Sentence examples for uniformly valid from inspiring English sources

Simple closed-form solutions, uniformly valid in time, are obtained.

Then for all and Also, is uniformly valid on.

The two expansions are matched in an appropriate manner to yield a uniformly valid solution.

A solution which is uniformly valid throughout the duct is also derived.

In this case, direct perturbation ansatz yields a uniformly valid solution to the first-order approximation.

This quite simple approach is uniformly valid in the whole range of subsonic Mach numbers and frequencies.

Thus, (lim_{lambda rightarrowinfty} ( P_{11} x,lambda -1 ) =0) is valid uniformly with respect to x.

Throughout this section, unless otherwise stated, every limit relation is understood as valid uniformly for all (xgeqgamma n) as (nrightarrowinfty).

Each term is a concatenation of Fourier multipliers with powers of η and its derivatives and is valid uniformly in wavenumber.

(2omega x ll gt) or (2omega x gg gt), would be imposed upon them (see Figures 2 and 3). Figure 4 Asymptotic expression of η valid uniformly when (pmb{2omega xsim gt}).

Since all properties are uniform and since the global return mechanism is sufficiently smooth up to and including the singular limit, the method for showing SNPO branches is valid uniformly in ε. □. Figure 10 summarises all observed codimension-2 bifurcations and the bifurcating codimension-1 branches.