1 Different Ways of Representing T • The speed of sound, a, is formally defined as (∂p/∂ρ) s. It is a function of that thermodynamic state variables of the gas. The stagnation enthalphy of a steady flow streamtube is defined by " h • ≡ h + 1 2 u 2. (1) It depends not only of the thermodynamic state of the gas, but also on the magnitude of the flow velocity u. Using the perfect gas approximation...

The detection of partial discharge by analyzing the components of SF6 gas in gas-insulated switchgears is important to the diagnosis and assessment of the operational state of power equipment. A gas sensor based on anatase TiO2 is used to detect decomposed gases in SF6. In this paper, first-principle density functional theory calculations are adopted to analyze the adsorption of SO2, SOF2, and ...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we assume the gas is in a pure state of macroscopically well-defined energy. We show that, in general, for single-particle distributions, such a state is strictly ...

By using recent results from graph theory, including the Strong Perfect Graph Theorem, we obtain a unifying framework for a number of tractable classes of constraint problems. These include problems with chordal microstructure; problems with chordal microstructure complement; problems with tree structure; and the “all-different” constraint. In each of these cases we show that the associated mic...

A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least 5 or the complement of one. The “strong perfect graph conjecture” (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by C...

Our proof (with Robertson and Thomas) of the strong perfect graph conjecture ran to 179 pages of dense matter; and the most impenetrable part was the final 55 pages, on what we called “wheel systems”. In this paper we give a replacement for those 55 pages, much easier and shorter, using “even pairs”. This is based on an approach of Maffray and Trotignon.