The averaging lemma

The Averaging Lemma

Averaging lemmas arise in the study of regularity of solutions to nonlinear transport equations. The present paper shows how techniques from Harmonic Analysis, such as wavelet decompositions, maximal functions, and interpolation, can be used to prove averaging lemmas and to establish their sharpness. Let f(x, v) be a real-valued function defined on R × Ω, where Ω is a bounded domain in R. In ap...

On a Lemma of Milutin concerning Averaging Operators in Continuous Function Spaces

We show that any infinite compact Hausdorff space S is the continuous image of a totally disconnected compact Hausdorff space S', having the same topological weight as S, by a map 95 which admits a regular linear operator of averaging, i.e., a projection of norm one of C(S') onto <p°C(S), where <p°: C(S) -*■ C(S') is the isometric embedding which takes fe C(S) into/« ¡p. A corollary of this the...

THE FULL AVERAGING OF FUZZY DIFFERENTIAL INCLUSIONS

In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.

Lecture 19 : The Vanishing Lemma and Lemma 8 . 8

The Generalized XOR Lemma

The XOR Lemma states that a mapping is regular or balanced if and only if all the linear combinations of the component functions of the mapping are balanced Boolean functions. The main contribution of this paper is to extend the XOR Lemma to more general cases where a mapping may not be necessarily regular. The extended XOR Lemma has applications in the design of substitution boxes or S-boxes u...