Sentence examples for solution the breakdown of from inspiring English sources

The addition of the acid modified zeolite increased the number of protons (hydroxonium ions from subcritical water and H+ from the surface of acid modified zeolite), with the excess number of protons in the solution, the breakdown of linking bonds of the cellulose and hemicellulose became significantly increasing and as the results the yield of monomeric sugars also increases as seen in Table 3.

Lipase activity was measured by changes in turbidity of an olive oil solution due to the breakdown of triacylglycerol to free fatty acids and monoacylglycerol.

Subsequently, with the increased of H+ in the surface of zeolite catalyst also increased the number of protons in the solution leading to the increase of the breakdown of linking bonds of the cellulose and hemicellulose to produce monomeric sugars.

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).

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

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

However, the addition of Tween-80 does not prevent the breakdown of stored capsaicin solutions.