Singular sets of planar hyperbolic billiards are regular

Many planar hyperbolic billiards are conjectured to be ergodic. This paper represents a first step towards the proof of this conjecture. The Hopf argument is a standard technique for proving the ergodicity of a smooth hyperbolic system. Under additional hypotheses, this technique also applies to certain hyperbolic systems with singularities, including hyperbolic billiards. The supplementary hypotheses concern the subset of the phase space where the system fails to be C ² differentiable. In this work, we give a detailed proof of one of these hypotheses for a large collection of planar hyperbolic billiards. Namely, we prove that the singular set and each of its iterations consist of a finite number of compact curves of class C ² with finitely many intersection points.     

Chemical and bioactivity evaluation of the bark of Neonauclea purpurea

Bioassay-guided fractionation of the MeOH extract from the stem bark of Neonauclea purpurea used in traditional medicine, resulted in the isolation of 2 indole alkaloids, cadambine (1) and alpha-dihydrocadambine (2), as well as a quinolic compound, 2,6-dimethoxy-1,4-benzoquinone (3). Antimalarial activity evaluation showed that compounds 2 and 3 exhibited mild in vitro antimalarial activity against Plasmodium falciparum, the chloroquine-resistant strain K1 with IC50 values of 6.6 and 11.3 microM, respectively. Compounds 1 and 2 showed no cytotoxicity to monkey (Vero) cells, but compound 3 showed weak cytotoxicity with an IC50 value of 1.19 microM.     

Photosensitive, all-glass AgPO3/silicaphotonic bandgap fiber

Photonic bandgap (PBG) guidance is observed in a solid core photonic crystal fiber (PCF) consisting of silver metaphosphate (AgPO(3)) glass embedded into a silica cladding, realized by vacuum-assisted infiltration of the molten glass into the hollow channels of a commercial silica PCF. Morphologic analysis of the cladding microstructure by optical and scanning electron microscopy reveals the formation of highly homogeneous glass strands along the PCF length. The characteristic transmission spectrum of the fiber shows PBG guidance in the range between 350 and 1650 nm. The exposure of the cladding glass matrix, using 355 nm, 150 ps laser irradiation, allows photo-induced enhancement of the transmission-to-stop-band extinction ratio by ～60 dB/cm and bandwidth tuning. Numerical calculations of the transmission pattern of the fabricated AgPO(3)/silica bandgap fiber are in good agreement with experiments.     

FLAMEnGO: a fuzzy logic approach for methyl group assignment using NOESY and paramagnetic relaxation enhancement data

Building on a recent method by Matthews and co-workers [1], we developed a new and efficient algorithm to assign methyl resonances from sparse and ambiguous NMR data. The new algorithm (FLAMEnGO: Fuzzy Logic Assignment of MEthyl GrOups) uses Monte Carlo sampling in conjunction with fuzzy logic to obtain the assignment of methyl resonances at high fidelity. Furthermore, we demonstrate that the inclusion of paramagnetic relaxation enhancement (PRE) data in the assignment strategy increases the percentage of correct assignments with sparse NOE data. Using synthetic tests and experimental data we show that this new approach provides up to ～80% correct assignments with only 30% of methyl-methyl NOE data. In the experimental case of ubiquitin, PRE data from two spin labeled sites improve the percentage of assigned methyl groups up to ～91%. This new strategy promises to further expand methyl group NMR spectroscopy to very large macromolecular systems.     

Entry to nitrogen-containing heterocycles by based-promoted heterocyclization on allenylamides of l-α-aminoacids

Allenylamides of Boc-protected α-aminoacids easily gave in basic medium heterocyclic products arising from attack of the NH group on the inside C-C double bond of the 1,2-diene moiety, namely imidazolidinones, pyrazinones, and a pyrrole compound. The microwave-assisted heterocyclization occurred cleanly at C-β of the allenyl group with formation of pyrazin-2-ones having an endo- or exocyclic double bond.     

A Degenerate Birdcage with Integrated Tx/Rx Switches and Butler Matrix for the Human Limbs at 7 T

The theoretically known degeneracy condition of the band-pass birdcage coil has rarely been exploited in transmit coil designs. We have created an eight-channel degenerate birdcage for the human limbs at 7 T, with dedicated Tx/Rx switches and a Butler matrix. The coil can be split into two half cylinders, as required for its application to patients with limited mobility. The design of the coil, the Butler matrix, and Tx/Rx switches relied on a combination of analytical, circuital, and numerical simulations. The birdcage theory was extended to the degenerate case. The theoretical and practical aspects of the design and construction of the coil are presented. The performance of the coil was demonstrated by simulations, workbench, and scanner measurements. The fully assembled prototype presents good performance in terms of efficiency, B₁ homogeneity, and signal-to-noise ratio, despite the asymmetry introduced by the splittable design. The first in vivo images of the knee are also shown. A novel RF coil design consisting of an eight-channel splittable degenerate birdcage has been developed, and it is now available for 7 T MRI applications of the human lower limbs, including high-resolution imaging of the knee cartilages and of the patellar trabecular structure.     

