Sentence examples for rigorously stated from inspiring English sources

Most clinical trials were too small and exploratory in nature to evaluate the medical merits of the treatment; they lacked adequate controls and rigorously stated goals.

One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated.

Second, the Hamilton principle is rigorously stated by defining the domain D of the action integral and the space Da of admissible directions.

A similar extremal principle in mechanics, the principle of least action, was proposed by the French mathematician and astronomer Pierre-Louis Moreau de Maupertuis but rigorously stated only much later, especially by the Irish mathematician and scientist William Rowan Hamilton in 1835.

This is rigorously stated in Lemma 8 and its consequence in (27).

The latter group therefore holds a less strict, or "weaker", definition of emergentism, which can be rigorously stated as follows: a property P of composite object O is emergent if it is metaphysically impossible for another object to lack property P if that object is composed of parts with intrinsic properties identical to those in O and has those parts in an identical configuration.

Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments.

Lighting up a cigarette (the tobacco kind) can get you booted from many venues in this rigorously antitobacco state.

This paper introduces a recently developed family of local, self-contained contact solutions which can be used to compare rigorously the states of stress in the microslip region of a range of contacts.

The results obtained in this section are first stated and then proved rigorously in an Appendix.

This is still, in my mind, a hypothesis - not a rigorously proven fact, and should be stated as such.