Sentence examples for three formulas of from inspiring English sources

Following the work of Carlitz and Kim et al., He and Wang [18] extended Carlitz's [15] three formulas of products of the Frobenius-Euler polynomials, by virtue of which some analogues to the summation formula (1.9) were obtained.

In 1933, Łukasiewicz found three formulas of length eleven that each could act as a single axiom for the calculus here's one of them: e(e x,y),e(e z,y),e x,z)))—and he also showed that no shorter single axiom existed.

In [15], Nielsen investigated three formulae of products of the classical Bernoulli and Euler polynomials.

Catherine appointed a mixed commission of moderates that devised two formulas of consummate ambiguity, by which they hoped to resolve the basic, Eucharist controversy.

Premultiplying two formulas of (3.7) by and, respectively, yields (3.14).

The idea is that if two formulas of LPCR, when embedded into FLR, have differing normal forms, the two formulas have different senses.

In another formulation (6 380 81) he says that right concerns universality as a formal condition of freedom while virtue concerns a necessary end beyond the mere formality of universality, thus appearing to tie the distinction to the first two formulas of the categorical imperative in the Groundwork.

Four formulas of feed, with different types and doses of dsRNA, were tested; 16 6 mg of WSSV051-dsRNA, 2) 6 mg of VP28-dsRNA, 3) 6 mg of multi-WSSV dsRNA and 4) 12 mg of multi-WSSV dsRNA.

We will use the following two formulae of Carlitz presented in [7] that concern properties of Rogers-Szegö polynomials.

A default rule consists of three formulas: the prerequisite, the justification, and the consequent.

Compositions of the three formulas are detailed in Table 1.