Sentence examples for formulate without from inspiring English sources

Next, using more natural conditions when (beta>0) we can formulate, without proofs, the following theorems.

We now formulate (without proofs) two stability properties for approachable maps essential to the proofs of the main results in Section 3.2 below.

Using the reduction theorem, fewer invariants are required and some invariants are easier to discover and formulate without considering the internal structure of the final implementation.

It is formulated without chemicals and can be used safely for children as well (01386 792642; www.drhauschka.co.uk).

The parents were unhappy about a compensation plan made public this week, saying the amounts were too low and the plan was formulated without any input from families.

In June he wrote in the well-respected Egyptian daily, Shorouk: "What is the value of a constitution formulated without the real participation of the people?

Shorten said he believed "complementary safeguards" could be formulated without delaying the agreement's timely implementation, and it would be best to find a bipartisan approach.

The far-reaching claims these thinkers have made for liberal values can be detached from their theistic beginnings; a liberal morality that applies to all human beings can be formulated without any mention of religion.

The products are formulated without animal testing, and a percentage of profits each year is donated to animal rights groups, homeless shelters, Amnesty International, rain-forest preservation groups, and other social causes.

This is not to say that the general idea of writing was not paralleled by or imported from an adjoining culture but rather that the specific symbols and systems of writing were in such cases formulated without explicit prior models.

The nanofluids were formulated without the use of any dispersant/surfactant.