Statistical theory of turbulence-II

On the Statistical Theory of Turbulence.

The expression for ci is in agreement with the conclusions arrived at above. It shows that the form (14) of the equation of diffusion is a good guide to the physicist as it brings in evidence the quantities significant from his point of view. On the other hand, Kolmogoroff's equations (3) and (4) are more general since they include the case of transition probabilities which are inhomogeneous in...

Statistical theories of turbulence

Statistical properties of turbulence

It is now convenient to reexamine some questions of fundamental nature with the purpose of analyzing the possible consequences of Ruelle’s principle introduced in §5.7. We shall make frequently reference to the general description of motions given in Chap. 5 in a context in which we imagine that the considered motions are attracted by some attracting set in phase space, which will have zero vol...

On Some Problems of a Statistical Group-theory. Ii

if only co(n) -> with n . Hence log O(P) is for almost all P's much less than its maximum, which is as LANDAU 2 proved, 1/n log n . Though several questions in the first paper were left to later papers of this series and we intend indeed to return to them in paper 111, in this paper we launch another trend which seems to us equally interesting in itself and perhaps even more inherent to the alg...

Math 541 : Statistical Theory II Methods of Evaluating Estimators

A difficulty that arises is that since we can usually apply more than one of these methods in a particular situation, we are often face with the task of choosing between estimators. Of course, it is possible that different methods of finding estimators will yield the same answer (as we have see in the MLE handout), which makes the evaluation a bit easier, but, in many cases, different methods w...