because S is “unbiased” and T 2 is “biased.” That means E(S) = σ 6= E(T ), i.e., an “unbiased estimator” is a statistic whose expected value is the quantity to be estimated. The goodness of an estimator is sometimes measured by the smallness of its “mean squared error,” defined as E ( ([estimator]− [quantity to be estimated]) ) . By that criterion the biased estimator T 2 would be better than t...

The paper is concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. In dimension two, we establish both interior and boundary regularity theorem for such a flow under smallness conditions. As a consequence, we establish the existence of global weak solutions that are smooth away from at most finitely many singular times ...

The linear and nonlinear evolution of unstable disturbances in high-Reynolds-number flows is reviewed from the perspective of asymptotic theory. For non-parallel and/or unsteady flows, quasiparallel and quasi-steady approximations can only be strictly justified by asymptotic expansions based on the smallness of the inverse Reynolds number. Further, such an asymptotic approach allows the inclusi...

The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the repulsive Vlasov-Poisson system with only integrable initial distribution function with finite energy. These solutions have a well-defined Lagrangian flow. ...

Botswana, Ghana, Mauritius and South Africa are sub-Saharan African countries that stand out for their development progress. Each of these countries has succeeded against the odds, against expectations. This paper synthesizes the common ingredients of these countries’ success, and derives lessons. It concludes that smallness, landlockedness, tropical location, distance from world markets, racis...

Are neutrinos their own antiparticles? We explain why they very well might be. Then, after highlighting the fact that, to determine experimentally whether they are or not, one must overcome the smallness of neutrino masses, we discuss the one approach that nevertheless shows great promise. Finally, we turn to the consequences of neutrinos being their own antiparticles. These consequences includ...

This paper is concerned with electron transport in semiconductors when electron-phonon interaction is considered. Smallness of the mean free path compared to a characteristic length scale and of the phonon energy compared to the thermal energy of the crystal are assumed. The corresponding limits in the transport problem are carried out and shown not to commute. An intermediate limit leads to a ...

Theoretical aspects of neutrino physics are reviewed, with emphasis on possible explanations of the smallness of neutrino masses and of the peculiar mixing pattern observed in the lepton sector. Some theoretically motivated frameworks, such as those based on spontaneously broken discrete flavour symmetries, are discussed, stressing the importance of low-energy observables, like anomalous magnet...

We prove upper and lower bounds for the metastability of a statespace decomposition for reversible Markov processes in terms of dominant eigenvalues and eigenvectors of the corresponding transfer operator. The bounds are explicitly computable and sharp. In contrast to many other approaches, the results do not rely on any asymptotic expansions in terms of some smallness parameter, but rather hol...

The smallness of the transverse dimensions of the colliding beams leads to suppression of bremsstrahlung cross section. This beam-size effect was discovered and investigated at INP, Novosibirsk. Different mechanisms of radiation are discussed. Separation of coherent and incoherent radiation is analyzed in detail. For linear collider this suppression affects the whole spectrum. It is shown that ...