Sesquiterpenoids from the Aerial Parts of Inula japonica

Fourteen sesquiterpenoids with an eudesmane C‐atom skeleton, including four new ones, (1β,5α,7β,8β,11β)‐5‐hydroperoxy‐1‐hydroxyeudesm‐4(15)‐eno‐12,8‐lactone ( 1 ), (1β,5α,7β,8β)‐8‐(acetyloxy)‐5‐hydroperoxy‐1‐hydroxycostic acid methyl ester ( 12 ), and a mixture of (1β,3β,4β,7β,8β)‐1,3‐dihydroxyeudesma‐5,11(13)‐dieno‐12,8‐lactone ( 7 ) and (1β,3β,4β,7β,8β,11β)‐1,3‐dihydroxyeudesm‐5‐eno‐12,8‐lactone ( 8 ), were isolated from the aerial parts of Inula japonica (Asteraceae). Their structures were determined by extensive spectroscopic methods, and those of 7 and 12 confirmed by means of single‐crystal X‐ray diffraction analysis.     

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.     

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.     

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。     

Analytical derivation of a formula for the reduction of computation time by the voxel crossing technique used in room acoustical simulation

Computation times of room acoustical simulation algorithms still suffer from the time consuming search for ray-wall-intersections. Spatial subdivision may speed up ray tracing considerably. For room acoustics, where the number of surface polygons (walls) is not so high, the voxel technique appears suitable. The voxel crossing algorithm is very fast. However, its performance was not yet investigated up to now. Voxels are small cubes by which the space is subdivided periodically. The advantage: Only in the rare case a voxel intersects a wall the intersection point needs to be computed. In this paper, by estimating the probabilities of such intersections, an analytical formula is derived, by which the optimum degree of spatial subdivision and the factor of acceleration of the algorithm can be forecasted. It turns out that the computation time increases only with instead of with K₀ (the number of polygons of the room). Thus, on a modern PC, computation time for a full room acoustical simulation even for highly complicated rooms may be reduced by a factor in the order of 100, i.e. to a few seconds.     

Analysis of ray tube area in geometrical shock dynamics

We provide a rigorous analysis of structure of a ray tube in geometrical shock dynamics. Our aim is to shed more lights on the cross-sectional area function of a ray tube. We have shown that for a given ray tube and a given initial value of cross-sectional area, then its cross-sectional area can be determined uniquely everywhere. We give a definition of cross-sectional area of a ray tube in precise mathematical terms and from that we derive a set of relations, each describing the cross-sectional area for an arbitrary ray tube in geometrical shock dynamics. We have shown that from our results one can deduce Whitham’s area function relation as a partial differential equation from our general formulations. Some applications are discussed.     

Asymptotic analysis of the Hermite polynomials from their differential–difference equation

We analyze the Hermite polynomials H _n (x) and their zeros asymptotically, as n → ∞ We obtain asymptotic approximations from the differential–difference equation which they satisfy, using the ray method. We give numerical examples showing the accuracy of our formulas.