gauss–Manin connection. In this way, we recover a result of Yamaguchi–Yau and Alim–Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi–Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.