華東師范大學(xué)數(shù)學(xué)研究所建所10周年大會(huì)-免費(fèi)閱讀
【正文】 39。s problem asks whether the fixed subfield K(G) is rational (=purely transcendental).Noether39。AbstractsThe 10th Anniversary (19942004) Conference for the Institute of Mathematics, ECNUamp。s problem for finite abelian groups is solved by Swan, Voskresenskii, Ends and Miyata, Lenstra, etc. Thus we will consider the nonabelian case. In particular, it will be proved that K(G) is rational if G is a metacyclic pgroup and K contains enough roots of unity.Jianyi Shi (時(shí)儉益，East China Normal University)Title: Presentations for the plex reflection groups G(m,1,n) and G(m,m,n)In the present talk, we give a graphtheoretic description for all the congruence classes of presentations for the imprimitive plex reflection groups G(m,1,n) and G(m,m,n). We establish a bijection between the set of all the congruence classes of presentations for the group G(m,1,n) and the set of isomorphism classes of all the rooted trees of n nodes. We also establish a bijection between the set of all the congruence classes of presentations for the group G(m,m,n) and the set of isomorphism classes of all the connected graphs with n nodes and n edges. We show that any generator set S of G=G(m,1,n) or G(m,m,n) of n reflections, together with the respective basic relations on S, form a presentation of G. Shanyu Ji (稽善瑜，University of Houston)Title: Proper holomorphic mappings between balls of different dimensionsIt will give a survey on recent progress on study proper holomorphic mappings between balls of different dimensions.Gerard Jennhwa Chang (張鎮(zhèn)華，Taiwan University)Title: Distancetwo Labelings of GraphsThe problem of vertex labeling with a condition at distance two, proposed by Griggs and Roberts , arose from a variation of the channel assignment problem introduced by Hale . Suppose a number of transmitters are given. Our duty is to assign a channel to each of the given transmitters such that the interference is avoided. In order to reduce the interference, any two “close” transmitters must receive channels by at least k apart, and any two “very close” transmitters must receive channels by at least j apart, where j ≥ k are two given positive integers. One can construct an interference graph for this problem so that the transmitters are the vertices and there is an edge joining two “very close” transmitters. Two transmitters are defined “close” if the corresponding vertices are of distance two.Then, for a given graph G, an L(j,k)labeling is defined as a function f : V(G) →{0, 1, 2, ...} such that |f(u) f(v)| ≥ j when dG(u,v) = 1 and |f(u) f(v)| ≥ k when dG(u,v) = 2, where dG(u,v), the distance of u and v, is the minimum length of a path between u and v. The L(j,k)labeling number λj,k(G) of G is the smallest number m such that G has an L(j,k)labeling with no label greater than m. A λj,k labeling of G is an L(j,k)labeling using labels not greater than λj,k (G).The L(j,k)labeling problem, in particular the L(2,1) case, has been extensively studied during the past decade (see the references). This talk is to survey the results of the problem in the past decade. These include bounds for general graphs as well as special graphs such as trees, chordal graphs, strongly chordal graphs。.In tumor growth, tumor releases chemotactic substances, this chemical bine with the receptors on the endothelial cell wall, this process produce substances which cause the eventual sprouting lining of new capillaries. We want study the stability of such a system, and find the conditions for a global attractor, which may predict the location of t
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