Synthesis of Benzimidazoles by Phosphine‐Mediated Reductive Cyclisation of ortho‐Nitro‐anilides

Heating ortho‐nitro‐anilides 1 – 3 and 2‐methyl‐N‐(3‐nitropyridin‐2‐yl)propanamide ( 5 ) with 4 equiv. of a phosphine led to the 2‐substituted benzimidazoles 6 – 8 and to the imidazo[4,5‐b]pyridine 10 , respectively, in yields between 45 and 85%. Heating 1 with (EtO)₃P effected cyclisation and N‐ethylation, leading to the 1‐ethylbenzimidazole 6b . The slow cyclisation of the N‐pivaloylnitroaniline 2b allowed isolation of the intermediate phosphine imide 11 that slowly transformed into the 1H‐benzimidazole 7b . The structure of 11 was established by crystal‐structure analysis. While the N‐methylated ortho‐nitroacetanilide 3 cyclised to the 1,2‐dimethyl‐1H‐benzimidazole ( 8 ), the 2‐methylpropananilide 4 was transformed into 1‐methyl‐3‐(1‐methylethyl)‐2H‐benzimidazol‐2‐one ( 9 ).     

Trace Analysis of Al on Silicon Surfaces by Ultra‐soft X‐Ray Emission Spectroscopy

It is shown that near normal incidence, low‐energy electron excitation of Al on silicon surfaces by ultra‐soft X‐Ray emission spectroscopy yielded limits of detectibility (LD) in the picogram region. This result on L band emission via electron excitation is fully competitive with photon excitation using K‐α lines via grazing incidence total reflection techniques (TXRF). Surprisingly, it was also found that normal incidence synchrotron photon excitation on the same sample yielded much higher values of LD than low‐energy electron excitation, undoubtedly due to the use of a poor transmission grating used in the entrance optics.     

Ray Model of an Incident Gaussian Beam for Analyzing a Micro-Optical Communication Device with a GRIN Lens System

For the design of reliable micro-optical devices with a high coupling efficiency, a source-modeling method necessary for ray tracing is newly proposed. This method is based on the ray-division of an incident wavefront estimated by Gaussian beam optics. The simulation result obtained using the proposed method was compared with those of the conventional methods, and its accuracy was confirmed by the experimental results. Finally, the method was used to design a micro-optical device with two GRIN lenses and a thin-film filter.     

Generalized space-time paraxial acoustic ray tracing

Paraxial ray tracing has gained popularity in seismology and underwater acoustics for modelling the propagation of sound when the medium is stationary and time independent. In this article differential geometry is used to derive a generalized paraxial ray-tracing procedure valid for any fluid media described by a local sound speed and velocity depending arbitrarily on position and time. Geodesic deviation is used to model acoustic beam deformation, and the sectional curvature along a ray to determine convergence and divergence zones in space. The resulting paraxial equations presented here are the most general that can be derived for the acoustic field and apply to any environment including those with time dependence and fluid motion. Applied to layered media the geodesic deviation equation is solved exactly. Some illustrative examples are included.     

On geodesic structures of weakly median graphs—II: Compactness, the role of isometric rays

We prove that the vertex set of a K_ℵ0-free weakly median graph G endowed with the weak topology associated with the geodesic convexity on V(G) is compact if and only if G has one of the following equivalent properties: (1) G contains no isometric rays; (2) any chain of interval of G ordered by inclusion is finite; (3) every self-contraction of G fixes a non-empty finite regular weakly median subgraph of G. We study the self-contractions of K_ℵ0-free weakly median graphs which fix no finite set of vertices. We also follow a suggestion of Imrich and Klavzar [Product Graphs, Wiley, New York, 2000] by defining different centers of such a graph G, each of them giving rise to a non-empty finite regular weakly median subgraph of G which is fixed by all automorphisms of G.     

Application of the ray tracing method in studying tracks in SSNTDs

The ray tracing method was applied to study etched tracks from α-particles in CR-39 solid-state nuclear track detectors. The transmission mode of a microscope operation was simulated. A track was considered as a set of small triangular elements, and the brightness of all elements was calculated systematically through the entire track to create the final image. Preliminary results are given for α-particle tracks in the CR-39 detector for initial energies of 4 and 4.5 MeV, and incident angles of 40 and 90°, respectively. Total reflection, as well as the slope of a surface element in the track wall, were identified as the main factors that affect the brightness of that element. At this stage, comparisons with experimental results can be made in terms of the average grey levels for the entire tracks.     

GRIN光学中光线追迹的一种新方法

由哈密顿光学中的拉格朗日方程推出光线方程，用Runge—Kutta方法求解光线方程，给出光线追迹的新方法。     

Ray aberrations of two-dimensional oblique lattices on the self-image plane

We extend the geometrical theory of aberration for a self-imaging system to the case of two-dimensional oblique lattices. In our approach, the fundamental translation vectors of the lattice are not restricted in both length and orientation. Evaluating the disturbance of light through the oblique lattice under coherent illumination, we find the conditions of constraint which limit the self-imaging of the oblique lattice. Various types of oblique lattices are shown to obey the self-imaging conditions. We derive the equations to trace the optical paths of self-imaging rays and then analyze the ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of the corresponding actual ray. The ray aberrations are shown to disappear when the periods of the lattice are large compared with the wavelength of light. We find that the ray aberrations carried by self-imaged oblique lattices are totally undercorrected and the aberrated image patches are displaced along the direction tangent vector of a chief ray.     

D形截面环流器中的磁面及LHCD的研究

本文利用环形系统的Ｇｒａｄ－Ｓｈａｆｒａｎｏｖ方程得到了Ｄ形截面的托卡马克磁面位形，并利用射线追踪技术研究了Ｄ形磁面位形下低杂波的运动形态。定性地研究了Ｄ形磁面位形下利用低杂波驱动电流的可行性，优化地给出了驱动电流的最佳方式。     

A Public-Key Traitor Tracing Scheme with Revocation Using Dynamic Shares

We proposed a new public-key traitor tracing scheme with revocation capability using dynamic shares and entity revocation techniques. Our schemes traitor tracing and revocation programs cohere tightly. The size of the enabling block of our scheme is independent of the number of receivers. Each receiver holds one decryption key only. The distinct feature of our scheme is that when traitors are found, we can revoke their private keys (up to some threshold z) without updating the private keys of other receivers. In particular, no revocation messages are broadcast and all receivers do nothing. Previously proposed revocation schemes need update existing keys and entail large amount of broadcast messages. Our traitor tracing algorithm works in a black-box way. It is conceptually simple and fully k-resilient, that is, it can find all traitors if the number of them is k or less. The encryption algorithm of our scheme is semantically secure assuming that the decisional Diffie-Hellman problem is hard.AMS Classification: 11T71, 68P30