Sentence examples for minimum solutions to from inspiring English sources

For a bounded and convex -sublattice of a Hilbert lattice, the behavior of its maximum and minimum solutions to a problem should be noticeable.

In this paper, we study this theme and provide some results about the existence of maximum and minimum solutions to some general variational inequalities in Hilbert lattices.

Now, we state and prove the main theorem of this paper below, which provides the existence of maximum and minimum solutions to general variational inequalities in Hilbert lattices.

Section 3 provides some results about the existence of maximum and minimum solutions to some general variational inequalities defined on some closed, bounded, and convex subsets in Hilbert lattices.

We apply the variational characterization of the metric projection to prove some results about the solvability of general variational inequalities and the existence of maximum and minimum solutions to some general variational inequalities in the Hilbert lattices.

Then, we provide some results about the existence of maximum and minimum solutions to some general variational inequalities defined on some closed, bounded, and convex subsets in Hilbert lattices.

The condition that has upper (lower) bound -closed values for some function, is not necessary for the problem to have a -maximum (minimum) solution to.

Example 3.7 leads us to consider some conditions on the mapping that are weaker than that in Theorem 3.1 which still guarantees the existence of a -maximum (minimum) solution to.

By using the optimization method of genetic algorithms (GAs), we can get minimum and maximum solutions to satisfy inequality.

(1 the problem is solvable, (2 there are both of -maximum and -minimum solutions to.

Solvent selection is pivotal in determining the critical minimum solution concentration to allow the transition from electrospraying to electrospinning, thereby significantly affecting solution spinnability and the morphology of the electrospun fibres.