ω‐saturated quasi‐minimal models of Th(ℚω, +, σ, 0)

We show that (ℚ^ω, +, σ, 0) is a quasi-minimal torsion-free divisible abelian group. After discussing the axiomatization of the theory of this structure, we present its ω-saturated quasi-minimal model. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A counterexample to the dominating set conjecture

The metric polytope met _n is the polyhedron associated with all semimetrics on n nodes and defined by the triangle inequalities x _ij − x _ik − x _jk ≤ 0 and x _ij + x _ik + x _jk ≤ 2 for all triples i, j, k of {1,..., n}. In 1992 Monique Laurent and Svatopluk Poljak conjectured that every fractional vertex of the metric polytope is adjacent to some integral vertex. The conjecture holds for n ≤ 8 and, in particular, for the 1,550,825,600 vertices of met₈. While the overwhelming majority of the known vertices of met₉ satisfy the conjecture, we exhibit a fractional vertex not adjacent to any integral vertex.     

Probability of Local Bifurcation Type from a Fixed Point: A Random Matrix Perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectrum is considered both numerically and analytically using previous work of Edelman et al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion does not hold, e.g., real random matrices with Gaussian elements with a large positive mean and finite variance. PACS numbers: 05.45.−a, 05.45.Tp, 89.75.−k, 89.75.Fb     

Bordeaux 3-color conjecture and 3-choosability

A graph G=(V,E) is list L-colorable if for a given list assignment L={L(v):v∈V}, there exists a proper coloring c of G such that c(v)∈L(v) for all v∈V. If G is list L-colorable for every list assignment with |L(v)|?k for all v∈V, then G is said to be k-choosable.In this paper, we prove that (1) every planar graph either without 4- and 5-cycles, and without triangles at distance less than 4, or without 4-, 5- and 6-cycles, and without triangles at distance less than 3 is 3-choosable; (2) there exists a non-3-choosable planar graph without 4-cycles, 5-cycles, and intersecting triangles. These results have some consequences on the Bordeaux 3-color conjecture by Borodin and Raspaud [A sufficient condition for planar graphs to be 3-colorable. J. Combin. Theory Ser. B 88 (2003) 17-27].     

Remarks on coarse embeddings of metric spaces into uniformly convex Banach spaces

We study the support and convergence conditions for a metric space to be coarsely embeddable into a uniformly convex Banach space. By using ultraproducts we also show that the coarse embeddability of a metric space into a uniformly convex Banach space is determined by its finite subspaces.     

Euler函数ψ(n)的同余性

本文引入模p子系的素化概念,得出Euler函数ψ（n）在某些素化系上的整体同余性质,并用于Lebmer问题的研究.     

The coarse geometric Novikov conjecture and uniform convexity

The coarse geometric Novikov conjecture provides an algorithm to determine when the higher index of an elliptic operator on a noncompact space is nonzero. The purpose of this paper is to prove the coarse geometric Novikov conjecture for spaces which admit a (coarse) uniform embedding into a uniformly convex Banach space.     

Three-step Harmonic Solvmanifolds

The Lichnerowicz conjecture asserted that every harmonic Riemannian manifold is locally isometric to a two-point homogeneous space. In 1992, E. Damek and F. Ricci produced a family of counter-examples to this conjecture, which arise as abelian extensions of two-step nilpotent groups of type-H. In this paper we consider a broader class of Riemannian manifolds: solvmanifolds of Iwasawa type with algebraic rank one and two-step nilradical. Our main result shows that the Damek–Ricci spaces are the only harmonic manifolds of this type.