Sentence examples for definite assumptions from inspiring English sources

More complex models have since been built, incorporating different saving ratios for different groups in the population, technical conditions for each industry, definite assumptions about the character of technical progress in the economy, monetary and financial equations, and much more.

It was this paper that first brought to light the fact that in the case of elliptic equations degenerating on the boundary, under definite assumptions, a portion of the boundary may be free from the prescription of boundary conditions.

RidgeRace does not assume any underlying model of evolution, and thus, the method allows large flexibility when no definite assumptions can be made about the type of evolutionary process.

We suggest using RidgeRace in studies aiming to reconstruct ancestral character states of continuous characters when no definite assumptions can be made about the type of evolutionary process, or when the assumption of a model for phenotypic evolution is not appropriate at all.

By the positive definite assumption of matrix A, we conclude ((z^{ k)})^=0), and the proof is then complete.

We find that all eigenvalues of the matrix (Dmathcal{M}+mathcal{M}^{T}D) in Example 1 are negative, which implies that the (Dmathcal{M}) is negative definite, hence our assumption in the convergence analysis is valid, and the numerical results are consistent with Theorem 2.

Relaxing the assumption of definite retirement in the next period a+1 or considering the possibility of searching now or in the future, introduces new elements into the calculation, but the essential intertemporal trade-off is unchanged.

In [19], we established the well-posedness of multipoint nonlocal boundary value problem { − d 2 u ( t ) d t 2 + A u ( t ) = g ( t ) ( 0 ≤ t ≤ 1 ), d u ( t ) d t − A u ( t ) = f ( t ) ( − 1 ≤ t ≤ 0 ), u ( 1 ) = ∑ i = 1 J α i u ( λ i ) + φ, − 1 ≤ λ 1 < ⋯ < λ J ≤ 0 (1). in a Hilbert space H with the self-adjoint positive definite operator A under assumption ∑ i = 1 J | α i | ≤ 1. (2).

Not definitive, just definite.

The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions.

In "Kennedy's Wars" (Oxford, 2000), the historian and strategist Lawrence Freedman maintains that despite anecdotal evidence of a desire for a withdrawal from Vietnam after the 1964 elections, it was "less of a definite decision than a working assumption, based on a hope for stability rather than an expectation of chaos".