Sentence examples for certain inequalities from inspiring English sources

Unlike previous results, the scaling utilizes arbitrary powers (instead of requiring successive powers) of the high-gain parameter with the powers chosen to satisfy certain inequalities depending on system nonlinearities.

We obtain analogous factorization theorems, prove that the algebras that we obtain are dual operator algebras and show that for many domains, supremums over all commuting tuples of operators satisfying certain inequalities are obtained over all commuting tuples of matrices.

It is known that the data triplets (λi, ui, θi)∞0 must satisfy certain inequalities and asymptotic trends if the reconstructed beam is to have positive area and second-moment-of-area profiles.

The former focuses on the equalisation of opportunity for those with the requisite capacities or abilities to obtain a particular advantaged social position – it focuses on the elimination of arbitrary discrimination in the process of selection for such positions and, by definition, justifies certain inequalities of outcome.

We use certain inequalities proved later in Section 4.

Throughout history, people and emancipatory movements use the language of justice to pillory certain inequalities.

We prove a certain inequality for a subsolution of the heat equation associated with a regular Dirichlet form.

In settling a curious question about estimation of the model's variance parameter, a certain inequality arises that involves the normal probability density function and its first two integrals.

The key idea is to split the set of parameters into smaller subsets, design a controller for each of them, and switch the controller if, after a dwell-time period, the derivative of the Lyapunov function does not satisfy a certain inequality.

In this paper we prove certain coincidence point results in partially ordered metric spaces for functions which satisfy a certain inequality involving three control functions.

Equivalently, the conditional hazard rates are the univariate hazard rates of conditional distributions of each variate, given certain inequality of the remainder.