Sentence examples for assuming the functions from inspiring English sources

Based on Theorem 5.1 and Lusin's theorem, we are going to extend the strong duality Theorem 2.2 by assuming the functions f and g to be measurable and bounded on ([0,T]).

Assuming the functions to be differentiable, we may rewrite this conservation law via the chain rule and the equation (4) as ∇ d σ ( d ) div x f ( d ) = div x ϕ ( d ), (10).

Suneja et al. [4] formulated a pair of Wolfe-type multiobjective symmetric dual programs over arbitrary cones, in which the objective function is optimized with respect to an arbitrary closed convex cone by assuming the functions involved to be cone-convex.

In the present paper, we introduced generalized ( H p, r ) -invex functions and consider two types of dual program for a class of semi-infinite programming problem to establish the weak, strong and strict converse duality theorems assuming the functions involved to be generalized ( H p, r ) -invex functions.

Even assuming the function of taxes is to redistribute wealth, it's a leap to say the current system does so in any reliable way.

Subsequently, assuming the function belongs to, we deduce the a priori estimates (2.3) and (2.4) for the adjoint operator.

What Péladan took from Wagner, above all, was the idea that art could assume the functions of religion.

The PMAC was administered by the Derg and assumed the functions of government, with Lieut.

The Superior Court of the District of Columbia, a single trial court, assumed the functions of the previous five courts.

The Commission on Narcotic Drugs was authorized by the General Assembly in 1946 to assume the functions of the League of Nations Advisory Committee on Traffic in Opium and Other Dangerous Drugs.

Gentil has asked for Bellamy because he wishes the inspector to hear his confession the decent cop, in a godless world, having tacitly assumed the functions of a priest.