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Kraft's inequality limits the lengths of codewords in a prefix code: if one takes an exponential of the length of each valid codeword, the resulting set of values must look like a probability mass function, that is, it must have total measure less than or equal to one. Kraft's inequality can be thought of in terms of a constrained budget to be ...
The Bugatti was the first bag designed by Hermès specifically as a women's handbag and is notable for being the first handbag to utilize a zipper pull. In 1935, Hermès's son-in-law Robert Dumas redesigned it as a spacious travel bag called Sac à main de Voyage. It was a sharp contrast to the dominant handbags of the time, which were simple ...
In mathematics, Grönwall's inequality (also called Grönwall's lemma or the Grönwall–Bellman inequality) allows one to bound a function that is known to satisfy a certain differential or integral inequality by the solution of the corresponding differential or integral equation. There are two forms of the lemma, a differential form and an ...
In this case the lemma implies that the smaller is the probability to be in a certain state (or close to it), the longer is the time of return near that state. [ 4 ] In formulas, if A {\displaystyle A} is the region close to the starting point and T R {\displaystyle T_{R}} is the return period, its average value is:
The S-procedure or S-lemma is a mathematical result that gives conditions under which a particular quadratic inequality is a consequence of another quadratic inequality. The S-procedure was developed independently in a number of different contexts [ 1 ] [ 2 ] and has applications in control theory , linear algebra and mathematical optimization .
In differential geometry, a branch of mathematics, the Moser's trick (or Moser's argument) is a method to relate two differential forms and on a smooth manifold by a diffeomorphism such that =, provided that one can find a family of vector fields satisfying a certain ODE.