Recently quasi-Monte Carlo algorithms have been successfully used for multivariate integration of high dimension d, and were signiicantly more eecient than Monte Carlo algorithms. The existing theory of the worst case error bounds of quasi-Monte Carlo algorithms does not explain this phenomenon. This paper presents a partial answer to why quasi-Monte Carlo algorithms can work well for arbitrari...

Ground states and dynamical properties of a dipolar Bose–Einstein condensate are analyzed based on the Gross–Pitaevskii–Poisson system (GPPS) and its dimension reduction models under an anisotropic confining potential. We begin with the three-dimensional (3D) GPPS and review its quasi-two-dimensional (2D) approximate equations when the trap is strongly confined in the z-direction and quasi-one-...

We classify the real and strongly real conjugacy classes in GLnðqÞ and SLnðqÞ. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This paper is the first of two that together classify the real and strongly real classes in GLnðqÞ, SLnðqÞ, PGLnðqÞ, PSLnðqÞ, and all quasi-simple covers of PSLnðqÞ.

We classify the real and strongly real conjugacy classes in PGLnðqÞ, PSLnðqÞ, and all quasi-simple covers of PSLnðqÞ. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This is a companion paper to [4] in which we classified the real and strongly real conjugacy classes in GLnðqÞ and SLnðqÞ.

We classify the real and strongly real conjugacy classes in GLnðqÞ and SLnðqÞ. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This paper is the first of two that together classify the real and strongly real classes in GLnðqÞ, SLnðqÞ, PGLnðqÞ, PSLnðqÞ, and all quasi-simple covers of PSLnðqÞ.