Comparison of volumes by means of the areas of central sections

The Busemann–Petty problem asks whether origin-symmetric convex bodies in Rⁿ with smaller areas of all central hyperplane sections necessarily have smaller n-dimensional volume. The solution was completed in the end of the 1990s, and the answer is affirmative if n4 and negative if n5. Since the answer is negative in most dimensions, it is natural to ask what information about the volumes of central sections of two bodies does allow to compare the n-dimensional volumes of these bodies in all dimensions. In this article we give an answer to this question in terms of certain powers of the Laplace operator applied to the section function of the body.     

Sample path analysis of level crossings for the workload process

We examine level crossings of sample paths of queueing processes and investigate the conditions under which the limiting empirical distribution for the workload process exists and is absolutely continuous. The connection between the density of the workload distribution and the rate of downcrossings is established as a sample path result that does not depend on any stochastic assumptions. As a corollary, we obtain the sample path version of the Takács formula connecting the time and customer stationary distributions in a queue. Defective limiting empirical distributions are considered and an expression for the mass at infinity is derived.This research has been supported in part by NSF Grants ECS-8811003 and DDM-8905638.     

Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.     

HL－1装置辅助加热等对能量约束的影响

在ＨＬ－１托卡马克上进行了辅助加热、加料、电流驱动的物理实验研究。在改善等离子体约束方面，某些实验取得了较好的结果。在适当的稳定放电条件下，低杂波电流驱动和弹丸注入辅助加料，均能使等离子体能量约束得到一定程度的改善，与相同密度条件下的欧姆加热放电相比，能量约束时间提高了约３０％。在电子回旋共振加热等离子体实验中，等离子体总能量明显增加，但与相同密度条件下的欧姆加热放电相比，能量约束时间减少了约２０％。     

Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.

     

氟氧化物陶瓷的多谱线上转换发光

以氧化硅、氟化铅为基质制备了Er3 :Yb3 共掺杂氟氧化物陶瓷 ,X 射线分析表明陶瓷中存在着 β PbF2 晶相 ,沉积在其中的稀土离子由于具有很低的无辐射跃迁几率而显示出良好的上转换性能。Er3 ,Yb3 离子之间存在的多种能量传递通道 ,导致稀土离子十分丰富的上转换谱线的出现。     

Methods in carbon K-edge NEXAFS: Experiment and analysis

Near-edge X-ray absorption spectroscopy (NEXAFS) is widely used to probe the chemistry and structure of surface layers. Moreover, using ultra-high brilliance polarised synchrotron light sources, it is possible to determine the molecular alignment of ultra-thin surface films. However, the quantitative analysis of NEXAFS data is complicated by many experimental factors and, historically, the essential methods of calibration, normalisation and artefact removal are presented in the literature in a somewhat fragmented manner, thus hindering their integrated implementation as well as their further development. This paper outlines a unified, systematic approach to the collection and quantitative analysis of NEXAFS data with a particular focus upon carbon K-edge spectra. As a consequence, we show that current methods neglect several important aspects of the data analysis process, which we address with a combination of novel and adapted techniques. We discuss multiple approaches in solving the issues commonly encountered in the analysis of NEXAFS data, revealing the inherent assumptions of each approach and providing guidelines for assessing their appropriateness in a broad range of experimental situations.     

X光光电子能谱法测定胶片中氟,硅和铝的研究

应用Ｘ光光电子能谱法测定了几种彩色胶片表面层中氟的１ｓ能级的结合能；分别比较了水处理前后、溅蚀前后胶片护膜层氟的变化，表明氟化物分布在护膜最表层，是一种易溶于水的氟化物；测定了彩色片护膜层所含硅２ｐ能级的结合能，与自制彩色片护膜层测定结果比较，优质片含一种较多负电性，用与自制片的无机硅不同的硅化物作毛面剂；对溅蚀前后优质片和自产彩色片中的硅铝比变化进行比较，提出优质彩色片Ｆ－４００的护膜层可能是双     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

On characterizing the bivariate exponential and geometric distributions

In this note, a characterization of the Gumbel's bivariate exponential distribution based on the properities of the conditional moments is discussed. The result forms a sort of bivariate analogue of the characterization of the univariate exponential distribution given by Sahobov and Geshev (1974) (cited in Lau and Rao ((1982), Sankhy Ser. A, 44, 87)). A discrete version of the property provides a similar conclusion relating to a bivariate geometric distribution.