We show the properties of the blowup limits of Kähler Ricci flow solutions on Fano surfaces if Riemannian curvature is unbounded. As an application, on every toric Fano surface, we prove that Kähler Ricci flow converges to a Kähler Ricci soliton metric if the initial metric has toric symmetry. Therefore we give a new Ricci flow proof of existence of Kähler Ricci soliton metrics on toric surfaces.

Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see [KMM] for introduction. In [SH2] it was conjectured that many of the interesting sets, associated with these varieties have something in common: they satisfy the ascending chain condition, which means that every increasing chain of elements terminates (in [SH2] it was called the upper se...

We establish the dichotomy property of [7] for multi-conclusion stable canonical rules of [1]. This yields an alternative proof of existence of bases of admissible rules for such well-known systems as IPC, S4, and K4.

In [I] we introduced the notion of transfer from a group over a local field to an associated endoscopic group, but did not prove its existence, nor do we do so in the present paper. Nonetheless we carry out what is probably an unavoidable step in any proof of existence: reduction to a local statement at the identity in the centralizer of a semisimple element, a favorite procedure of Harish Chan...

In this note, we prove the existence of Nash equilibria in infinite normal form games with compact sets of strategies and continuous payoffs by constructing Nash mappings. © 2010 Elsevier Ltd. All rights reserved.

We prove existence of a competitive equilibrium in a version of a Ramsey model in which leisure enters the utility function. The analysis is carried out by means of a direct and technically simple approach that allows us to obtain detailed results concerning the behavior of equilibrium allocations and prices.

We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying structure of atoms, we prove decidability of the problem. The core result is parameter-elimination: existence of an isomorphism definable with parameters implies e...

Relational learners need to be able to handle the information contained in a set of related tuples. Most current relational learners are biased either towards the use of aggregate functions that summarize that set, or towards checking the existence of specific kinds of elements in that set. Learning patterns that contain a combination of both is a challenging task. In this paper we introduce a ...

Relational interpretations of type systems are a useful tool for establishing properties of programming languages. For languages with recursive types the existence of a relational interpretation is often di cult to establish. The most well-known approach is to pass to a domaintheoretic model of the language, using the structure of the domain to de ne a suitable system of relations. Here we stud...