There is thus an integrability condition at work, and Cartan's method for realizing integrability conditions was to introduce a differential form.
22.
There is thus an integrability condition at work, and Cartan's method for realizing integrability conditions was to introduce a differential form.
23.
Several structures on manifolds, such as a K�hler structure, are " G "-structures with an additional integrability condition.
24.
That is, Riemann-integrability is a " stronger " ( meaning more difficult to satisfy ) condition than Lebesgue-integrability.
25.
That is, Riemann-integrability is a " stronger " ( meaning more difficult to satisfy ) condition than Lebesgue-integrability.
26.
The idea here is that a Sobolev space provides the natural setting for both the idea of square-integrability and the idea of differentiation.
27.
In 1987 Irene Dorfman introduced the Dorfman bracket [, ] D, which like the Courant bracket provides an integrability condition for Dirac structures.
28.
In particular a theory for Lie equations formulated by Malgrange emerged, giving a very broad formulation of the notion of " integrability ".
29.
His work with Giuseppe Modica on the local higher integrability properties of solutions to elliptic systems has had an influence on the development of partial regularity theory.
30.
Square integrability is equivalent to saying that a Cauchy sequence converges to a finite value under the weak topology : the space contains it's limit points.
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