Sentence examples for equivalent to the relation from inspiring English sources

To see this, we notice that the relation is equivalent to the relation.

Hence, (v(t)= I^{mu}_{0^w(t)), Remark 2.5 implies that it is equivalent to the relation (w=D^{mu}_{0^v).

This statement is equivalent to the relation between the elements of the matrices (A=(a_{mnkl})) and (E=(e_{mnkl})) begin{aligned} &a_{mnkl}=sue_{mn,m-1,n-1}+ste_{mn,m-1,n}+rue_{mnm,n-1}+rte_{mnmn} quad text{or equivalently} &e_{mnkl}=sum_{i,j=k,l}^{infty} biggl( frac{-s}{r} biggr)^{i-k} biggl(frac{-u}{t} biggr)^{j-l}frac{a_{mnij}}{rt} end{aligned} (4.3) for all (m,n,k,linmathbb{N}).

The new set of equations is equivalent to the relations of Thompson (1987) [5] but it has the advantage to provide a physical interpretation of the characteristics for nonlinear perturbations.

which are equivalent to the recurrence relation (Gradshteyn and Ryzhik [1994], Eq. 8.733.2) for associated Legendre functions and, together with Θ n n = ( 2 n − 1 ) x + i y r 2 Θ n − 1 n − 1 and ϒ n n = x + i y 2 n ϒ n − 1 n − 1 (54).

Note that the L1-norm of a variable × is equivalent to the following relation: | x | = min α ≥ 0 ; s.t. - �� ≤ x ≤ α.

As a consequence, rg can be considered equivalent to the partitive relation has-part, which would improve the semantic clarity in these cases.

The scale on the right represents the concentration in ion bicarbonate equivalent to the coccolith mass from the relation proposed in Beaufort et al. (2011).

Introduced by von Holst in the thirties of the last century (see references in [ 11, 15- 17]), (relative) coordination is equivalent to the existence of certain phase relations without claiming that these phase relations are due to real coupling mechanisms.

In this paper, by the study of the integral equation equivalent to the Blasius problem, we obtain the relation between the velocity function f ′ and the shear stress functions f ″, upper and lower bounds of ∥ f ″ ∥ and a new lower bound of β ∗.

Two arbitrary screws in space are equivalent to the sum of the mutual moment relation.