Sentence examples for regularity requirement from inspiring English sources

In Section 4, an optimal-order weighted norm error analysis with a low regularity requirement for the optimal control problem is discussed.

The dimension of the corresponding eigenspace X 0 ( e ) was m < n and it turned out that the following regularity requirement M y ( 0 ) = 0 has to be satisfied.

An optimal regularity requirement on the domain for the Lp-theory is investigated, assuming that the principal coefficients are supposed to be in the John Nirenberg space with small BMO semi-norms and that the domain is a Reifenberg flat domain.

Note that the regularity requirement M y ( 0 ) = 0 contains n − l linearly independent conditions and can be equivalently expressed by H y ( 0 ) = 0, y ( 0 ) = R y ( 0 ) or y ( 0 ) ∈ Ker M. The remaining l free constants have to be uniquely specified by appropriately prescribed initial conditions.

Fourth-order convergence is proved under mild regularity requirements.

All the regularity requirements of the vector field at the origin and the physical boundary conditions at a circumferential boundary are exactly satisfied by adjusting the additional tau-coefficients of the radial expansion polynomials of the highest order.

A reformulation of (4.2) which presupposes reduced regularity requirements on the solution is as follows.

Under hypotheses close to the existence theory of nonlinear evolutionary inequalities, dispensing with unnatural regularity requirements on the exact solution to the problem, we are able to establish a convergence result for the piecewise constant in time interpolant.

Note also that the requirement of regularity seems to afford a new argument for the non-existence of God as traditionally conceived: an omniscient agent, who gives probability 1 to all truths, would be convicted of irrationality.

4. Indeed, according to the requirement of regularity (to be discussed further in §3.3), one should not be certain of anything stronger than T, on pain of irrationality! 5. Some authors simply define 'coherence' as conformity to the probability calculus.

Some otherwise extreme subjectivists impose the further rationality requirement of regularity: only a priori falsehoods get assigned probability 0. This is sometimes also called 'strict coherence', and it is advocated by authors such as Kemeny (1955), Jeffreys (1961), Edwards et al. (1963), Shimony (1970), and Stalnaker (1970).