Sentence examples for under which assumptions from inspiring English sources

Helmholtz investigates the question of which systems of geometry (Euclidean, Lobachevskian, and Riemannian) are possible under which assumptions.

Under which assumptions can algorithm (4) be adapted to produce a converging sequence to a common fixed point for a family of mappings?

Thus, it is natural to ask under which assumptions these properties are valid also for (2) (when q is not constant) and for the more general case (1).

Abbring and van den Berg (2003) show under which assumptions one can identify the true causal effect of the treatment from the spurious effect induced by the aforementioned selection effects.

Both frameworks can be adapted from the particular case of probabilities on a domain (Omega subset mathbb R^d) to the more general case of metric measure spaces, and the question whether the two flows coincide, or under which assumptions they do, is natural.

Also it would be interesting to study if our approach can be used to study undirected networks like the protein interaction network and under which assumptions.

In particular, CB is supposed to be nonzero, under which assumption it is easy to check that for a given desired output (y_{d}(t)), (t in S) there exist such desired state (x_{d}(t)), (t in S) and desired control input (u_{d}(t)), (t in S^) that left { textstylebegin{array}{l} x_{d}(t + 1) = Ax_{d}(t) + Bu_{d}(t),quad t in S^, y_{d}(t) = Cx_{d}(t), quad t in S. end{array}displaystyle right.

In the next sections we examine circumstances under which the assumptions used to derive (9) and (10) may break down, and we use insights from this analysis to design a more robust approach to parameter rescaling.

Our objective was to determine the conditions under which the assumption of a single-rate sorption parameter will be applicable to systems with heterogeneous sorption rates.

Some conditions under which this assumption is satisfied are described below and are the direct transductions of those of the general case in the context of semi-homogeneous solutions.

This will make clear under which extra assumption the BREM describes the distribution of study specific ROCs and the calculated SROC can be considered to be a real overall SROC.