Asymptotic Normality of Cross-correlogram Estimates of the Response Function

The problem of estimation of an unknown response function of a time-invariant continuous linear system is considered. Discrete-time sample input–output cross-correlograms are taken as estimates of the response function. The inputs are supposed to be zero-mean stationary Gaussian processes close, in some sense, to a white noise. Both asymptotic normality of finite-dimensional distributions of the estimates and their asymptotic normality in spaces of continuous functions are studied. Our basic tool is a new integral representation for cumulants of the estimate as a finite sum of integrals involving cyclic products of kernels. Some inequalities for these integrals are obtained and their asymptotic behaviour is studied.     

Composition and Antimicrobial Activity of the Essential Oil of Origanum × dolichosiphon P. H. Davis

The essential oil obtained by hydrodistillation from aerial parts ofOriganum × dolichosiphonP. H. Davis (Lamiaceae), a hybrid ofO. AmanumPost ×O. LaevigatumBoiss., was analyzed by GC/MS. Ninety-five compounds were characterized representing 92% of the oil. The major compounds were bicyclogermacrene (19.9%),-caryophyllene (13.0%), and germacrene D (10.8%). The antimicrobial activity of the oil was also determined     

Toeplitz Operators with Semi-Almost-Periodic Matrix Symbols on Hardy Spaces

We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces H ^p (1<p<). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p=2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol.     

Densité des Points à Coordonnées Multiplicativement Indépendantes

Nous montrons que pour toute sous-variété algébrique d'un tore multiplicatif (non contenue dans un sous-groupe algébrique propre), on peut choisir un ensemble Zariski dense de points algébriques de hauteur contrôlée, dont toutes les coordonnées sont multiplicativement indépendantes. Cet énoncé précise et généralise un théorème de S. Zhang qui lie la hauteur projective d'une varété au minimum essentiel de la hauteur des points algébriques de celle-ci. En tenant compte d'un résultat précédent des auteurs sur le problème de Lehmer généralisé à un tore, nous en déduisons une minoration pour la hauteur normalisée d'une sous-variété d'un tore. Cette dernière est optimale à un «-prés» en le degré géométrique de la variété étudiée (confer une conjecture du second auteur avec P. Philippon).In this article, we prove that on any subvariety of a multiplicative torus which is not contained in a proper algebraic subgroup, one can find a Zariski dense set of algebraic points of small height whose coordinates are multiplicatively independent. This statement generalizes an earlier result of S. Zhang which links the projective height of a variety with the essential minimum of its algebraic points. Taking into account an earlier result of the authors on the Lehmer problem generalized to a multiplicative torus, one deduces a lower bound for the normalized height of subvarieties of multiplicative groups. This lower bound is optimal up to an in the geometric degree of the variety studied (confer a conjecture by the second author and P. Philippon).     

A bracket power characterization of analytic spread one ideals

The main theorem characterizes, in terms of bracket powers, analytic spread one ideals in local rings. Specifically, let be regular nonunits in a local (Noetherian) ring and assume that , the integral closure of , where . Then the main result shows that for all but finitely many units in that are non-congruent modulo and for all large integers and it holds that for and not divisible by , where is the -th bracket power of . And, conversely, if there exist positive integers , , and such that has a basis such that , then has analytic spread one.

     

���ڸ�ά���ݵĸ���Hotelling'sT-square ����

The paper is concerned with the two-sample mean testing problem in high-dimension settings. We propose a composite Hotelling's T-square test, establish its asymptotical normality and study its local power. The finite-sample priority of the proposed test over existing high-dimensional tests is shown by simulations and illustrated by a real data-set analysis.     

气相色谱-质谱法分析橡苔浸膏中的挥发性化学成分

用挥发油提取器提取橡苔浸膏中的挥发油 ,利用气相色谱 -质谱法 ( GC- MS)分析了其中的化学成分 ,采用GC峰面积归一化法定量 ,鉴定出 2 4种化合物 ,共占挥发油总量的 83%以上     

Adaptive nonparametric estimation of a multivariate regression function

We consider the kernel estimation of a multivariate regression function at a point. Theoretical choices of the bandwidth are possible for attaining minimum mean squared error or for local scaling, in the sense of asymptotic distribution. However, these choices are not available in practice. We follow the approach of Krieger and Pickands (Ann. Statist.9 (1981) 1066–1078) and Abramson (J. Multivariate Anal.12 (1982), 562–567) in constructing adaptive estimates after demonstrating the weak convergence of some error process. As consequences, efficient data-driven consistent estimation is feasible, and data-driven local scaling is also feasible. In the latter instance, nearest-neighbor-type estimates and variance-stabilizing estimates are obtained as special cases.     

The constitutive equation resemblance of elastic — Plastic multiphase solid

Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.