Sentence examples for pair of equations from inspiring English sources

Equating the right-hand sides of the above pair of equations then yields       (43) This is one of four Maxwell relations (the others will follow shortly).

For instance, instead of the equation y = x2, which is in Cartesian form, the same equation can be described as a pair of equations in parametric form: x = t and y = t2.

Substituting this in equation 6 gives If one chooses to use P to designate the parent atom, the expression assumes its familiar form: This pair of equations states rigorously what might be assumed from intuition, that minerals formed at successively longer times in the past would have progressively higher daughter-to-parent ratios.

The latter pair of equations expresses the constraint imposed by the VCMs.

It is characterised by a pair of equations: system equation and measurement equation.

The following theorem provides us with a characterization via a pair of equations.

We call ( λ, x ) ∈ [ 0, + ∞ ) × C T ( M ) a T-periodic pair of equation (1.1) if x : R → M is a solution of (1.1) corresponding to λ.

The technique is then applied to a more complicated coupled pair of equation sets, the hyperbolic period- and depth-averaged ray-type wave conservation and modified shallow water equations that describe wave current interaction in the nearshore zone at the coast.

Indeed, the pairs of Equations 3 and 4 are equivalent in some applications, but are not in some others.

We have obtained the Lax pairs of equations (88), (89), (96), and (98), from which we could investigate their infinite conservation laws and different Darboux transformations just like in the ways presented before.

Then there exists a connected subset of Ω of nontrivial T-periodic pairs of equation (3.1) whose closure in Ω is noncompact and intersects { 0 } × C T ( M ) in a (nonempty) subset of { ( 0, p − ) ∈ Ω : w ( p ) = 0 }.