Edge intersection graphs of linear 3-uniform hypergraphs

Let be the class of edge intersection graphs of linear 3-uniform hypergraphs. It is known that the problem of recognition of the class is NP-complete. We prove that this problem is polynomially solvable in the class of graphs with minimum vertex degree ≥10. It is also proved that the class is characterized by a finite list of forbidden induced subgraphs in the class of graphs with minimum vertex degree ≥16.     

Characterizing path graphs by forbidden induced subgraphs

A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are minimal with this property. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 369–384, 2009     

Intersection models of weakly chordal graphs

We first present new structural properties of a two-pair in various graphs. A two-pair is used in a well-known characterization of weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal ()-free graph if and only if G is an edge intersection graph of subtrees on a tree with maximum degree 4. This characterizes the so called [4, 4, 2] graphs. The proof of the theorem constructively finds the representation. Thus, we obtain an algorithm to construct an edge intersection model of subtrees on a tree with maximum degree 4 for such a given graph. This is a recognition algorithm for [4, 4, 2] graphs.     

Edge intersection graphs of systems of paths on a grid with a bounded number of bends

We answer some of the questions raised by Golumbic, Lipshteyn and Stern and obtain some other results about edge intersection graphs of paths on a grid (EPG graphs). We show that for any d≥4, in order to represent every n vertex graph with maximum degree d as an edge intersection graph of n paths on a grid, a grid of area Θ(n²) is needed. We also show several results related to the classes B_k-EPG, where B_k-EPG denotes the class of graphs that have an EPG representation such that each path has at most k bends. In particular, we prove: For a fixed k and a sufficiently large n, the complete bipartite graph K_m,n does not belong to B_2m−3-EPG (it is known that this graph belongs to B_2m−2-EPG); for any odd integer k we have B_k-EPG B_k+1-EPG; there is no number k such that all graphs belong to B_k-EPG; only 2^O(knlog(kn)) out of all the labeled graphs with n vertices are in B_k-EPG.     

On intersections of independent anisotropic Gaussian random fields

Let XH = {XH(s),s ∈RN1} and X K = {XK(t),t ∈R N2} be two independent anisotropic Gaussian random fields with values in R d with indices H =(H1,...,HN1) ∈(0,1)N1,K =(K1,...,KN2) ∈(0,1) N2,respectively.Existence of intersections of the sample paths of X H and X K is studied.More generally,let E1■RN1,E2■RN2 and FRd be Borel sets.A necessary condition and a sufficient condition for P{(XH(E1)∩XK(E2))∩F≠Ф}>0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space(RN1+N2+d,) are proved,where  is a metric defined in terms of H and K.These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.     

The extended S1/S0 conical intersection seam for the photochemical 2 + 2 cycloaddition of two ethylene molecules

The extended S₁/S₀ conical intersection seam for the photochemical 2_s?+?2_s, 2_s?+?2_a and 2_a?+?2_a cycloadditions of two ethylene molecules has been documented using the methodology described by Sicilia et al. (J. Chem. Theory Comput. 4, 257 (2008)). Two additional critical points on this prototype crossing seam were found as a result, although both lie more than 100?kcal?mol^?1 above the rhomboidal crossing located previously, and are not minima in the intersection space. Using VB theory, the branching space conditions for the conical intersection can be derived analytically, in fair agreement with calculated CASSCF results. Woodward–Hoffmann symmetry forbidden and allowed reactions are associated with the same extended conical intersection seam in this case.     

平面上Brown运动的重正化自交局部时的光滑性

本文运用实插值理论中的K-方法证明了平面上Brown运动自交局部时属于分数次Sob0lev空间Dpa,其中p＞1及α＜1/3.     

环丁酮光化学反应中S1/T1/S0交叉点的重要作用

势能面间的交叉在光化学反应中起着重要的作用 ,是由激发态反应物到基态产物发生无辐射跃迁的机制 .在本文中 ,我们用 CASSCF和态平均 CASSCF方法分别对环丁酮光化学反应的势能剖面及 S1,T1和 S0三个势能面间交叉进行了研究 .结果发现 ,基态和三态产物的形成是通过 S1,T1和 S0三个势能面交叉于同一区域 (称为 S1/T1/S0交叉点 )这一有效途径完成的 .　　60年代末 ,实验 [1－ 9]发现环丁酮和其它烷基酮 ,如丙酮、环戊酮的光化学反应机理很不一致 .主要体现在 ,i)环丁酮 (n,π态 )的α解离发生在 S1态势能面上 ,而其它烷基酮 (n,π态 …     

Inverse functions of pseudo regular mappings and regularity conditions

We show that, even for monotone directionally differentiable Lipschitz functionals on Hilbert spaces, basic concepts of generalized derivatives identify only particular pseudo regular (or metrically regular) situations. Thus, pseudo regularity of (multi-) functions will be investigated by other means, namely in terms of the possible inverse functions. In this way, we show how pseudo regularity for the intersection of multifunctions can be directly characterized and estimated under general settings and how contingent and coderivatives may be modified to obtain sharper regularity conditions. Consequences for a concept of stationary points as limits of Ekeland points in nonsmooth optimization will be studied, too. Received: May 20, 1999 / Accepted: February 15, 2000?Published online July 20, 2000     

Multipermutation-Based Intersection Theorem and Its Applications

In this paper, we introduce a multipermutation-based intersection theorem on the product space of several unit simplices, called the simplotope. This theorem gives a substantial generalization of an intersection result of Scarf on the unit simplex (Ref. 1). By using this new result, we also obtain a multipermutation-based generalization of the Brouwer fixed-point theorem on the simplotope. Furthermore, we apply this new result to an economic equilibrium model with indivisibilities and obtain an equilibrium existence theorem.