浅议物理实验教学环节改革

为进一步提高大学物理实验的教学质量，本文就实验课的预习、操作、实验报告的撰写及考核方法进行了探讨。     

Recent developments in the statistical processing of textual data

Statisticians are accustomed to processing numerical, ordinal or nominal data. In many circumstances, such as socio-economic, epidemiologic sample surveys and documentary data bases, this data is juxtaposed with textual data (for example, responses to open questions in surveys). This article presents a series of language-independent procedures based upon applying multivariate techniques (such as correspondence analysis and clustering) to sets of generalized lexical profiles. The generalized lexical profile of a text is a vector whose components are the frequencies of each word (graphical form) or ‘repeated segment’ (sequence of words appearing with a significant frequency in the text). The processing of such large (and often sparse) vectors and matrices requires special algorithms. The main outputs are the following: (1) printouts of the characteristic words and characteristic responses for each category of respondent (these categories are generally derived from available nominal variables); (2) graphical displays of the proximities between words or segments and categories of respondents; (3) when analysing a combination of several texts: graphical displays of proximities between words or segments and each text, or between words or segments and groupings of texts. The systematic use of ‘repeated segments’ provides a valuable help in interpreting the results from a semantic point of view.     

Time saving fluid dynamic predictions in a wetting-drying process: A hypothesis for vertisols

This paper is aimed at investigating the effect of the initial water content in a vertisol sample on the whole wetting-drying process leading the system to a change in volume. In order to do this, an experimental setup was realized and employed with very thin soil layers wetted from below (“per ascensum”). The results show that the effect of the initial water content on the swelling-shrinkage process is to shift the corresponding curve e-ϑ towards bigger-smaller values of the humidity but does not seem to affect the dynamics of the process. The text was submitted by the authors in English.     

Reformulation of the support set selection problem in the logical analysis of data

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging results are obtained and discussed.     

One-dimensional stochastic Burgers equation driven by Lévy processes

In this paper, we proved the global existence and uniqueness of the strong, weak and mild solutions for one-dimensional Burgers equation perturbed by a Poisson form process, a Poisson form and Q-Wiener process with the Dirichlet bounded condition. We also proved the existence of the invariant measure of these models.     

INITIAL VALUE TECHNIQUES FOR THE HELMHOLTZ AND MAXWELL EQUATIONS

We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging.     

The crystal structure on the set of Mirkovi?-Vilonen polytopes

In an earlier work, we proved that MV polytopes parameterize both Lusztig's canonical basis and the Mirkovi?-Vilonen cycles on the affine Grassmannian. Each of these sets has a crystal structure (due to Kashiwara-Lusztig on the canonical basis side and due to Braverman-Finkelberg-Gaitsgory on the MV cycles side). We show that these two crystal structures agree. As an application, we consider a conjecture of Anderson-Mirkovi? which describes the BFG crystal structure on the level of MV polytopes. We prove their conjecture for sln and give a counterexample for sp₆. Finally we explain how Kashiwara data can be recovered from MV polytopes.     

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

Norms and perfect graphs

The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods.In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.This is a written account of an invited lecture delivered by the second author on occasion of the 12. Symposium on Operations Research, Passau, 9.–11. 9. 1987.     

成像光谱技术中机上实时数据压缩方法研究

根据成像光谱仪的特点用一系列串行的一维压缩实现二维图像压缩.提出了在机上对原始数据从光谱方向进行实时压缩的“二真值线性预测方法”.该法可做到压缩/复原后光谱特征信息不丢失.实验表明,对大多数光谱数据在1%的重建精度下,至少可获得2:1的压缩比.从总体而言,压缩后原始数据率可降低3～4倍.文中还对压缩数据的编码和误差进行了讨论.