larger mean in this context? Two interpretations can be put forward. According to the first, a "larger" domain of validity means that the hypothesis allows for more numerical predictions for variables and parameters about which no empirical data are available. The larger domain is obtained by extending the range of variables for which the model can provide outputs. The second interpretation relies on the capacity of certain hypotheses to explain phenomena besides allowing for predictions. This capacity is usually considered to hold in a larger domain than the one in which empirical agreement obtains. The distinction between the two interpretations of a "larger" domain of validity than the one determined by empirical agreement is easy to establish in retrospect or "from above", that is, from a towering point of view that is inaccessible to scientists engaged in a research work. (We borrow the expressions "from above" and "from within" to xxx Xxxxxxxx (2008)). At the frontier of research, however, it is by definition not known with certainty which hypotheses are explanatory and which are only predictive. When one adopts the perspective "from within", that is, the perspective of the scientists who build up a new model and try to assess the quality of the hypotheses they have used therein, without being able to rely on established knowledge, the distinction is not readily apparent. Is it however possible to find out elements allowing modelers to decide whether the first or the second interpretation is relevant in the case at hand. A tentative answer is that hypotheses remaining valid under systematic variations are better candidates than hypotheses that do not yield empirically plausible results when twisted in order to explore domains neighbouring the original domain. To put it in other terms, robust hypotheses are better candidates than phenomenological hypotheses. Here, robust hypotheses are not only assessed within a set of models that all represent a same target system (as in climate science; see Xxxxxx 2010a, 2010b, 2013) but more generally within as broad as possible a set of models used to represent distinctive target systems for different purposes. This distinction would solve the problem if only it could be defined unequivocally. However, assessing the robustness of a hypothesis can no more be done by any algorithm than any kind of model validation. This assessment is a matter of the modeler's judgment and is always open to discussion and criticism. The not...
larger here means a body with at least 25 staV and which normally relies on grant-in-aid for 50% of its income or trades mainly with Government departments.
larger means to the right on the number line...) Rather than derive special cases for one or both of the radii being negative, we’ll just proceed with what we have.)
More Definitions of larger
larger von Neumann algebra by means of the elements π(a) and the shift operators λs(ξ)(t) = ξ(t s). The crossed product is known to admit a dual action of R in the form of an automorphism group (θs) indexed by R and a normal faithful semi-finite trace τ characterized by the property that τ θs = e−sτ . (See [40].)