A class of “absolutely continuous functions” ofnvariables is introduced. The absolute continuity implies continuity, weak differentiability with gradient inLn, differentiability almost everywhere, area, coarea and degree formulae. This gives a unified approach to some previously known conditions for the mentioned results based on monotonicity, finite dilatation or Nike Air Max 97 Milan
higher integrability of the gradient.
In this paper, the extention to interval theory of the classical Legendre Air Max 90 For Sale
polynomials is considered. The so-called interval Legendre polynomials are introduced and some properties are studied. Based on these polynomials an interval minimum square approximation is introduced when continuous and discrete data are taken.
For a sequence of i.i.d. zero mean random variables belonging to the domain of attraction of the normal law, two results concerning the rescaled range statistic are investigated in this paper. More specifically, we obtain precise asymptotics in the law of the logarithm related to complete convergence and a.s. convergence under some mild conditions.
We study the effects of spontaneously generated coherence on steady-state population distribution of a closed ∧-type atomic system. We find that the unexpected population inversions can be achieved on both of the optical transitions due to these coherent effects.