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In plane kinematics, the knowledge of the location of the instantaneous centre — deriving from the eighteenth century — affords information which is partial and very incomplete. But it is the case that there always exists an enumerable set of$cardinal points$, as they may be named, having the following characteristic: all the properties of the path of any, and every, element or series of elements, fixed in the moving plane, are completely determined by the configuration of this set of cardinal points. In this manner is given a very simple and complete synthesis of the whole realm of plane kinematics.

Results are obtained on the scattering theory for the Schrödinger equation $$i\partial _t u(t,x) = - \Delta _x u(t,x) + V(t,x)u(t,x) + F(u(t,x))$$ in spaces$L$^{$r$}($R$;$L$^{$q$}($R$^{$d$})) for a certain range of$r, q$, the so-called space-time scattering. In the linear case (i.e.$F$≡)) the relation with usual configuration space scattering is established.

We give an elementary proof of the formula χ($K$^{$n$}A)=$n$^{3}σ($n$) for the Euler characteristic of the generalized Kummer variety$K$^{$n$}$A$, where σ($n$) denotes the sum of divisors function.

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