Sentence examples for breakdown solution from inspiring English sources

The analysis of A. aeolicus returned a plausible set of genomes, although the exclusion of groups such as Thermotogae and Epsilon-proteobacteria from the main solution set (both groups were represented in the role category breakdown solution set) was surprising.

This requires the development of a system solution breakdown structure that will guide the development of the overall solution.

It has been discussed that the strength in the brittle-ductile transition zone gradually changes because of the onset of several different mechanisms such as semi-brittle flow, power-law breakdown, and pressure solution precipitation (Shimamoto1993; Hirth and Tullis1994; Chester1995; Kohlstedt et al.1995; Bos and Spiers2002).

With respect to the use of Tween-80 to prevent the breakdown of capsaicin solutions over time, when stored at various environmental conditions, we found that solutions of 2 μM and less of both the Tween-80 containing and non-Tween-80 containing solutions did significantly decrease in concentration after 2 months compared to the higher concentration.

The authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3-D Euler equations.

A criterion for the breakdown of classical solutions to (1.1) with zero viscosity and positive resistivity in R 3 was derived in [9].

Lei and Zhou [31] derived a criterion for the breakdown of classical solutions to the incompressible magneto-hydrodynamic equations with zero viscosity and positive resistivity.

In this paper, we will get the Beale-Kato-Majda type criterion for the breakdown of smooth solutions to the incompressible ideal MHD equations in R 3 as follows: { u t + u ⋅ ∇ u + ∇ ( p + 1 2 | h | 2 ) = h ⋅ ∇ h, h t + u ⋅ ∇ h = h ⋅ ∇ u, ∇ ⋅ u = 0, ∇ ⋅ h = 0, t = 0 : u = u 0, h = h 0, (1).

Figure 6 shows the breakdown of LP solutions for each category.

Also, the addition of Tween-80 does not prevent the breakdown of capsaicin solutions over time.

We analyze the linear instability of the numerical scheme, which explains the numerical blow-up of large data solutions and connects to the analytical breakdown of regularity of solutions to quasilinear Schrödinger equations.