Let G be a toroidal graph without cycles of a fixed length k, and l (G) the list chromatic number of G. We establish tight upper bounds Contract grant sponsor: RGC; Contract grant number: CUHK4165/01E (to L. C.); Contract grant sponsor: NSFC; Contract grant number: 10771197 (to W. W.); Contract grant sponsor: ZJNSFC; Contract grant number: Z6090150 (to W. W.); Contract grant sponsor: NSC97-2115...

Introduction. A classical dynamical r-matrix is an l-equivariant function r : l∗ → g ⊗ g (where l, g are Lie algebras), such that r21 + r = Ω is g-invariant, which satisfies the classical dynamical Yang-Baxter equation (CDYBE). CDYBE is a differential equation, which generalizes the usual classical Yang-Baxter equation. It was introduced in 1994 by G.Felder [Fe], in the context of conformal fie...

It is well known that the Haar and Shannon wavelets in L2(R) are at opposite extremes, in the sense that the Haar wavelet is localized in time but not in frequency, whereas the Shannon wavelet is localized in freqency but not in time. We present a rich setting where the Haar and Shannon wavelets coincide and are localized both in time and in frequency. More generally, if R is replaced by a grou...

This chapter presents DISCIPLE, a multi-strategy integrated learning s y s t e m illustrating a theory and a methodology for learning expert knowledge in the con tex t of an imperfect domain theory. DISCIPLE integrates a learning system and an e m p t y expert system, both using the same knowledge base. It is initially provided with a n imperfect (nonhomogeneous) domain theory and learns proble...

DPLL Modulo Theories Works with any DPLL engine and T -solver but is best with 1. an on-line DPLL engine and 2. an incremental T -solver Tableaux 2007 – p.29/40 Abstract DPLL Modulo TheoriesDPLL Modulo Theories Works with any DPLL engine and T -solver but is best with 1. an on-line DPLL engine and 2. an incremental T -solver It consists of the following rules: Propagate, Decide, Fail, Restart (...

A set S of vertices in a graph G is a dominating set of G if every vertex of V (G)\S is adjacent to some vertex in S. The minimum cardinality of a dominating set of G is the domination number of G, denoted as γ (G). Let Pn and Cn denote a path and a cycle, respectively, on n vertices. Let k1(F) and k2(F) denote the number of components of a graph F that are isomorphic to a graph in the family {...

which is part of a certain 2d Hamiltonian cohomological field theory [11]. Here we use this map to study the topology of ΩHam(M, ω) and its Hofer geometric properties via a kind of virtual Morse theory for the positive Hofer length functional, L : ΩHam(M, ω) → R . We also use Ψ to prove a kind of index theorem for some critical points of L . We apply this theory to get some concrete application...