Properties of Catlin's reduced graphs and supereulerian graphs

A graph $G$ is called collapsible if for every even subset $R\subseteq V(G)$, there is a spanning connected subgraph $H$ of $G$ such that $R$ is the set of vertices of odd degree in $H$. A graph is the reduction of $G$ if it is obtained from $G$ by contracting all the nontrivial collapsible subgraphs. A graph is reduced if it has no nontrivial collapsible subgraphs. In this paper, we first prove a few results on the properties of reduced graphs. As an application, for 3-edge-connected graphs $G$ of order $n$ with $d(u)+d(v)\ge 2(n/p-1)$ for any $uv\in E(G)$ where $p>0$ are given, we show how such graphs change if they have no spanning Eulerian subgraphs when $p$ is increased from $p=1$ to 10 then to $15$

Quasilocal Center-of-Mass for Teleparallel Gravity

Asymptotically flat gravitating systems have 10 conserved quantities, which lack proper local densities. It has been hoped that the teleparallel equivalent of Einstein's GR (TEGR, aka GR${}_{||}$) could solve this gravitational energy-momentum localization problem. Meanwhile a new idea: quasilocal quantities, has come into favor. The earlier quasilocal investigations focused on energy-momentum. Recently we considered quasilocal angular momentum for the teleparallel theory and found that the popular expression (unlike our ``covariant-symplectic'' one) gives the correct result only in a certain frame. We now report that the center-of-mass moment, which has largely been neglected, gives an even stronger requirement. We found (independent of the frame gauge) that our ``covariant symplectic'' Hamiltonian-boundary-term quasilocal expression succeeds for all the quasilocal quantities, while the usual expression cannot give the desired center-of-mass moment. We also conclude, contrary to hopes, that the teleparallel formulation appears to have no advantage over GR with regard to localization.Comment: 12 pages, to appear in the proceedings of the 10th Marcel Grossman meeting (Rio de Janeiro, 2003

The Architecture of Complexity Revisited: Design Primitives for Ultra-Large-Scale Systems

As software-intensive systems continue to grow in scale and complexity the techniques that we have used to design and analyze them in the past no longer suffice. In this paper we look at examples of existing ultra-large-scale systems—systems of enormous size and complexity. We examine instances of such systems that have arisen spontaneously in nature and those that have been human-constructed. We distill from these example systems the design primitives that underlie them. We capture these design primitives as a set of tactics— fundamental architectural building-blocks—and argue that to efficiently build and analyze such systems in the future we should strongly consider employing such building-blocks

3-(3-Bromo­phen­yl)-N-phenyl­oxirane-2-carboxamide

There are two independent mol­ecules in the asymmetric unit of the title compound, C15H12BrNO2. In both mol­ecules, the two benzene rings adopt a cis configuration with respect to the ep­oxy ring. In one mol­ecule, the ep­oxy ring makes dihedral angles of 60.5 (2) and 77.92 (19)° with the two benzene rings; in the other mol­ecule, the values are 61.0 (2) and 81.43 (19)°. Inter­molecular N—H⋯O and C—H⋯O hydrogen bonding is present in the crystal structure

5-(4-Nitro­benz­yl)-1H-1,2,3,4-tetra­zole

In the title compound, C8H7N5O2, the dihedral angle between the benzene and tetra­zole rings is 63.13 (8)°. The crystal structure exhibits inter­molecular N—H⋯N hydrogen bonds which lead to the formation of one-dimensional chains along the [010] direction

Service - Oriented Challenges for Design Science: Charting the “E”-volution

This article links service-dominant (S-D) logic and design science to advance service system design, which is characterized by the indeterminacy of the design problems and outcome measures. Although much progress has been made in IT and IS toward service-orientation, these developments are often adaptations of goods-dominant (G-D) logic, rather than a full transition to a service orientation. In this paper, the “e”-volution of systems design, transitioning from G-D logic to S-D logic, is described and the IS design challenges implied by S-D logic are identified. To devise new, service-oriented modeling, methods and evaluation measurements, S-D logic endorses a fundamental shift in design thinking for design science from “bounded rationality” for problem solving to “expandable rationality” for design for the unknown. Available at: https://aisel.aisnet.org/pajais/vol2/iss1/3