Complex System Reliability Analysis Method: Goal‐Oriented Methodology

Goal‐oriented (GO) methodology is a success‐oriented method for complex system reliability analysis based on modeling the normal operating sequence of a system and all possible system states. Recently, GO method has been applied in reliability and safety analysis of a number of systems, spanning defense, transportation, and power systems. This chapter provides a new approach for reliability analysis of complex systems, first, by providing its development history, its engineering applications, and the future directions. Then, the basic theory of GO method is expounded. Finally, the comparison of GO method, fault tree analysis and Monte‐Carlo simulation is discussed

The linear arboricity of planar graphs with no short cycles

AbstractThe linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that ⌈Δ(G)2⌉≤la(G)≤⌈Δ(G)+12⌉ for any simple graph G. In the paper, it is proved that if G is a planar graph with Δ≥7 and without i-cycles for some i∈{4,5}, then la(G)=⌈Δ(G)2⌉

Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation

In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of $\theta$, we obtain global regularity results with improved growth estimate on $| \nabla^{\bot} \theta |$. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum $| \nabla^{\bot} \theta |$. The numerical results indicate that the assumptions on the local geometric regularity of the level sets of $\theta$ in our theorems are satisfied. Therefore these theorems provide a good explanation of the double exponential growth of $| \nabla^{\bot} \theta |$ observed in this and past numerical simulations.Comment: 25 pages, 10 figures. Corrected a few typo

[1,1′-Bis(dicyclo­hexyl­phosphino)cobalto­cenium-κ2 P,P′]chlorido(η5-cyclo­penta­dien­yl)ruthenium(II) hexa­fluorido­phosphate

In the title structure, [CoRu(C5H5)(C17H26P)2Cl]PF6, the RuII atom is bonded to a cyclo­penta­dienyl ring, a Cl atom and two P atoms of the chelating 1,1′-bis­(dicyclo­hexyl­phosphino)cobaltocenium (di-cypc) ligand, leading to a three-legged piano-stool coordination. Part of the PF6 − counter-anion is disordered over two positions, with a site-occupancy ratio of 0.898 (7):0.102 (7). The components are linked by C—H⋯F and C—H⋯Cl hydrogen bonds