Sentence examples for most exponentially with from inspiring English sources

From Theorem 4.1, we see that the pth moment will grow at most exponentially with exponent (frac{M_{2}}{ 1-k_{0})^{ 1-k_{

In [3], the author presented a result stating that, for initial value x ( t 0 ) = x 0, the p th moment of the unique solution x ( t ), t 0 ≤ t ≤ T of equation (2.1) under Lipschitz condition and linear growth condition will grow at most exponentially with exponent pα.

Let 0 < p ≤ 2. In view of Theorem 3.1 and Corollary 3.2, we know that the p th moment of the solution satisfies E | x ( t ) | p ≤ [ 1 + E | x 0 | 2 ] p 2 exp ( 2 p ( a + b ) ( t − t 0 ) ). for all t ≥ t 0. This means that the p th moment will grow at <span class="lh">most exponentially with exponent 2 p ( a + b ).

The quality of statistical decisions for exclusion of irrelevant SNPs from the output of GLL is determined by the combined, or effective, significance threshold, which decreases at most exponentially with the number of statistical independence tests applied to each irrelevant SNP.

Globally, natural gas vehicles have increased exponentially, with most of the growth in the past decade in Asia and Latin America.

The number of journals that have published a larger number of most-cited papers decreases exponentially with very good fit to a Lotka law.

At Thiruvananthapuram, in most of the months, NT increased exponentially with rain rate up to some value of R, which was different in different months, and then remained more or less constant or decrease slightly.

For most time constants, the moduli increase "exponentially" with length, even though there are some obvious differences between the various curves.

The risk for death increases exponentially with increasing age and dominates most other risk factors for old age mortality [ 29, 30].

However, in most difficult problems the number of possible solutions grows exponentially with the size of the problem (for example, the number of solutions might double for every town added).

Of these approaches, the Gompertz function produces the most realistic patterns of human mortality by allowing the risk of death to increase exponentially with age [24], [25].