Principal components in the nonnormal case: The test of equality of Q roots

The limiting distribution of the likelihood ratio statistic W_q for testing the hypothesis of equality of q characteristic roots of a covariance matrix is studied in the case of nonnormal populations. It is shown, both theoretically and empirically, that the limiting distribution of W_q is not robust to departures from normality and that W_q cannot be used for nonnormal populations with long tails. For the class of elliptical populations the limiting distribution of W_q can be expressed in close form. A corrected test statistic, W_q^*, is proposed that can be used in principal component analysis when sampling from elliptical populations.     

Centroaffine First Order Invariants of Surfaces in IR4

An investigation of the centroaffine geometry of surfaces in IR⁴ leads to the centroaffine first order invariants: the vector bundle valued second fundamental form, the affine semiconformal structure, the h³-semiconformal structure and the centroaffine metric. A classification of surfaces by their semiconformal structures according to signature and rank is given. This involves the study of the orbits of two pencils of symmetric bilinear forms on IR² under a change of basis. Combined with previous results ([Nomizu-Sasaki 93]) a complete classification of the zero-degenerate surfaces is obtained and examples of the other surface types are constructed.     

Derivate von 4,5-dihydroxypyridonen durch ringerweiterung

The epimeric bromoghydrins 13/14 as well as their ethers 5/6 rearrange in the presence of silver ions to the 5-hydroxypyridones 15 or their ketals 9 respectively. with the bromohydrin ethers 5/6a and b this transformation is effected also with sodium methoxide. Under these reaction conditions the ring expansion is presumend ot proceed via bicyclic aziridines of which 7 could be issolated, The N-methylated compounds 5c/6c which cannot react likewise, form with sodium methoxide the 6-methoxypyridone 12 .     

On the fluid limit of the M/G/∞ queue

The paper deals with the fluid limits of some generalized M/G/∞ queues under heavy-traffic scaling. The target application is the modeling of Internet traffic at the flow level. Our paper first gives a simplified approach in the case of Poisson arrivals. Expressing the state process as a functional of some Poisson point process, an elementary proof for limit theorems based on martingales techniques and weak convergence results is given. The paper illustrates in the special Poisson arrivals case the classical heavy-traffic limit theorems for the G/G/∞ queue developed earlier by Borovkov and by Iglehart, and later by Krichagina and Puhalskii. In addition, asymptotics for the covariance of the limit Gaussian processes are obtained for some classes of service time distributions, which are useful to derive in practice the key parameters of these distributions.