Mathias like criterion for the extender based Prikry forcing

We suggest a genericity criterion for the extender based Prikry forcing analogous to the Mathias genericity criterion for Prikry forcing.     

Mechanism and kinetics of polymerization of propylene in a microwave plasma

Flowing microwave plasma of propylene and propylene with argon was studied by mass spectrometry. Plasma composition was investigated as a function of external parameters such as pressure, argon/propylene ratio, and microwave-induced power. It was found that the propylene broke down to C₂H₂ and CH₄, or reacted further with propylene. Two main products, leading to the determination of three main chain reactions for the polymerization of propylene by ion-molecule interactions, were observed, namely, C₂H₂ and CH₄. These were the propylene, acetylene, and ethylene chain reactions. It was also found that the propylene disappeared in a pseudo-first-order reaction. Consequently an overall rate constant for the polymerization was determined (50 sec^–1 at 1 torr pressure for propylene plasma). This constant is found to be linearly dependent upon the propylene percent concentration, and nonlinearly dependent upon plasma pressure.Partly presented at the 157th meeting of the Electrochemical Society, St. Louis, Missouri, May 11–16, 1980.     

Energy stability of channel flows

Zusammenfassung Die Energiemethode wird zur Untersuchung der Stabilität einer beliebigen Kanalströmung angewandt. Es wird eine auf Eigenwertabschätzungen basierte qualitative Beschreibung der Fläche (, ) gegeben, welche die Schranke für den Instabilitätsbereich in Abhängigkeit von Längs- bzw. Querwellenzahl der Störungen darstellt. Eine allgemeine untere Grenze für die minimalisierende Querwellenzahl und den zugehörigen Eigenwert (0, ) wird angegeben. Das Problem der Energiestabilität wird dann für eine Klasse von Geschwindigkeitsprofilen mit Wendepunkt gelöst. Die durch numerische Integration erhaltenen Ergebnisse werden mit den Ergebnissen der linearen Stabilitätstheorie verglichen.     

Limited path percolation in complex networks

We study the stability of network communication after removal of a fraction q=1-p of links under the assumption that communication is effective only if the shortest path between nodes i and j after removal is shorter than al(ij)(a> or =1) where l(ij) is the shortest path before removal. For a large class of networks, we find analytically and numerically a new percolation transition at p(c)=(kappa(0)-1)((1-a)/a), where kappa(0) [triple bond] / and k is the node degree. Above p(c), order N nodes can communicate within the limited path length al(ij), while below p(c), N(delta) (delta<1) nodes can communicate. We expect our results to influence network design, routing algorithms, and immunization strategies, where short paths are most relevant.