Sentence examples for expansion consequently from inspiring English sources

This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme.

The 2D subspace problem is easy to handle, as shown above; but the search for (18) may be quite difficult, because the projection operator would make the objective function nondifferentiable and lose the common Taylor expansion, consequently it is nontrivial to search for proper stepsize α.

This warming causes a localized thermal expansion and consequently a localized upwarping or doming of the Earth's surface, as in the case of the Yellowstone area or the Massif Central in France.

In particular, the regular bipartite dynamical networks, reported here by the first time, have the best possible expansion and consequently are the most robust ones against node/link failures or intentional attacks.

A carefully selected preformed shape can be considered as a key factor for successful THF, since thinned sections may not be able to endure internal pressure during expansion, and consequently burst, whereas excessive thickening may lead to wrinkles.

Recently, Si-based alloys have been developed to overcome the two disadvantages; the Si-M (M = Mg [6, 7], Sn [8, 9], Ag [10, 11], Zn [12, 13], Fe [14, 15], and Ni [16, 17]) alloys are able to alleviate the volume expansion and consequently increase the cyclability for the batteries.

In the setting of caloric excess, it may be that some individuals have 'healthier' subcutaneous fat, capable of significant hyperplastic expansion, and consequently a lesser degree of fat overflow and omental adipocyte hypertrophy.

The substantial geological age of the genus Rhizophora (estimated at 50 million years) [ 22] and its coastal distribution presented opportunities for repeated population contraction and expansion—and consequently reproductive isolation and introgression among its species during the glacial-interglacial cycles.

In Japan, as the LTCI system became established, certified users of LTCI have increased rapidly, and the demand for LTCI services has experienced a remarkable expansion and, consequently, the expenditures of the LTCI are growing dramatically, threatening the financial sustainability of the system [ 9, 22].

Climatic conditions prevailing at different time periods strongly influenced the extent of each habitat type in the past, which should in turn influence the length of time during which a species underwent isolation or range expansion and, consequently, the opportunities for genetic diversification [ 3, 5].

While this depression might have facilitated range expansion and, consequently, low differentiation across the alpine area as a whole [ 9, 48], previous studies on geographic subsets of Australia's high country have found high endemism among mountain suggesting relatively stable population histories and isolation among mountains [ 17, 21, 22].