Sentence examples for been proved for example from inspiring English sources

The following result has been proved for example in [34], using Laplace transforms, and also in [26] using only the definition of AB derivatives and integrals.

But we do need something more than band aid solutions when it has been proven, for example, that texting while driving is actually worse than driving drunk and real people are dying as a result of uncontrollable texting habits.

This is proved, for example, in [14].

This can be proved for example by performing the substitution (nrightarrow2n-1) (whish is motivated by the fact that (B_{2n+1}=0) (forall n>0)) and by using the following asymptotic expansion of the Bernoulli numbers: B_{2n}sim (-1 )^{n-1}4sqrt{pi n} biggl( frac{n}{pi e} biggr)^{2n}, quad nrightarrowinfty, and the Stirling approximation of ((2n-1 )!).

It also follows that condition A1* is also satisfied when (4.9) holds, that is the mapping Q given by Q ( x, y, z ) = 2 z 2 D Φ + z ( x - y ) 1 + z 2 | x - y | 2 is one to one in x, for 0 < z < z 0 ( x, y ), which can be proved for example from the quadratic structure of the equation, Q ( x, y, z ) = q.

The improved wettability was proved, for example, by V. B. Yadav and A. V. Yadav [ 15].

Contrary to expectations, the gain of novel introns by other mechanisms could not be proved, for example, by insertion of a spliceosomal intron via reverse splicing into a new position, by insertion of a transposable element or by gene conversion with an intron-containing paralog.

Several existence and uniqueness theorems have been proved for equation (4.1) (see, for examples, [22 25]. We are now ready to give an application of Theorem 3.1 to an iterative solution of the nonlinear Hammerstein type Equation (4.1).

The algorithm guarantees that with high probability the lookup delay to visit every peer is of O log N) hops, comparable to the delay of the exact-match search over the DHTs, which is proved for two example DHTs, Chord and Pastry in the paper.

This technique has been proven beneficial for example in tibial fracture healing [8].

Cost-effectiveness of preoperative PET has been proven with, for example, prevention of unnecessary surgery in one out of five patients with suspected non-small-cell lung cancer after the addition of [18F]FDG-PET imaging to conventional staging [32].