The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family X p → S. Consequently we show that the generalized Futaki invariant is the leading term in the asymptotics of the reduced K-energy of the generic fiber of the map p. Properness of the K-energy implies that the generalized Futaki invariant is strictly negative.

We extend work of G. Ahlbrandt and M. Ziegler to give a classiication of the nite covers with bre group of prime order p for the projective space over the eld with p elements, and for the Grassmannian of k-sets from a disintegrated set (for k 2 N). AMS classiication: 03C35 and 20B27. This paper is a contribution to the study of the ne detail of the class of (countable) totally categorical struc...

This improves an earlier result of the first author for k = n = 2, namely Theorem II below, which dealt with B2 -sequences. This notion arose from a paper of Sidon [6]. A strictly increasing sequence A of natural numbers a,, a2 . . . . is called a B2-sequence, if for any two pairs (i, j) + (k, m) of natural numbers i <j, k < m there holds aj a i + ak a„„ in short, if A has no double-differences...

In an unpublished note, Golomb proposed a family of “strange” recursions of metafibonacci type, parameterized by k, and, for each k, identified what he speculated was the unique increasing solution. We show that, to the contrary, there are many increasing solutions for each k, and we indicate explicitly how to construct them. We also provide some additional general results concerning the nature...

Let p be an odd prime number and let K be an imaginary quadratic number field whose class number is not divisible by p. For a set S of primes of K whose norm is congruent to 1 modulo p, we introduce the notion of strict circularity. We show that if S is strictly circular, then the group G(KS(p)/K) is of cohomological dimension 2 and give some explicit examples.

‎A full Nesterov-Todd (NT) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using Euclidean Jordan algebra‎. ‎Two types of‎ ‎full NT-steps are used‎, ‎feasibility steps and centering steps‎. ‎The‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...