一类高次系统极限环的存在与唯一性

本文对系统dxdt=-y(1-ax2n)(1-bx2n) δx-lx4n 1dydt=x2n-1(1-cx2n)(1-bx2n)进行定性分析,得出其极限环的存在性,不存在性及唯一性的一系列充分条件.     

Derived Brackets

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and of Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp., even) Poisson brackets on supermanifolds are derived brackets of canonical even (resp., odd) Poisson brackets on their cotangent bundle (resp., parity-reversed cotangent bundle). Lie algebras have analogous properties, and the theory of Lie algebroids unifies the results valid for manifolds on the one hand, and for Lie algebras on the other. We outline the role of derived brackets in the theory of Poisson structures with background'.     

Odd subgraphs and matchings

Let G be a graph and f : V(G)→{1,3,5,…}. Then a subgraph H of G is called a (1,f)-odd subgraph if deg_H(x){1,3,…,f(x)} for all xV(H). If f(x)=1 for all xV(G), then a (1,f)-odd subgraph is nothing but a matching. A (1,f)-odd subgraph H of G is said to be maximum if G has no (1,f)-odd subgraph K such that |K|>|H|. We show that (1,f)-odd subgraphs have some properties similar to those of matchings, in particular, we give a formula for the order of a maximum (1,f)-odd subgraph, which is similar to that for the order of a maximum matching.     

无8-,9-和10-圈的平面图的3-可选择性

寻找平面图是3-或者4-可选择的充分条件是图的染色理论中一个重要研究课题,本文研究了围长至少是4的特殊平面图的选择数,通过权转移的方法证明了每个围长至少是4且不合8-圈,9-圈和10-圈的平面图是3-可选择的．     

平面图的强边染色

图$G$的强边染色是在正常边染色的基础上, 要求距离不超过$2$的任意两条边染不同的颜色, 强边染色所用颜色的最小整数称为图$G$的强边色数。本文首先给出极小反例的构型, 然后通过权转移法, 证明了$g(G)\geq5$, $\Delta(G)\geq6$且$5$-圈不相交的平面图的强边色数至多是$4\Delta(G)-1$。     

Periodic solutions to a kind of neutral functional differential equation in the critical case

In this paper, we consider a kind of neutral functional differential equation as follows:

     

The girth of a 4-homogeneous bipartite graph

In this paper, it is proved that the girth of a 4-homogeneous bipartite graph with valency greater than 2 is at most 12.     

Nuclear Physics in Norway, 1933–1955

In the late 1940s and the 1950s, Norwegian nuclear scientists, engineers, and administrators were deeply split over their nation’s goals, organization, politics, and tools for research in nuclear physics. One faction was determined to build a nuclear reactor in Norway, while another fiercely opposed the reactor plans and focused on particle accelerators. The first faction comprised scientific entrepreneurs and research technologists, the second academic scientists, most of whom began their research careers in nuclear physics in the 1930s. To understand this conflict, I trace the development of nuclear research in Norway from the early 1930s to the mid-1950s, placing it within an international context. Roland Wittje is working on his habilitation thesis in the History of Science Unit at the University of Regensburg, Germany.     

A sufficient condition for the bicolorability of a hypergraph

In this note we prove a long-standing conjecture of Sterboul [P. Duchet, Hypergraphs, in: R. Graham, M. Grötschel, L. Lovász (Eds.), Handbook of Combinatorics, 1995, pp. 381-432 (Chapter 7)], which states that a hypergraph is bicolorable provided it does not contain a specific kind of odd cycle. This is currently the strongest result of its kind, improving on results by Berge [Graphs and Hypergraphs, North-Holland, American Elsevier, Amsterdam, 1973] and Fournier and Las Vergnas [Une classe d’hypergraphes bichromatiques II, Discrete Math. 7 (1974) 99-106; A class of bichromatic hypergraphs, Ann. Discrete Math. 21, in: C. Berge, V. Chvátal (Eds.), Topics on Perfect Graphs, 1984, pp. 21-27].