Score sets in oriented 3-partite graphs

Let D(U, V, W) be an oriented 3-partite graph with |U|=p, |V|=q and |W|= r. For any vertex x in D(U, V, W), let d x and d-x be the outdegree and indegree of x respectively. Define aui (or simply ai) = q r d ui - d-ui, bvj(or simply bj) = p r d vj - d-vj and Cwk (or simply ck) = p q d wk - d-wk as the scores of ui in U, vj in V and wk in Wrespectively. The set A of distinct scores of the vertices of D(U, V, W) is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai(2≤i≤n - 1) are even positive integers and an is any positive integer, then for n≥3, there exists an oriented 3-partite graph with the score set A = {a1,2∑i=1 ai,…,n∑i=1 ai}, except when A = {0,2,3}. Some more results for score sets in oriented 3-partite graphs are obtained.     

MFI型沸石晶体的择优定向生长

首次采用"双模板剂"法在SiO2-Na2O-正丙胺-溴化N-乙基-六亚甲基四胺(EtHMTA^+)-NaF-H2O体系中合成得到了b轴择优取向的ZSM-5(MFI型)晶体,并用扫描电镜(SEM)和XRD进行表征。择优取向程度与所用的两种模板剂的比例有关,当正丙胺:EtHMTA^+比为0.7:0.3时,ZSM-5晶体择优取向最明显。     

HIGH VISCOUS STRESS OF ORIENTED POLYOLEFINS UNDER UNIAXIAL TENSILE DEFORMATION

In this communication, by means of stress relaxation experiments, the viscous stress at various strains during tensile deformation of oriented polyolefin samples including high density polyethylene （HDPE）, linear low density polyethylene （LLDPE） and isotactic polypropylene （iPP）, has been determined. The viscous stress in the oriented samples takes up to 50%-70% of the total stress, which is unusually high compared with their isotropic counterparts. The unusual high viscous stress was discussed based on mainly the existence of shish structure in oriented polyolefins, which could enhance the inter-lamella coupling significantly.