We shall in fact prove it with C = 2. In the same situation, Aschbacher and Guralnick proved in Theorem A of [1] that \H\G, V)\<\V\. Guralnick has recently improved this bound to \H(G, V)\^\V\l, which is the best possible. At the present time, a proof of the intermediate result \H(G, V)\ «= |V|S is available in preprint form [13]. By using this result, it should be possible with a little extra ...

We give a short and elementary proof of the theorem Lutz Weis that growth bound positive $C_0$-semigroup on $L_p(\mu)$ equals spectral its generator. In addition, we generalise result to case uniformly eventually semigroups.

Among the mostly investigated parameters for noisy channels are code size, error probability in decoding, block length; rate, capacity, reliability function; delay, complexity of coding. There are several statements about connections between these quantities. They carry names like “coding theorem”, “converse theorem” (weak, strong, ...), “direct theorem”, “capacity theorem”, “lower bound”, “upp...

New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous differenc...

Abstract We introduce a notion of embedding codimension an arbitrary local ring, establish some general properties and study in detail the case arc spaces schemes finite type over field. Viewing as measure singularities, our main result can be interpreted saying that singularities space are maximal at arcs fully embedded singular locus underlying scheme, progressively improve we move away from ...

This paper deals with the quantitative Schmidt's subspace theorem and general from of second main theorem, which are two correspondence objects in Diophantine approximation theory Nevanlinna theory. In this paper, we give a new below bound for Chow weight projective varieties defined over number field. Then, apply it to prove version polynomials higher degree subgeneral position respect variety...

Statements of Shannon’s Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the domain of application is clarified. An examination of the bounds of the Theorem leads to a new symmetric restatement. It is shown that the extended upper bound ...

Clarkson Local Minima of Arrangements 6 Next to show that if v has outdegree i then v 0 is an i-minimum. Since v 0 j < 0 if and only if v 0 is below h j , we need to show that a coordinate v 0 j 6 = 0 corresponds to an oriented edge (v; q) where wv ? wq = w(v ? q) has the same sign as v 0 j. Suppose (v; q) is an edge of P. Then ^ Av = ^ b ^ Aq, with one strict inequality a j v = b j > a j q, an...

We establish a pointwise estimate of \(\vert A\vert \) along the mean curvature flow in terms initial geometry and HA\vert bound. As corollaries we obtain blowup rate an extension theorem with respect to \).