Sentence examples for are explicitly determined from inspiring English sources

Here the Fourier series of the higher-order Bernoulli functions (B_{m}^{(r)}( langle x rangle)) are explicitly determined.

The degenerate Cauchy numbers of the third kind (C_{n,lambda,3}) are explicitly determined by the Stirling numbers of the first kind (Theorem 1).

The corresponding "G-closure problem" of a three-phase isotropic composite is also addressed and exact bounds on effective isotropic properties are explicitly determined in these regions where the stress energy bound is optimal.

In this paper, we considered the Fourier series expansion of the higher-order Bernoulli functions (B_{m}^{(r)}( langle x rangle )) which are obtained by extending by periodicity of period 1 the higher-order Bernoulli polynomials (B_{m}^{(r)}(x)) on ([0, 1)). The Fourier series are explicitly determined.

The corresponding y∗ can be explicitly determined as follows.

Nonetheless, as we show below, the wave stability can in fact be explicitly determined.

The impact of waste variations, of recuperation ratio and of furnace temperature is explicitly determined.

In this note the dependence of Markstein number on mixture strength is explicitly determined.

From this asymptotic behavior, the diversity order and its dependence on the number of relays (M) can be explicitly determined.

There has been substantial progress in this area, with all pairs ((X,G)) having been explicitly determined for (dim Gge N^2+1) (see, e.g., [49]).

Upon a condition on the aerodynamic characteristics of the vehicle, we show that the equilibrium orientation can be explicitly determined as a function of the desired flight velocity.