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The p-layer of H, L_(p^')(H) is the unique minimal normal subgroup of H which maps onto E(H/O_(p^')(H)).

The hyperbolic cosine is defined as coshz=1/2(e^z+e^(-z)). (1) The notation chx is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). This function describes the ...

A tubular neighborhood of a submanifold N in M is an embedding of the normal bundle (nu_N) of N into M, i.e., f:nu_N->M, where the image of the zero section of the normal ...

The probability Q_delta that a random sample from an infinite normally distributed universe will have a mean m within a distance |delta| of the mean mu of the universe is ...

The determination of a test for the equality of means for two normal distributions with different variances given samples from each. There exists an exact test which, ...

Let G be a group having normal subgroups H and K with H subset= K. Then K/H⊴G/H and (G/H)/(K/H)=G/K, where N⊴G indicates that N is a normal subgroup of G and G=H indicates ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

Let A be a sum of squares of n independent normal standardized variates X_i, and suppose A=B+C where B is a quadratic form in the x_i, distributed as chi-squared with h ...