Dominants and submissives of matching polyhedra

LetP be the convex hull of perfect matchings of a graphG=(V, E). The dominant ofP is {y∈R ^E ∶y≥x for somex∈P}. A theorem of Fulkerson implies that, ifG is bipartite, then the dominant ofP can be described by linear inequalities having {0, 1}-valued coefficients. However, this is far from true in general. Here it is proved that, for every positive integern, there exists a graph for which the dominant has an essential valid inequality whose coefficient-set includes the firstn positive integers. A similar result holds for the submissive ofP, {y∈R ^E ∶0≤y≤x for somex∈P}. Research partially supported by a grant from NSERC of Canada.     

THEORETICAL ANALYSIS OF THE DECREASE OF THE STRENGTH OF REINFORCED SOIL1)

从理论上推导出了加筋土强度的数学表达式,分析了土的黏聚力与土筋界面参数变化对加筋土强度的影响,研究表明,当发生拉断型破坏时,黏聚力的减少比筋材提供的拉力占优势的情况下,加筋土的强度会低于素土的强度;当发生黏着型破坏时,黏聚力的减少比筋材提供的摩阻力占优势的情况下,加筋土的强度也会低于素土的强度。加筋土强度的降低程度与筋材在土中形成的夹层、土筋界面透水性、加筋间距有关。     

一类算子的凸性条件(英文)

In this paper,we find a subclass of starlike functions on the unit disk,which are mapped by a operator,given by F（z）=1＋u/zu∫z0 f（t）tu-1dt（Re u≥0）,onto convex functions.The main results extend some known results.