Sentence examples for regular solutions to from inspiring English sources

The next result describes the precise blow-up scenario for sufficiently regular solutions to system (1.2).

The new algorithm surmounts limitations of previous simulations, where approximate critical conditions for flame stability were determined, and extends sensitivity of regular solutions to critical solutions having a singular Jacobian.

Its minimization (adjusting regular solutions to fit with the firing rate adaptation time scale) shows a rather complex interplay between different possible states.

The problem of sphere packing, in a volume of 3D space, is a well-known mathematical problem, and it is known since the time of Gauss that any of these infinite optimal solutions can be described in terms of two fundamental arrangements, called face centered cubic (FCC) and hexagonal close packed (HCP), that represent the only two regular solutions to the problem.

Then the existence and uniqueness of maximal regular solution to nonlinear abstract parabolic problem is derived.

In Section "Preliminaries" we give some preliminaries, carefully explain the closed-loop strategies, and introduce the regular solution to the generalized Riccati equation.

Roughly speaking, the open-loop solvability is equivalent to the solvability of a forward-backward stochastic differential equation (FBSDE, for short), and the closed-loop solvability is equivalent to the existence of a regular solution to a Riccati equation.

Remark 3.6 The proof of Theorem 3.5 is inspired by the argument of Ai et al. [12] in the study of the low regular solution to a generalized DGH equation.

10.7554/eLife.05913.003 Figure 2. Regular optimal solutions to the sphere packing problem in 3D.

The simplest kind of nonideality, exemplified by strictly regular solutions, can lead to large jumps in the equilibrium concentrations with only small parameter changes, in analogy to behavior known for open systems.

Then it follows from Theorem 3.3 that the GRE (2.6) admits a regular solution (P. To determine u ∗, let (X ∗,Y ∗,Z ∗ be the adapted solution of (3.1).