Sentence examples for estimates existence from inspiring English sources

They proved a priori estimates, existence of least energy solutions and the concentrative properties of the solution.

With the asymptotic expansions and the lemma of lower and upper solutions established in Section 2, the asymptotic estimates, existence, and uniqueness of the solution for the problem (1.1 - 1.3 1.1 - 1.3ined in Section 3.

Moreover, priori estimate, existence and uniqueness of the numerical solutions are discussed.

The estimated existence of a significant relationship between genotype and phenotype values based on analysis of variance (ANOVA), as in association analysis, is determined when a number of individuals are plotted to the same cell.

Then in [14] energy estimates and existence and uniqueness results are established.

In [17] and ensuing work the monotonicity condition A4w is relaxed and local boundary regularity is also considered, yielding an alternative approach to that in [10] which deals with estimates and existence of globally smooth solutions.

It has been argued that paternal leakage, leading to the expression of paternal genes, plays a pivotal role to stop Muller's ratchet [ 13] that otherwise would have driven the species to extinction in less time than its current estimates of existence [ 11].

The n-value of N14 showed 13.6, whereas other two wires showed lower n-value, estimating the existence of micro-cracks.

Also, we challenge to estimate an existence of slab/2D structure of solar wind turbulence during the Fd in September 9 23, 2005 based on the distribution of average turbulence energy among the IMF's components.

As applications, we prove some Lp-estimates and existence theorems for the de Rham operator as well as some vanishing theorems for the Lp-cohomology and the Lp-torsion over complete non-compact Riemannian manifolds with suitable geometric conditions.

Thereafter, the SD value based on information theory is used to estimate the existence probability.