Sentence examples for corresponding expansions from inspiring English sources

In this paper, we study the existence and resonant interaction of oscillatory wave trains in one space dimension, giving a rigorous proof of the validity of the corresponding expansions of weakly nonlinear optics.

Gene copy number appears to be another protein feature that co-evolves, in the sense that gene expansion in one family could be 'accommodated' by corresponding expansions in a related family, and vice versa.

Corresponding expansions could not be detected in spectratyping analyses from lymphocytes of wild type mice.

Europe's territorial expansion has not been matched by any corresponding expansion of its strategic vision.

However, as the population of the urban areas increases, there is a corresponding expansion of informal housing.

Marx's work highlighted the involvement of communication and information technologies in surveillance and he noted what James Rule called the corresponding expansion of surveillance capacities as a result.

The NVIC points out that nine new vaccines have been recommended since 1986, but that the NCVIA Vaccine Injury Table has not undergone a corresponding expansion.

Further, the corresponding expansion at the normal direction at the inner surface of the mould is improved.

Moreover, we show that the corresponding expansion coefficients are precisely the coefficients of the associated Raleigh Schrödinger series.

The repeated Mongol invasions certainly affected the fortunes of some northwestern cities, but on the whole the period was marked by a flourishing urban economy and corresponding expansion in craft production and commerce.

The substantial increase in the number of private cars since the early 1980s with no corresponding expansion of the basic street system has subjected the city to unprecedented congestion, especially in the administrative and commercial centre.