Sentence examples for bounds in which from inspiring English sources

I read attempts to expand the bounds in which God can be encountered: "We can never see Christianity from the catechism," Ralph Waldo Emerson says, "from the pastures, from a boat in the pond, from amidst the songs of the wood-birds we possibly may".

The fractional order interval quasi-polynomial is decomposed into several vertex characteristic quasi-polynomials by the lower and upper bounds, in which the value set of the characteristic quasi-polynomial for vertex quasi-polynomials in the complex plane is a polygon.

One sufficient condition for Lipschitz continuity is that the l2-norm of the Hessian matrix of F x) is bounded, in which case this bound can be used for the Lipschitz constant.

The producers gave them dozens of clips from movies like "Bound," in which Gina Gershon and Jennifer Tilly had a notoriously explicit affair.

His sole theatre credit was in a Folkestone amateur production of Outward Bound, in which, the Folkestone Herald said, he was "a constant source of surprise and wonderment... his easy confidence, nonchalant cynicism and expressive gestures conveyed everything necessary for the part, and he won a richly deserved triumph".

In applying the multiantenna secrecy capacity results, we develop an outer bound in which the source and relay are modeled jointly as a multiantenna transmitter.

It is clear that the sequence is bounded in which ensures the existence of a weakly convergent subsequence of, denoted again by, such that (3.28).

(c) g is locally Riemann integrable if and only if it is locally bounded, in which case g has a locally Lipschitz continuous CD primitive.

We provide here a novel similar lower bound in which the channel distribution corresponding to the perfect CSIT is actually that of the estimated channels, thus providing a much tighter lower bound compared to the one in [15], where the usual perfect CSIT channel distribution is that of the true channel.

5. g is Bochner integrable if and only if it has a locally absolutely continuous CD primitive that has the left limit at supI. 6. g is locally Riemann integrable if and only if it is locally bounded, in which case g has a locally Lipschitz continuous CD primitive.

Assume that,,,, and is a normal function on, then is compact if and only if is bounded, and for any bounded sequence in which converges to zero uniformly on compact subsets of as, one has.