High-order conservative finite difference GLM–MHD schemes for cell-centered MHD

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities.     

Peptide‐Coated Platinum Nanoparticles with Selective Toxicity against Liver Cancer Cells

Peptide‐stabilized platinum nanoparticles (PtNPs) were developed that have significantly greater toxicity against hepatic cancer cells (HepG2) than against other cancer cells and non‐cancerous liver cells. The peptide H‐Lys‐Pro‐Gly‐d Lys‐NH₂ was identified by a combinatorial screening and further optimized to enable the formation of water‐soluble, monodisperse PtNPs with average diameters of 2.5 nm that are stable for years. In comparison to cisplatin, the peptide‐coated PtNPs are not only more toxic against hepatic cancer cells but have a significantly higher tumor cell selectivity. Cell viability and uptake studies revealed that high cellular uptake and an oxidative environment are key for the selective cytotoxicity of the peptide‐coated PtNPs.     

Hybrid URANS/LES Turbulence Simulation of Vortex Shedding Behind a Triangular Flameholder

In this study a detached eddy simulation (DES) model, which belongs to the group of hybrid URANS/LES turbulence models, is used for the simulation of vortex shedding behind a triangular obstacle. In the near wall region or in regions where the grid resolution is not sufficiently fine to resolve smaller structures, the two-equation RANS shear-stress transport (SST) model is used. In the other regions with higher grid resolution a LES model, which uses a transport equation for the turbulent subgrid energy, is applied. The DES model is first investigated for two standard test cases, namely decaying homogeneous isotropic turbulence and the backward facing step, respectively. For the decaying homogeneous isotropic turbulence test case the evolution of the energy spectra in wavenumber space for different times are studied for both the DES and a Smagorinsky type LES model. Different grid resolutions are analyzed with a special emphasis on the modeling constant connecting the filter length scale to the grid size. The results are compared to experimental data. The backward facing step test case is used to study the model behavior for a case with a transition region between a RANS modeling approach close to the wall and LES based modeling in the intense shear flow region. The final application is the simulation of the vortex shedding behind a triangular obstacle. First, the influence of the inlet condition formulation is studied in detail as they can have a significant influence especially for LES based models. Detailed comparisons between simulation and experiment for the flow structure past the obstacle and statistical quantities such as the shedding frequency are shown. Finally the additional temporal and spatial information provided by the DES model is used to show the predicted anisotropy of turbulence.     

基于光谱指数波段优化算法的小麦玉米冠层含氮量估测

作物关键生育时期冠层氮素含量的实时监测对于优化氮肥用量和减少环境风险具有重要的意义。为了寻求预测不同作物氮素含量的最佳光谱参数,实现作物氮素无损营养诊断。本研究通过2008年—2011年在德国慕尼黑弗莱辛和河北曲周的不同氮量的小麦玉米田间试验,采用高光谱仪获取小麦玉米冠层的反射光谱,利用光谱理论模型进行光谱指数波段的优化,从而抽取不同冠层结构条件下的小麦玉米氮素营养敏感波段。结果表明与传统的基于红光的光谱指数相比,优化光谱指数显著提高了小麦玉米冠层氮素含量的预测能力,克服了传统的基于红光光谱指数的饱和问题。优化光谱指数的波段结合随着作物品种及其冠层结构的变化而变化,其优化波段范围主要集中在红边(730～760 nm)和红边向近红外的过渡区域(760～880 nm)。优化结果显示玉米最佳光谱指数为R_λ766/R_λ738-1,小麦最佳光谱指数为R_λ796/R_λ760-1,玉米小麦相结合优化后的最佳光谱指数为Rλ₈₇₆/Rλ₇₃₀-1。结果进一步验证了优化光谱指数估测的不同作物含氮量的预测值与实测值相关性最高,且验证偏差最小,证实了优化后的光谱特征参数可对不同作物氮素丰缺状况进行快速、准确、无损估测。试验结果也为设计作物冠层氮素传感器和更好的利用现有基于卫星的传感器实施区域上的作物氮素营养监测提供了理论基础。