Inverting graphs of rectangular matrices

This paper addresses the question of determining the class of rectangular matrices having a given graph as a row or column graph. We also determine equivalent conditions on a given pair of graphs in order for them to be the row and column graphs of some rectangular matrix. In connection with these graph inversion problems we discuss the concept of minimal inverses. This concept turns out to have two different forms in the case of one-graph inversion. For the two-graph case we present a method of determining when an inverse is minimal. Finally we apply the two-graph theorem to a class of energy related matrices.     

One-dimensional PtO2 at Pt steps: formation and reaction with CO

Using core-level spectroscopy and density functional theory we show that a one-dimensional (1D) oxide structure forms at the steps of the Pt(332) surface after exposure. The 1D oxide is found to be stable in an oxygen pressure range, where bulk oxides are only metastable, and is therefore argued to be a precursor to the Pt oxidation. As an example of the consequences of such a precursor exclusively present at the steps, we investigate the reaction of CO with oxygen covered Pt(332). Albeit more strongly bound, the oxidic oxygen is found to react more easily with CO than oxygen chemisorbed on the Pt terraces.     

Two-dimensional oxide on Pd(111)

The oxidation of Pd(111) leads to an incommensurate surface oxide, which was studied by the use of scanning tunneling microscopy, surface x-ray diffraction, high resolution core level spectroscopy, and density functional calculations. A combination of these methods reveals a two-dimensional structure having no resemblance to bulk oxides of Pd. Our study also demonstrates how the atomic arrangement of a nontrivial incommensurate surface can be solved by molecular dynamics in a case where experimental techniques alone give no solution.     

Domination Graphs with Nontrivial Components

 A tournament is an oriented complete graph. Vertices x and y dominate a tournament T if for all vertices z≠x,y, either (x,z) or (y,z) are arcs in T (possibly both). The domination graph of a tournament T is the graph on the vertex set of T containing edge {x,y} if and only if x and y dominate T. In this paper we determine which graphs containing no isolated vertices are domination graphs of tournaments. Received: May 20, 1998 Final version received: May 26, 1999     

The anomalous magnetisation of amorphous metglas 2826-A

Magnetisation measurements made on the amorphous ferromagnet Metglas 2826-A, (T_C = 254.5 K), in the temperature range 4.2 ≤ T ≤ 450 K indicate that it obeys the static scaling law hypothesis over an unusually wide temperature range. Analysis of the data give for the critical exponents δ = 5.07, β = 0.41, γ = 1.67. Moreover, above T_C a superparamagnetic model is discussed.