Molecular Dynamics in 1- and 2-D Confinement as Studied for the Case of Poly(Cis-1,4-Isoprene)

Broadband Dielectric Spectroscopy (BDS) is used to probe the molecular dynamics of Type A polymer, poly(cis-1,4-isoprene), when confined in the 1-dimensional (1D) exploring space of thin layers and the 2-dimensional (2D) constraining geometry of unidirectional anodic aluminum oxide (AAO) nanopores. For both cases, it was observed that the structural relaxation remains bulk-like in its mean relaxation rate, although the distribution of its relaxation times is broadened in 2D confinement. Furthermore, the fluctuation of the end-to-end vector is interrupted, with the 1D case being relatively less pronounced. By this clear-cut comparison, it is demonstrated that the effects of confinement on molecular dynamics depend, inter alia, on the dimensionality of the restricting space.     

Waiting times of entangled electrons in normal–superconducting junctions

We consider a normal–superconducting junction in order to investigate the effect of new physical ingredients on waiting times. First, we study the interplay between Andreev and specular scattering at the interface on the distribution of waiting times of electrons or holes separately. In that case the distribution is not altered dramatically compared to the case of a single quantum channel with a quantum point contact since the interface acts as an Andreev mirror for holes. We then consider a fully entangled state originating from splitting of Cooper pairs at the interface and demonstrate a significant enhancement of the probability to detect two consecutive electrons in a short time interval. Finally, we discuss the electronic waiting time distribution in the more realistic situation of partial entanglement.     

An analysis of cross-correlations in an emerging market

We apply random matrix theory to compare correlation matrix estimators C$C$ obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg stock exchange (JSE) from January 1993 to December 2002. We test the spectral properties of C$C$ against random matrix predictions and find some agreement between the distributions of eigenvalues, nearest neighbour spacings, distributions of eigenvector components and the inverse participation ratios for eigenvectors. We show that interpolating both missing data and illiquid trading days with a zero-order hold increases agreement with RMT predictions. For the more realistic estimation of correlations in an emerging market, we suggest a pairwise measured-data correlation matrix. For the data set used, this approach suggests greater temporal stability for the leading eigenvectors. An interpretation of eigenvectors in terms of trading strategies is given, as opposed to classification by economic sectors.     

Diffusion-direction-dependent imaging: a novel MRI approach for peripheral nerve imaging

A novel magnetic resonance imaging approach, called diffusion-direction-dependent imaging (DDI), is introduced. Due to inherent anisotropic diffusion properties, peripheral nerves can be visualized on diffusion tensor imaging (DTI). The largest signal attenuation on DTI correlates with the direction of a nerve fiber, and the least signal attenuation correlates with the direction perpendicular to the nerve fiber. Since low signal-to-noise ratio is a concern in peripheral nerve DTI, we explored a new approach focusing on the perpendicular diffusion direction. A 36-gradient diffusion direction scheme was used. A mean expected curve specific for peripheral nerves was calculated based on the sciatic nerve and its division into the common peroneal nerve and the tibial nerve in three healthy volunteers. By a simple postprocessing method, a comparison of the mean expected curve and the measured curve was made voxel by voxel, and the sciatic nerve and its division were reconstructed, excluding other tissues. More studies are needed to investigate whether other postprocessing methods or other diffusion direction schemes are more suited for peripheral nerve imaging with DDI. Further studies may also be of interest to investigate whether DDI can be a complementary method to conventional T(1)-weighted and T(2)-weighted sequences in the imaging of peripheral nerve pathology or even in the visualization of other tissues, possibly with different diffusion direction schemes.     

