Spacetime and Euclidean geometry

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.This article is dedicated to Michael P. Ryan on the occasion of his sixtieth birthday. Mike's passion for, and deft practice of, both geometry and pedagogy is legendary at Maryland. We are pleased with this opportunity to present our pedagogical effort to elucidate the geometry of Minkowski spacetime, the most homogeneous of cosmologies.     

过两个样本点的最小一乘回归线

本文用一种选代法，求过两个样本点的最小一乘回归线．     

浅谈东方插花历史及其风格

本文从东方式插花的历史渊源、风格特征、命名三个方面进行了阐述。东方式插花受中国历史的影响较大,由于中国的美学思想是崇尚自然,因此在插花艺术中表现为“自然之真”、“人文之善”、“艺术之美”、“圣洁尊崇”的意境,常以命名的方式来加强意境和主题的表现。     

带孔的圆形窗口上的直线裁剪问题

详尽地分析了带孔的圆形窗口上的直线裁剪问题,并给出了算法。     

Pathwidth of Planar and Line Graphs

 We prove that for every 2-connected planar graph the pathwidth of its geometric dual is less than the pathwidth of its line graph. This implies that pathwidth(H)≤ pathwidth(H ^*)+1 for every planar triangulation H and leads us to a conjecture that pathwidth(G)≤pathwidth(G ^*)+1 for every 2-connected graph G. Received: May 8, 2001 Final version received: March 26, 2002 RID="*" ID="*" I acknowledge support by EC contract IST-1999-14186, Project ALCOM-FT (Algorithms and Complexity - Future Technologies) and support by the RFBR grant N01-01-00235. Acknowledgments. I am grateful to Petr Golovach, Roland Opfer and anonymous referee for their useful comments and suggestions.     

Cusp satellite bands in the spectrum of molecule

We report measurements and a theoretical explanation of the cusp-shaped satellite bands in the blue wing of the cesium D₂ resonance line which have been observed for the first time. The bands are identified as transitions where the upper state dissociates into the 6 ²P _3/2 + 6 ² S _1/2 atomic asymptote. The experiment has been performed using a standard absorption setup, computer controlled data acquisition and computer data processing. We have shown that the peculiar shape of the difference-potential curve is solely responsible for the spectrum containing the cusp-shaped satellite bands. The appearance of these satellite bands has been discussed and explained relating the theory of satellite bands to the catastrophe theory. The shape of the line wing and of the satellite bands have been calculated using the Fourier transform technique. To ensure a more stringent comparison between the experimental and the theoretical spectrum, we have analyzed and compared the derivatives of the measured and the calculated satellite band shape. On the contrary to the customary direct comparison between the measured and the calculated absorption coefficient, the derivative clearly shows all differences and resemblances between satellite band profiles. The degree of coincidence of the experimentally observed and the theoretically calculated satellite band shape can be used as an ultimate check on the assessment of the quality of potential-energy curves involved in the formation of satellite bands. Received: 1 October 1997 / Revised: 14 January 1998 / Accepted: 24 February 1998     

Line bundle Laplacians over isospectral nilmanifolds

We show that nontrivial isospectral deformations of a big class of compact Riemannian two-step nilmanifolds can be distinguished from trivial deformations by the behaviour of bundle Laplacians on certain non-flat hermitian line bundles over these manifolds.

     

Temperature dependence of lattice distortions in polyethylene

Summary Melt-crystallized samples of polyethylene show a reversible change of the line-width in X-ray wide angle scattering. The width increases with decreasing temperature, the largest changes occur in the temperature ranges of the- and-relaxation processes. Fourier analyses of the line profiles using the method of Warren and Averbach are indicative of strain variances which can be attributed to stress variances over larger domains in the semi-crystalline superstructure. An explanation for this effect is found in the stress parallel to the planes of the lamellae produced by the differences of the thermal expansion coefficients of the crystalline and amorphous domains in the lamellar two-phase systems. The magnitude of the stress is determined by the difference of the thermal expansion coefficients as well as the Young's moduli of the domains whereas the stress variances are related to the statistics of the lamellar thicknesses.With 23 figures and 3 tables