Sentence examples for expression for the third from inspiring English sources

The analysis indicates that the ignition is initiated by the breakdown of H2O2 to the highly reactive radical OH via the reaction H2O2 + M → 20H + M. A new analytical expression for the "third limit" is derived from the reaction mechanism by introducing the concept of a critical OH concentration; it is shown to be in agreement with the experimental data.

A simple, accurate analytic expression for the third explosion limit follows from identification of the critical conditions for existence of weakly reactive, diffusion reaction solutions, thereby providing the answer to a long-standing problem that in early work was characterized as being hopelessly difficult.

By using the approximate expression for the third order moment of the β-field and the general integral expression for the second term comprised of L1 and Λ1 established in Part I and Part II, explicit expressions for L1 and Λ1 are derived for spherical scatterers.

Since, the closed-form expression for the third term in Equation 47 can be calculated as shown below: (49).

We develop a theoretical expression for the third-order aberrations in these systems making use of the wavefront matching method.

Moreover, we calculate the expression for the second curvature coefficient, extending previous results using this formulation.

On Lolabelle's face, Anderson says, was a "brand-new expression": for the first time, the dog began to worry about the sky.

If the Court upheld the statute, it would create a new category of unprotected expression for the first time in twenty-seven years.

From this, an expression for the first term of this series is obtained in terms of the sizes and volume density of the scatterers.

An expression for the first-order particle velocity distribution function is derived, which includes the effects of particle rotation and friction.

However, finding a closed-form expression for the second-order statistics of this variable is challenging.