Sentence examples for basis of various theorems from inspiring English sources

Positivity of the Cauchy function C ( t, s ) of (2.1), (2.4) is a basis of various theorems about differential inequalities (under corresponding conditions, the solution of an inequality is greater than the solution of an equation).

Fixed-point theorem, any of various theorems in mathematics dealing with a transformation of the points of a set into points of the same set where it can be proved that at least one point remains fixed.

Moreover, these theorems often form the basis of various national building codes.

Different specifications were tried on the basis of various measures of education variable.

WQI can be evaluated on the basis of various physical, chemical and bacteriological parameters.

The perception system recognizes human emotional states on the basis of various indicators.

On the basis of Theorem 1.2 and Theorem 1.4, we can conclude the following result.

As Robinson showed, we can copy Leibniz's arguments using the infinitesimals in R′, and so prove that various theorems of calculus are true in R′.

By adding appropriate algebraic constraints to the semantics, one can validate various theorems of relevant logics, and provide the negation at issue with many intuitive inferential features.

The Bridge of Asses opens the way to various theorems on the congruence of triangles.

Various theorems have been derived from the axiom system to ensure that this approach is mathematically rigorous, thereby rendering it possible to develop efficient process synthesis methods on the basis of a rigorous mathematical foundation.