Tahun Terbit

2010

Sometimes a hyperbolic Kac–Moody algebra (KMA) admits an automorphic correction, meaning a generalized KMA with the same real simple roots and whose denominator function has good automorphic properties. These, for example, allow one to work out the root multiplicities. Gritsenko and Nikulin have formalized this in their theory of Lorentzian Lie algebras and shown that the real simple roots mu…

Tahun Terbit

2010

In this paper, we generalize the W2,p interior estimates of fully nonlinear elliptic equations that were obtained by Caffarelli [‘Interior a priori estimates for solutions of fully nonlinear equations’, Ann. of Math. 130 (1989) 189–213]. The generalizations are carried out in two directions. One is that we relax the regularity requirement on the ‘constant coefficients’ equations and …

Tahun Terbit

2010

This paper gives a simple criterion for a multiple Fourier series to be a Hilbert modular form.

A set of sets is called a family. Two families A and B are said to be cross-intersecting if each set in A intersects each set in B. For any two integers n and k with 1 <= k <= n, let ([n]<=k) denote the family of all subsets of {1, . . . , n} that have at most k elements. We show that if A is a subfamily of ([m]<=r), B is a subfamily of ([n]<=s), and A and B are cross-intersecting, then |A||B|…

Tahun Terbit

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In recent years, exciting scientific evidence has emerged highlighting the ecological importance of dead animals (i.e., carrion) and their consumption (i.e., scavenging), to the point that we could consider this the golden age of scavenging research. We now have a considerable body of theoretical and empirical work that indicates that scavenging is fundamental to properly understanding not only…

Tahun Terbit

2010