This is an account of three 1-hour lectures given at the Instructional Conference on Representation Theory of Algebraic Groups and Related Finite Groups, Isaac Newton Institute, Cambridge, 6–11 January 1997. In section 1, we define abelian categories following Grothendieck [12]. We then characterize module categories among abelian categories. Finally we sketch a proof of Mitchell’s full embeddi...

The extensive theory that exists on ~ca, the set of uitrafilters ov-.r the integers, suggests an analogous study of the family of g-complete ultrafih~rs over a measurable cardinal g > w. This paper is devoted to such a study, with emphasis on those aspects which make the uncountable case interesting and distinctive. Section 1 is a preliminary section, recapitulating some knov, n concepts and re...

We study Galois points for a hypersurface X with dimSing(X) ≤ dimX − 2. The purpose of this article is to determine the set ∆(X) of Galois points in characteristic zero: Indeed, we give a sharp upper bound of the number of Galois points in terms of dimX and dimSing(X) if ∆(X) is a finite set, and prove that X is a cone if ∆(X) is infinite. To achieve our purpose, we need a certain hyperplane se...

Version 1.6.0 of the code SusHi is presented. Concerning inclusive CP-even Higgs production in gluon fusion, the following new features with respect to previous versions have been implemented: expansion of the partonic cross section in the soft limit, i.e. around x = M H/ŝ → 1; N3LO QCD corrections in terms of the soft expansion; top-quark mass suppressed terms through NNLO; matching to the cro...

which depends Lipschitz continuously from the data and, by [12, Theorem 2.6], also from v and ~v. According to (2), at time t the pedestrian at x moves along a prescribed trajectory, an integral curve of ~v, with a speed v(ρ) that depends on ρ evaluated at point x and time t. On the contrary, Section 2 is devoted to (1) with the speed of the individual at x depending on an average of the densit...

Simple but accurate expressions for the total cross sections and energy-absorption cross sections for inelastic scattering of x rays from atomic, molecular, and condensed matter are developed. The starting point is the relativistic impulse approximation for Compton scattering of x rays. This gives the inelastic-scattering cross-section differential with respect to energy and solid-angle interva...

We characterize the class of copulas that can be constructed from the diagonal section by means of the functional equation C(x∨y, x∨y) = C(x, y)+ |x− y|, for all (x, y) in the unit square such that C(x, y) > 0. A simple construction method for copulas is also given.