Counting Hamilton cycles in sparse random directed graphs

Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if $p\ge(\log n+\omega(1))/n$ then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically $n!(p(1+o(1)))^{n}$. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically $n!(\log n/n(1+o(1)))^{n}$ directed Hamilton cycles

Plains-wanderer

The short story Plains-wanderer, is a historical fiction based upon the real-life experiences of a Jewish Polish tailor living in Europe during the era of World War II

Multijunction cells for concentrators: Technology prospects

Development of high-efficiency multijunction solar cells for concentrator applications is a key step in achieving the goals of the U.S. Department of Energy National Photovoltaics Program. This report summarizes findings of an issue study conducted by the Jet Propulsion Laboratory Photovoltaic Analysis and Integration Center, with the assistance of the Solar Energy Research Institute and Sandia National laboratoies, which surveyed multijunction cell research for concentrators undertaken by federal agencies and by private industry. The team evaluated the potentials of research activities sponsored by DOE and by corporate funding to achieve projected high-efficiency goals and developed summary statements regarding industry expectations. Recommendations are made for the direction of future work to address specific unresolved aspects of multijunction cell technology

Silicon-sheet and thin-film cell and module technology potential: Issue study

The development of high-efficiency low-cost crystalline silicon ribbon and thih-film solar cells for the energy national photovoltaics program was examined. The findings of an issue study conducted are presented. The collected data identified the status of the technology, future research needs, and problems experienced. The potentials of present research activities to meet the Federal/industry long-term technical goal of achieving 15 cents per kilowatt-hour levelized PV energy cost are assessed. Recommendations for future research needs related to crystalline silicon ribbon and thin-film technologies for flat-plate collectors are also included

Polycrystalline silicon study: Low-cost silicon refining technology prospects and semiconductor-grade polycrystalline silicon availability through 1988

Photovoltaic arrays that convert solar energy into electrical energy can become a cost effective bulk energy generation alternative, provided that an adequate supply of low cost materials is available. One of the key requirements for economic photovoltaic cells is reasonably priced silicon. At present, the photovoltaic industry is dependent upon polycrystalline silicon refined by the Siemens process primarily for integrated circuits, power devices, and discrete semiconductor devices. This dependency is expected to continue until the DOE sponsored low cost silicon refining technology developments have matured to the point where they are in commercial use. The photovoltaic industry can then develop its own source of supply. Silicon material availability and market pricing projections through 1988 are updated based on data collected early in 1984. The silicon refining industry plans to meet the increasing demands of the semiconductor device and photovoltaic product industries are overviewed. In addition, the DOE sponsored technology research for producing low cost polycrystalline silicon, probabilistic cost analysis for the two most promising production processes for achieving the DOE cost goals, and the impacts of the DOE photovoltaics program silicon refining research upon the commercial polycrystalline silicon refining industry are addressed

Enhancing Robustness and Immunization in geographical networks

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, the strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain the explicit form of the percolation threshold $q_{c}$ for networks containing arbitrary order cycles. For 3-cycles, the dependence of $q_c$ on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with an analytical evidence.Comment: 6 pages, 8 figure

Ten-Dimensional Super-Twistors and Super-Yang-Mills

Four-dimensional super-twistors provide a compact covariant description of on-shell N=4 d=4 super-Yang-Mills. In this paper, ten-dimensional super-twistors are introduced which similarly provide a compact covariant description of on-shell d=10 super-Yang-Mills. The super-twistor variables are Z=(lambda^alpha, mu_alpha, Gamma^m) where lambda^alpha and mu_alpha are constrained bosonic d=10 spinors and Gamma^m is a constrained fermionic d=10 vector. The Penrose map relates the twistor superfield Phi(Z) with the d=10 super-Yang-Mills vertex operator lambda^alpha A_alpha(x,theta) which appears in the pure spinor formalism of the superstring, and the cubic super-Yang-Mills amplitude is proportional to the super-twistor integral \int dZ Phi_1 Phi_2 Phi_3.Comment: 14 pages harvmac, added short clarificatio