Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.     

实二次函数域基本单位的范

作为Ｈ．Ｆ．Ｔｒｏｔｔｅｒ［３］中一个结果的模拟，本文给出实二次函数域Ｋ中基本单位ε的范为Ｎ（ε）＝ｇ的一些充分必要条件，其中ｇ为Ｋ的常数域Ｆｑ的非零乘法群Ｆｑ＾＊的生成元（２├ｑ）。利用图论的语言，本文还给出了Ｎ（ε）＝ｇ的一些充分条件，这些条件对于数域也同样地适用，从而推广了Ｔｒｏｔｔｅｒ［３］和前人工作中关于充分条件的结果。     

Intégalités de Sobolev et Temps d'Atteinte

We investigate the links between Sobolev and Nash inequalities, capacity and hitting times estimates and ultracontractive semigroups, in a non-symmetric setting.     

De Sitter空间中具有常均曲率的类空超曲面（Ⅱ）

设Ｍ＾ｎ是Ｄｅ Ｓｉｔｔｅｒ空间Ｓ１＾ｎ＋１中具有常数平均曲率且第二基本形式长度的平方为常数的完备类空超曲面，若Ｓ≤２（ｎ－１）＾１／２，则Ｍ＾ｎ是等参超曲面。     

Power expansions for the self-similar solutions of the modified Sawada-Kotera equation

The fourth-order ordinary differential equation that defines the self-similar solutions of the Kaup—Kupershmidt and Sawada—Kotera equations is studied. This equation belongs to the class of fourth-order analogues of the Painlevé equations. All the power and non-power asymptotic forms and expansions near points z = 0, z = ∞ and near an arbitrary point z = z ₀ are found by means of power geometry methods. The exponential additions to the solutions of the studied equation are also determined.      

Hermitian阵的 Hadamard积的Schur补的一些不等式（英文）

本文得到了正定Hermitian阵的Hadamard积的Schur补的一些不等式，进而，给出了他们的一些应用，这些改进了近期的一些结束．     

广义Schur补的广义逆

对四分块矩阵A=A(︿) A(︿,︿′)A(︿′,︿) A(︿′)来说 ,如果 A和 A(︿)都是非奇异的 ,则A- 1 (︿′) =(A/︿) - 1 ,这里 A/ ︿=A(︿′) -A(︿′,︿) A(︿) - 1 A(︿,︿′)是 A(︿)在 A中的 Schur补 .王伯英教授指出上述等式 ,对半正定的 Hermitian矩阵而言 ,一般也是不能推广到 Moore-Penrose逆上去的 .在某些限制条件下 ,我们证明了广义逆的主子矩阵与广义 Schur补的关系是密切的 ,它使经典结果成为特例     

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.     

On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

Metallocene copolymers of propene and 1‐hexene: The influence of the comonomer content and thermal history on the structure and mechanical properties

The relationships between the structure and properties have been established for copolymers of propylene and 1‐hexene synthesized with an isotactic metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is the comonomer content. The thermal treatment, that is, the rate of cooling from the melt, is also important. These factors affect the thermal properties, the degree of crystallinity, and therefore the structural parameters and the viscoelastic behavior. A slow cooling from the melt favors the formation of the γ phase instead of the α modification. Regarding the viscoelastic behavior, the β relaxation, associated with the glass‐transition temperature, is shifted to lower temperatures and its intensity is increased as the 1‐hexene content raises. The microhardness values are correlated with those of the storage modulus deduced from dynamic mechanical thermal analysis curves, and good linear relations have been obtained between these parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1253–1267, 2006