Sentence examples for with further assumptions from inspiring English sources

In effect, it is not very different from proposal (i), and with further assumptions for (i) even identical.

There have been attempts to refine these correction methods (e.g., Le & Schmidt, 2006), albeit with further assumptions and approximations for missing data, and, therefore, the debate continues.

In (17), b represents the original K-D image vector, {Φ(p)} are the RS image formation operators referred to as the PSF operators of the corresponding DEDR-VA-related imaging systems (or methods) where we have omitted the sub index D for notational simplicity, and {ν(p)} represent the system noise with further assumption that these are uncorrelated from system to system.

Acceptance of this view, together with two further assumptions, can lead to the conclusion that the kind of experience that occurs when one perceives the world isn't one that can occur when one hallucinates, which in turn can motivate a disjunctive approach to perceptual experience in general.

It is our purpose in this paper to extend Theorem 1.1 from Hilbert space to an arbitrary real Banach space with no further assumptions on the real sequences { α n } n ≥ 0, { a k } k ≥ 0. Theorem 2.1 Let C be a bounded closed convex subset of a Banach space E and T : C → C be a Lipschitz pseudocontraction with F ( T ) ≠ ∅.

Identifying individual cohort, period or age effects is impossible with making further assumptions, although this identifiability problem is not of concern when making projections.

Second (and these are points that tend to be baked into broader stand-alone articles), that this "trolling" is interchangeable with 4chan, with the further assumption that 4chan is interchangeable with Anonymous, itself framed to be the Ur alt-right.

With a further assumption on the sources being non-stationary, which has been exploited in [19], we arrive at a problem of jointly diagonalizing two sets of cross covariance and pseudo cross covariance matrices at different time instances.

With the further assumption that the participating phases have fixed compositions and that the interfacial diffusion process is driven by gradients in interfacial curvature, we obtain a unique solution for the growth of the product ω layer along the α/β interface.

Let the number of breeding females in year n be denoted b n ; that is, 1 the coefficient of 1/4 follows from the assumptions of equal sex ratio and biennial breeding with the further assumption that, for each age class, the proportions of females breeding in even and odd numbered years are equal.

In the second case the DNA sequence is scanned to predict the entire set of valid ORFs, defined as the DNA segments occurring between two stop codons and exceeding 100 nucleotides, with no further assumption about the presence or not of coding sequences.