Sentence examples for further equation from inspiring English sources

Further, Equation 6 adjusts for boundary effects.

One further equation completes the concepts for hypothesis testing: α < β, reflecting the higher costs of type I error.

Further, Equation 6 allows one to rewrite the squared norm of the function: ∥ f ∥ H 2 = f, f H = ∑ i, j β i β j k x i,., k., x j H.

Further, Equation (32) states that for each condition of that has to be evaluated to TRUE, there exists a condition of a scoped path in the original program that will imply the True evaluation of (by predicate ).

Further, equation (7) has the unique positive root (omega_{n}), and the characteristic equation (4) has purely imaginary roots (pm iomega_{n}), where omega_{n}=sqrt{frac{-P_{n}+sqrt{P_{n}^{2}-4Q_{n}}{{2}}, quad n=0,1,2,ldots, N_{2}.

However, all model states are observable in this case, and thus no further equation can be eliminated.

The throughflow equations contain blade force terms that model the effects of the real blades on the flow and are resolved by further equations.

Further equations were developed for the MP3 Model in Eq. 5 for other typical encoding rates of the MP3 codec, i.e. 64 and 96 kbps.

For the other heat transfer modes (apart of heat conduction), the formulation of further equations to include additional parameters (e.g. density changes, buoyancy forces, gravitational forces, etc)., has its foundations on Equations 2 and 3.

Further, Equations 7 and 21 can be used to approximate the optimum value of C W wu as, text{CW}^{text{opt}}_{text{wu}}approxfrac{n text{CW}_{text{ap}}-1)}{text{km}}+2.

The state variables and inputs depend on time t, the independent variable, that is dropped in further equations.