Sentence examples for basis of the normal from inspiring English sources

In this paper, the general expressions of long-range reverberation intensity in shallow water have been developed on the basis of the normal mode theory.

On the basis of the normal form, global bifurcation analysis of the parametrically excited rectangular thin plate is given by a global perturbation method developed by Kovacic and Wiggins.

The basic idea of the sorted QR ordering is to arrange the unknown integer parameters in the order of maximum conditional weightings on the basis of the normal matrix.

For any orthonormal basis { e 1, …, e n } of the tangent space T x M n and { e n + 1, …, e m } is an orthonormal basis of the normal space T x ⊥ M, then the scalar curvature τ at x is defined by τ ( x ) = ∑ 1 ≤ i < j ≤ n K ( e i ∧ e j ), and the normalized scalar curvature ρ of M is defined by ρ = 2 τ n ( n − 1 ).

If ({e_{1},ldots,e_{n}}) is an orthonormal basis of the tangent space (T_{p}M) and ({e_{n+1},ldots,e_{m}} ) is an orthonormal basis of the normal space (T_{p}^{perp}M), then the scalar curvature τ at p is given by tau(p)=sum_{1leq i< jleq n}K e_{i}wedge e_{j}) and the normalized scalar curvature ρ of M is defined as rho=frac{2tau}{n n-1)}.

Individual entries in Table 1 are each based on 1000 simulations, so their confidence limits are approximately ± 2 (on the basis of the normal approximation to the binomial).

Seed embryo and endosperm display distinct differentially expressed proteins, and their synergistic expression mechanisms provide a basis for the normal germination of wheat seeds.

A realistic target might be to finance on this basis half of the "normal replacement" needs of the system -- about $1 billion annually.

However, the mechanical basis of these normal cell cycle transformations, and abnormal nuclear shapes caused by intranuclear elongation of microtubules lacking spindle pole bodies, remain unknown.

On the basis of the trivariate normal distribution for the error terms, the logarithmic likelihood function for the system of Eqs.

Thus, this small sample of younger patients with type 2 diabetes had a prevalence of hypogonadism of 33% on the basis of the standard normal ranges.