Sentence examples for equations of proposition from inspiring English sources

The main contributions of this paper are the concrete equations of Proposition 4.1 for the corresponding CA=CVA+FVA+MVA and KVA metrics, the XVA algorithm and the numerical results on real datasets.

Applying the second equation of Proposition 1, we get (overline{w}in L^{2}(Q_{T})).

The techniques based on the original periodic successive approximations (3.4), the applicability of which is guaranteed by Proposition 3.1, lead one to the necessary and sufficient conditions for the solvability formulated in terms of determining equations (3.15) of Proposition 3.4.

An example of the solution curves to equation (37), illustrating the results of Proposition 5, appears in Figure 14.

Assuming Proposition 1, we first prove Proposition 2. Proof of Proposition 2 Let u be a solution of equation (4).

Equation (3.4) is exactly the conclusion of Proposition 3.7.

We now show for joint modelling imputation under a saturated multinomial model and a Dirichlet prior for θ, that the corresponding chained equations algorithm satisfies the non-informative margins condition of Proposition 1.

This equation implies that (S^=Be^{-beta I^tau}tau), which contradicts the proof of Proposition 3.

Proposition 2.2 Difference equations of the Apostol-Bernoulli and Apostol-Euler polynomials of order α: for a positive integer n, λ B n ( x + 1 ; λ ) − B n ( x ; λ ) = n B n − 1 ( α − 1 ) ( x ; λ ) ( B n ( 0 ) ( x ; λ ) = x n ), (2.4).

This section reports the results of the simulation study, where the chained equations conditional models were compatible with the same joint model but the non-informative margins condition of Proposition 1 was not satisfied.

So, from statement (i) of Proposition 3.2, zero is the unique nonnegative equilibrium of the fuzzy difference equation (1.6).