Sentence examples for using the representations for from inspiring English sources

Phase I: using the representations for alignments between (q, r i ) and (r i, d) pairs, our indirect alignment ϕ i between q and d through r i is simply the composition of relations δ i and ψ i.

By the monotonicity of with respect to its third argument,, and using the representation for any we obtain (5.6).

Next, in Section 4 we introduce our visual tool for event exploration using the representation for events and international relations that we have just presented.

In order to check the first and the third conditions, we shall use the representation for the bond prices from Lemma 2. Indeed, the last condition follows directly from representation (22)–(23), using the monotonicity of the function Open image in new window and the order preserving property of ϕ and ψ; cf. Lemma 1.

By using the representations which apply for the conventional treatment of Michaelis-Menten reaction scheme, data were successfully analyzed via the variations of nernstian equilibrium potentials with time.

This fact is derived by using the representation formula for a solution of the problem (1.1) and operator-valued multiplier in (L_{p,gamma } ( R^{n} E ) ).

Using the representation, we construct solutions for Dunkl-Poisson's equation.

In the case (b), let us use the representation (39) for the matrix A cp.

We use the representation formula for a solution of the Cauchy problem for nonhomogeneous equation in the form (2.7) for the control (i.e. ) and time.

Since, we can use the representation (3.35) for where and are nonzero solutions of (2.1).

An implicit expression for this bifurcation curve is obtained by using the explicit representation for σ H (Eq. 18) in the expression for T (δ, p) = 0 (Eq. 17).