Sentence examples for regularity analysis of from inspiring English sources

Using qualitative analysis we prove theorems on which we base a new method of regularity analysis of the firing map, that, contrasting with methods previously reported in the literature, does not requires analytic knowledge of the solutions of the differential equation and therefore it is also applicable to non-linear integrate and fire systems.

The main difficulty in proving (C^{1,1}) regularity is the analysis of points where the gradient of the function vanishes.

If the coefficients are Hölder continuous, the ACF method does not directly apply and under the stronger assumption that (inf lambda _1>0) and (inf -lambda _2>0), Edquist, Lindgren, Shahgholian [12] obtained the (C^{1,1}) regularity via an analysis of blow-up limits and a classification of global solutions (see also [12, Remark 1.3]).

The analysis of regularity in daily medication dosage was described previously (Bauer et al. 2013b) and is summarized here.

Thirty-six of the 144 patients were not included in our prior analysis of regularity in daily mood stabilizer dosage (Bauer et al. 2013b).

This method is capable of measuring the heart rate and heartbeat regularity simultaneously via the analysis of caudal blood flow in zebrafish embryos.

Proof The global existence of a unique strong solution to FBVP (1.1) and (2.1) can be established in terms of the short time existence carried out as in [7], the uniform a priori estimates and the analysis of regularities, which indeed follow from Lemmas 3.1-3.4 3.1-3.4

Based on careful analysis of the regularity of surface subsidence in mined-out area, we proposed a new time function based on Harris curve model in consideration of the shortage of current surface subsidence time functions.

This section is devoted to an analysis of the regularity of refinable functions (phi^{m,l,alpha}_{0}) with the mask (tau^{m,l,alpha}_{0} omega)) defined by (2).

It is worthwhile pointing out that, without consideration of the dividend policy, Han et al. in [10] deduced that (partial _{x} ugeq0), which plays an important role in the analysis of the regularities of the free boundary.

Based on the analysis of the regularities of the Ag nanostructures growth and corresponding kinetics of SERS-signal intensity change, we revealed a parameter crucial for the formation of the SERS-active substrates, which can be defined as a product of the Ag salt concentration by the immersion deposition time.