Sentence examples for concrete formula of from inspiring English sources

end{aligned}A concrete formula of (h_{{mathbb {D}}^*} z_1,z_2)) can also be given but its form is not so convenient [cf. (3.3) below].

Then, the problem is to find a concrete formula for each term of the expansion.

By using this description, when the polytopes are Delzant lattice, a concrete formula for each term of the expansion in two dimension and a formula for the third term of the expansion in arbitrary dimension are given.

The distinguished political thinker, Randall Robinson, admittedly, has no concrete formula for the enigma, but lays out the issue of reparations with utmost sensitivity and precision.

As for the concrete formula, we omit it here.

The model works on the basis of the final element method and also by appropriate way takes into account the concrete formula, treatment and also climate impacts.

Actually, instead of p the auxiliary atoms p ⊕ and p ⊖ are present in the concrete formula.

In a particular case when the matrix of linear terms is constant, a representation of the fundamental matrix given by a special matrix function (so-called delayed matrix exponential, etc)., for example, in [10, 11] (for a continuous case) and in [12, 13] (for a discrete case), can give concrete formulas expressing solution of the considered problem in analytical form.

Concrete formulas are mixtures of oils, waxes and other ingredients that are poured into containers such as tins to eventually harden.

For (beta=-frac{1}{p}), the cosine system is minimal since, as was proved above, the coefficients (B_{n}) are found by concrete formulas in the form of an integral.

The concrete formulae above are consequences of a more general mathematical duality called Pontryagin duality.