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Black Timberland Boots Women Uk Generalizations of the theory are indicated
The standard theory of frames in Hilbert spaces, using discrete bases, is generalized to one where the basis vectors may be labelled using discrete, continuous, or a mixture of the two types of indices. A comprehensive analysis of such frames is presented and various notions of equivalence among frames are introduced. A consideration of the relationschip between reproducing kernel Hilbert spaces and frames leads to an exhaustive construction for all possible frames in a separable Hilbert space. Generalizations of the theory are indicated and illustrated by an example drawn from the afline group. A model of the intestinal crypt, based on the results of the preceding paper, is presented. The model describes a steady state in which at the bottom of the crypt divisions give rise to cells which Black Timberland Boots Women Uk will in turn divide, and near the top of the crypt to cells which will differentiate without dividing. By means of theoretical phase distribution diagrams, the labelling and Timberland Stockists Bristol mitotic indices at various levels in the crypt are predicted and compared with those found by experiment; in this way the model is substantiated. The biological implications of the model are considered.