Sentence examples for weakly orders from inspiring English sources

A basic rationality constraint on the preference relation has already been discussed that it weakly orders the options (i.e., satisfies Transitivity and Completeness).

We say that \ \preceq\) weakly orders a set \(S\) of options whenever it satisfies the following two conditions: Axiom 1 (Completeness) For any \ A, B\in S\): either \(A\preceq B\) or \(B\preceq A\).

It is remarked that the notion of weakly order contractive mappings purely relies on order structure.

Cholesterol self-assembles into weakly ordered aggregates when tethered to a crosslinked hydrogel network of poly ethylene glycol) (PEG).

Here the conformational preferences of the widely used pharmaceutical ibuprofen were investigated in solution by NMR spectroscopy in weakly ordering phases.

We demonstrated that the particles are spontaneously weakly ordered in a three-dimensional cubic array along the ⟨100⟩-directions in the β-Ti matrix.

We establish the existence of common fixed points for weakly order contractive mappings by using only order-theoretic properties as follows: Theorem 24 Let (E, ≤) be a complete vector lattice and K its positive cone.

However, the highly ordered crystalline structure would irreversibly destroyed and transformed to a weakly ordered form when treated at about 180 °C, accompanied by the complete deprivation of crystal water.

Interestingly, the weakly ordered CaPim with residual ordered structure still showed a rather high β-selectivity with kβ values of 0.53 0.68, while the amorphous CaPim almost lost its β-nucleating ability.

The weakly ordered CaPim still maintained relatively high ordered degree at Ta range of 180 290 °C, but a further increase of Ta leads to the conversion of CaPim to disordered amorphous form.

Motivated by the work of Nemeth [15], we initiate the study of fixed points and common fixed points of weakly order contractive mappings in the framework of vector lattices.