The lack of measurability of the empirical process with respect to the sigma-field generated by the ‘natural’ l∞ metric, as illustrated in the previous notes, needs an extension of the standard weak convergence theory that can handle situations where the converging stochastic processes may no longer be measurable (though the limit will be a tight Borel measurable random element). Of course, an ...

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

0957+561 is the first gravitational lens system to be discovered and first for which a time delay was measured. Because the system is unusually rich in observables such as image positions, fluxes, VLBI structure, and polarization it has been modelled quite extensively. However, since it resides in a cluster providing substantial convergence, the velocity dispersion of the lensing galaxy is an i...

0957+561 is the first gravitational lens system to be discovered and first for which a time delay was measured. Because the system is unusually rich in observables such as image positions, fluxes, VLBI structure, and polarization it has been modelled quite extensively. However, since it resides in a cluster providing substantial convergence, the velocity dispersion of the lensing galaxy is an i...

The literature on income disparities across China’s provinces suggests that there has been (absolute) divergence in per capita incomes since 1978, a trend which has accelerated since the early 1990s. We contribute to this literature by updating the convergence analyses to include the most recent period (1994-2003). Four methods (beta and sigma convergence, Markov chain and kernel density analys...

Background and Aims: Six sigma is the latest version of total quality management. It is quantitative goal for process performance. With increasing demands for improved accuracy and reliability of the results, Six Sigma is gaining increased visibility in the clinical laboratory process outcomes. The aim of study was to evaluate the quality of analytical phase performance in a clinical biochemist...

We propose a general framework for studying last passage times, suprema and drawdowns of a large class of continuous-time stochastic processes. Our approach is based on processes of class Sigma and the more general concept of two processes, one of which moves only when the other is at the origin. After investigating certain transformations of such processes and their convergence properties, we ...