Sentence examples for better lower bound from inspiring English sources

Hence is a better lower bound for than (1.2) for.

To obtain a better lower bound of β ∗, we first prove.

To obtain a better lower bound, we give the following theorem by breaking N into disjoint subsets S and its complement S̅.

Remark 2. In case L ω > c ′ ≥ 0, a.e., we cannot get a better lower bound of lim inf n S n, k n ω.

where we use the well-known consequence that ℋ is bounded on L p ( R n ) with the sharp bound p p − 1 and the following relationship: ( q − p ) ( 1 − 1 p ) + p + ( β n − 1 ) q = 0. To obtain a better lower bound of ∥ H ∥ L p → L q, we can take f 0 ( x ) = | x | n C 1 p χ { | x | < 1 } ( x ), C 1 > − 1.

This motivates the following problem: under the conditions of Theorem 2, how to get a better lower bound of lim inf n S n, k n ω in case of L ω > c ′ ≥ 0, a.e.? Definition 2. (Generalized empirical distribution function) Let (X n )n∈Nbe identically distribution with common distribution function F, for each m, n ∈ N, let F m, n x = 1 n ∑ k = m m + n - 1 1 X k ≤ x.

A better register lower bound is computed considering overlapped lifetimes over II cycles, getting an array (called LiveVector) of II elements as described in [33].

This result is further enhanced in [29] wherein the authors proven that in most networks, the scheduling performance under GMS is much better than the lower bound.

In this paper, we study the Young and Hölder inequalities from the point of view of the deviation from equalities with better upper and lower bound estimates.

These new algorithms would help to obtain a better estimation of the lower bound of R min under the infinite site model.

Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF.