Sentence examples for mild hypotheses from inspiring English sources

In addition, approximate solutions of optimization problems are very important from both the theoretical and the practical points of view because they exist under very mild hypotheses and a lot of solution methods propose this kind of solutions.

The related critical exponent equations −Δu = K x) u(n + 2)/(n −2) in Rn (n = 3, 4), with K x) being asymptotically periodic in one of the variables, are also studied and infinitely many positive solutions (modulo translations by its periods) are obtained under some additional mild hypotheses on K x).

The first result is that under some mild hypotheses on the covariance function k of the Gaussian process, the expected improvement algorithm produces a dense sequence of evaluation points in the search domain, when the function to be optimized is in the reproducing kernel Hilbert space generated by k.

We show that this ansatz approximates very well the wave function in the semi-classical regime, and gives the semi-classical expansion under mild hypothesis on the potential at infinity, and no analyticity conditions.

Perhaps more surprising is the observation that the milder hypothesis (requiring only two layers of mutual knowledge of rationality) that consumers who burn more money are treated better is not supported by the data either.

In these systems trajectories converge generically towards an equilibrium under mild regularity hypotheses; see, e.g., [4 6].

Under mild additional hypotheses, when E=C, Mz, the operator of multiplication by z, is cellularly indecomposable and has the codimension one property; however, if M is invariant for Mz, M⊖MzM need not be a cyclic subspace for Mz restricted to M.

In the paper analytical expressions are found for the solution to this optimal tracking problem under mild simplifying hypothesis, and the traditional optimal control versus the new tracking approaches are compared.

Using this notion, they established best proximity point theorems under some mild conditions; indeed, their hypotheses were a combination of compactness and completeness conditions.

He sees both pain and low mood as warning mechanisms and thinks that, just as understanding chronic pain means first understanding normal pain, so understanding clinical depression means understanding mild depression.Dr Nesse's hypothesis is that, as pain stops you doing damaging physical things, so low mood stops you doing damaging mental ones in particular, pursuing unreachable goals.

This study was designed to test the hypothesis that mild to moderate DSLD is not worsened by consistent exercise.