A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (xn) statistically quasiCauchy if st − limn→∞ d(xn+1, xn) = 0, and lacunary statistically quasi-Cauchy if Sθ − limn→∞ d(xn+1, xn) = 0.Weprove that a subset E of ametric space is totally bounded if and only if any sequence of points in E has a subsequence...

A frequently encountered source of systematic error in quantum computations is imperfections the control pulses which are classical fields that qubit gate operations. From an analysis mechanical time-evolution operator spin wavefunction, it has been demonstrated composite can mitigate certain errors and appealing geometric interpretation was developed for design error-suppressing pulses. Here w...

We rigorously define the Liouville action functional for the finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that classical action – the critical value of the Liouville action functional, considered as a function on the quasiFuchsian deformation space, is an antiderivative of a 1-form ...