Carbon dots/Bi_2WO_6 composite with compensatory photo-electronic effect for overall water photo-splitting at normal pressure

Overall water photo-splitting is a prospective ideal pathway to produce ultra-clean H_2 energy by semiconductors.However,the band structure of many semiconductors cannot satisfy the requirement of H_2 and O_2 production at the same time.Herein,we illustrate that carbon dots(CDs)/Bi_2 WO_6 photocatalyst with compensatory photo-electronic effect has enhanced activity for overall water photo-splitting without any sacrificial agent.In this complex photocatalytic system,the photo-potential provided by CDs makes the CDs/Bi_2 WO6(C-BWO) composite could satisfy the band structure conditions for overall water photo-splitting.The C-BWO composite(3 wt% CDs content) exhibits optimized hydrogen evolution(oxygen evolution) of 0.28 μmol/h(0.12 μmol/h) with an approximate 2:1(H_2:O_2) stoichiometry at normal pressure.We further employed the in-situ transient photovoltage(TPV) technique to study the photoelectron extraction and the interface charge transfer kinetics of this composite catalyst.     

确定性矩阵可分离压缩成像

针对可分离压缩传感使用的可分离随机正交矩阵在处理大尺度图像等高维信号感知时难度太大或成本过高的问题,引入确定性测量矩阵,提出确定性矩阵可分离压缩传感,可将如托普利兹矩阵及循环矩阵等具有确定性结构的矩阵作为可分离压缩传感的左、右可分离矩阵.该方案可以降低独立元素的数目,从而显著降低前端物理实现的难度与成本.数值模拟实验分别评估了该方法在不同采样率及不同图像尺寸下的压缩重建性能,结果表明该方法在独立元素非常少的情形下得到与原随机正交矩阵相近的重建质量,证明了其可行性.     

Functional Differential Equations With Delay and Random Effects

The authors study the existence of mild solutions to a functional differential equation with delay and random effects. They use a random fixed point theorem with a stochastic domain. An example is included to illustrate their results.     

Joint distributions of random sets and their relation to copulas

Random sets are set-valued random variables. They have been applied in various fields like stochastic geometry, statistics, economics, engineering or computer science, and are often used for modeling uncertainty. In an earlier paper the author has defined joint capacity and joint containment functionals which are multivariate set functions describing the joint distribution of random sets. This paper is concerned with the question how copulas can be used to describe or model the dependence of random sets. It is demonstrated that a joint containment functional can be related to its margins by a family of copulas. Furthermore, the paper provides a first insight how copulas can be used to define joint containment functionals.     

GW invariants relative to normal crossing divisors

In this paper we introduce a notion of symplectic normal crossing divisor V and define the GW invariant of a symplectic manifold X relative to such a divisor. Our definition includes normal crossing divisors from algebraic geometry. The invariants we define in this paper are key ingredients in symplectic sum type formulas for GW invariants, and extend those defined in our previous joint work with T.H. Parker [16], which covered the case V   was smooth. The main step is the construction of a compact moduli space of relatively stable maps into the pair (X,V)$(X,V)$ in the case V is a symplectic normal crossing divisor in X.     

Comparative DFT study of Raman spectra of phosphorus-containing dendrimers built from thiophosphoryl,cyclotriphosphazene and phthalocyanine cores

The FT Raman spectra of the zero and first generations of phosphorus-containing dendrimers built from thiophosphoryl, cyclotriphosphazene and phthalocyanine core with terminal oxybenzaldehyde groups have been recorded and analyzed. The structural optimization and normal mode analysis were performed for dendrimers on the basis of the density functional theory (DFT). The calculated geometrical parameters, harmonic vibrational frequencies and Raman scattering activities are predicted in a good agreement with the experimental data. The experimental Raman spectra of dendrimers were interpreted by means of potential energy distribution. Relying on DFT calculations the lines of the cores, repeating units and terminal groups of dendrimers were assigned.The influence of the encirclement on the line frequencies and intensities was studied and due to the predictable, controlled and reproducible structure of dendrimers the information, usually inaccessible is obtained. The strong line at 1600 cm⁻¹ show marked changes of intensity in dependence of aldehyde (CHO) or azomethyne (CHN) substituents in the aromatic ring. The polarizabilities and lipophilicity of dendrimers were estimated.