Sentence examples for defined real from inspiring English sources

We prove that for anyN⩾1, the Korteweg de Vries equation (and thus the entire KdV-hierarchy) admits globally defined real analytic action-angle variables.

The contradiction between rationals and reals was finally resolved by Eudoxus of Cnidus, a disciple of Plato, who pointed out that two ratios of geometric quantities are equal if and only if they partition the set of (positive) rationals in the same way, thus anticipating the German mathematician Richard Dedekind (1831 1916), who defined real numbers as such partitions.

Weyl defined real functions as mappings correlating each interval in the choice sequence determining the argument with an interval in the choice sequence determining the value "interval by interval" as it were, the idea being that approximations to the input of the function should lead effectively to corresponding approximations to the input.

There are infinitely many of them, in contrast to the uniquely defined real logarithm.

The findings based on census tracts likely underestimate true associations related to contextually defined (real) neighborhoods that have substantive deprivation boundaries and transition zones.

A not fully defined real-estate value and vital market.

The problem is simple: they don't understand what defines real leadership today or if they do, it scares them.

Cantor himself had given a way of defining real numbers as certain infinite sets of rational numbers.

Defining Jews out of the body politic — by defining "real" citizens in racial, ethnic and/or religious terms — is perhaps the most common tactic.

In a securities filing, Iron Mountain disclosed that it learned that the I.R.S. formed a working group to define real estate for purposes of the REIT provisions.

Mr. Love, with a video crew, will ask fellow chefs how they define "real food" and how they pick their ingredients.