Sentence examples for formula that implies from inspiring English sources

Exact(1)

Therefore, it is important to note that the situations are not maximally consistent theories, rather they are theories possessing the property that for any pair of formulas they contain a formula that implies both of them.

Similar(59)

In formulas, this implies that she is active whenever w i 0 – w i r = y 1 i ≥ 0, where wo i is the expected wage offer, wr i is her reservation wage and y1i represents the (normalised) individual preference for labor market participation.

(iii) In the case where p=3, Paris and Vinogradov (2016, formula (2.4)) implies that representation (30) is equivalent to Vinogradov (2008a, formula (14))), since formula (20) stipulates that ({mathcal Z}_{3} = - sqrt {2 lambda + lambda ^{2}/mu ^{2}/mu

Notice that the combination formula of Genome implies that the larger the inter-loss gap size of a given pair, the greater the influence on the overall perceived quality.

The formula above implies that | λ ( A ) | ≺ w s ( A ).

A Cauchy integral formula then implies that ((E_m(0 -E_m(beta ))/beta ) has a representation of the form (3.42).

Formula (2) implies that only when the degree of performance incentives offered by the provincial government to prefectural (county) officials (denoted by q) surpass θp(c 2 ) will prefectural (county) officials choose to protect the rights of investors.

For p=3/2, Paris and Vinogradov (2015, formula (3.15)) implies that in this special case, our representation (37) can be simplified as follows: (V_{{mathcal Z}_{3/2}} (mu) = mu cdot sqrt {4 {mathcal Z}_{3/2}^{-1} cdot mu + 1}).

Since (31) is a convex optimization problem with a concave objective function, noting the optimality condition (refer to [29], Proposition 3.1), which is necessary and sufficient for (31), of the convex optimization problems, formula (31) implies that f S 1 S ¯ 1, …, S ¯ K, …, f S K S ¯ 1, …, S ¯ K · ( S 1 − S ¯ 1 ), …, ( S K − S ¯ K ) T ≤ 0, (32).

Inequality (1.4.2) together with formula (1.2.1) implies that begin{aligned} Vert f(A -f B Vert le {text {const}},sigma Vert fVert _{L^infty }Vert A-BVert end{aligned} (1.4.3 for arbitrary self-adjoint operators A and B with bounded (A-B) and for an arbitrary function f in (L^infty ({mathbb R})) whose Fourier transform is supported in ([-sigma,sigma ]).

The addition was proposed because it allowed for a better description of the weak interaction (the mechanism that allows quarks to decay), equalized the number of known quarks with the number of known leptons, and implied a mass formula that correctly reproduced the masses of the known mesons.

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