How to Obtain Maximum Environmental Applicability from Natural Silicates

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How To Obtain Powerful Parsers

How to Obtain Global Information From Computations Over Finite Fields

This is an extended version of the talk I gave at the summer school in Göttingen in July 2007. We discuss the Mordell-Weil Sieve and some applications.

How to Obtain Transience from Bounded Radial Mean Curvature

We show that Brownian motion on any unbounded submanifold P in an ambient manifold N with a pole p is transient if the following conditions are satisfied: The p-radial mean curvatures of P are sufficiently small outside a compact set and the p-radial sectional curvatures of N are sufficiently negative. The ‘sufficiency’ conditions are obtained via comparison with explicit transience criteria fo...

How to obtain the P value from a confidence interval.

We have shown in a previous Statistics Note how we can calculate a confidence interval (CI) from a P value. Some published articles report confidence intervals, but do not give corresponding P values. Here we show how a confidence interval can be used to calculate a P value, should this be required. This might also be useful when the P value is given only imprecisely (eg, as P<0.05). Wherever t...