Sentence examples for sole assumption from inspiring English sources

For a certain range of q, which depends on dimension and the order of the operators, this is done under the sole assumption that they generate an analytic semigroup in Lq.

In the following consequence of Theorem 3.1 we further assume that M is nonsingular and use the properties of the Brouwer degree to get a continuation result with the sole assumption that Ω # ∩ ( { 0 } × [ g ( 0, ⋅ ) ] − 1 ( 0 ) ) is a nonempty and compact subset of R m × R s.

Denoting by λ∈(−∞,2]⧹{0} the degree of homogeneity of the coagulation kernel a, measure-valued solutions are shown to be unique under the sole assumption that the moment of order λ of the initial datum is finite. A similar result was already available for the kernels a x,y)= 2, x+y and xy, and is extended here to a much wider class of kernels by a different approach.

This is the sole assumption and it is physically plausible.

The results of this work clearly show that the level of isogenicity and the genetic architecture of near-isogenic materials cannot, and must not, be taken for granted on the sole assumption of theoretical expectations.

In 1152 Baldwin, following his assumption of sole rule, had to suppress a civil war that broke out between his supporters and those of his mother.

Full loss offset may, therefore, be a realistic assumptions for sole proprietorships and partnerships.

That assumes that he is the sole owner of Olen, an assumption justified by what he originally led us (and has led folks in the real estate business) to believe.

China's nuclear strategy is still premised on the assumption that the sole purpose of nuclear weapons is to deter a nuclear attack.

Their unshakable assumption was that the sole responsibility of publicly owned corporations was to maximize shareholder profits.

Underlying this prohibition is the assumption that God is the sole author of life and that a person who produces a likeness of a living being seeks to rival God.