The (1,2)-Step Competition Graph of a Tournament

The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim, and Nam defined the m-step competition graph. In this paper, we offer another generalization of the competition graph. We define the (1,2)-step competition graph of a digraph D, denoted C1,2(D), as the graph on V(D) where {x,y}∈E(C1,2(D)) if and only if there exists a vertex z≠x,y, such that either dD−y(x,z)=1 and dD−x(y,z)≤2 or dD−x(y,z)=1 and dD−y(x,z)≤2. In this paper, we characterize the (1,2)-step competition graphs of tournaments and extend our results to the (i,k)-step competition graph of a tournament

Application of trajectory optimization techniques to upper atmosphere sampling flights using the F-15 Eagle aircraft

Atmospheric sampling has been carried out by flights using an available high-performance supersonic aircraft. Altitude potential of an off-the-shelf F-15 aircraft is examined. It is shown that the standard F-15 has a maximum altitude capability in excess of 100,000 feet for routine flight operation by NASA personnel. This altitude is well in excess of the minimum altitudes which must be achieved for monitoring the possible growth of suspected aerosol contaminants

A differential game solution to the Coplanar tail-chase aerial combat problem

Numerical results obtained in a simplified version of the one on one aerial combat problem are presented. The primary aim of the data is to specify the roles of pursuer and evader as functions of the relative geometry and of the significant physical parameters of the problem. Numerical results are given in a case in which the slower aircraft is more maneuverable than the faster aircraft. A third order dynamic model of the relative motion is described, for which the state variables are relative range, bearing, and heading. The ranges at termination are arbitary in the present version of the problem, so the weapon systems of both aircraft can be visualized as forward firing high velocity weapons, which must be aimed at the tail pipe of the evader. It was found that, for the great majority of the ralative geometries, each aircraft can evade the weapon system of the other

Application of trajectory optimization techniques to upper atmosphere sampling flights using the F4-C Phantom aircraft

Altitude potential of an off-the-shelf F4-C aircraft is examined. It is shown that the standard F4-C has a maximum altitude capability in the region from 85000 to 95000 ft, depending on the minimum dynamic pressures deemed acceptable for adequate flight control. By using engine overspeed capability and by making use of prevailing winds in the stratosphere, it is suggested that the maximum altitude achievable by an F4-C should be in the vicinity of 95000 ft for routine flight operation. This altitude is well in excess of the minimum altitudes which must be achieved for monitoring the possible growth of suspected aerosol contaminants

Physiological variation of Garry oak (Quercus garryana) seedlings to drought stress

The purpose of this study was to determine physiological differences in drought response among Garry oak (Quercus garryana Douglas ex Hook. [Fagaceae]) seedlings that grow in distinct populations in Washington state, in order to aid in restoration efforts by informing growers of the potential differences between the acorn collection sites. Acorns from six Washington populations east of the Cascades, as well as one population from Whidbey Island, were collected and grown in containers under controlled conditions. The plants were assessed with and without moderate and severe drought stress induced by withholding water. The most extreme differences in photosynthetic characteristics for non-stressed seedlings from different populations were in stomatal conductance rates, which in some cases differed between populations by 2 fold or more. Differences in response to drought occurred across populations after 14 days of withholding water (Fig 4). Seedlings from the northernmost population of Garry oak on the east side of the Cascades (Swauk Creek) were most susceptible to lowered photosynthetic rates induced by drought stress, while an island population from the west side of the cascades (Oak Harbor) showed the least drought-induced reduction of assimilation. Differences among populations were also observed in the occurrence of drought induced embolisms, and in changes in leaf water potential, relative water content, and production of the osmolyte proline in response to drought. This study shows that seedlings from different populations of Garry oak have distinct physiological responses to drought that may lead to changes in survivorship for seedlings used in reforestation efforts for Garry oak savannas as they are exposed to drought stress in the field

Radiation heat transfer analysis of a Czochralski furnace with a radiation shield

This paper reports on the radiation heat transfer from the melt in a Czochralski crystal growing furnace in the presence of a radiation shield The change of radiation heat transfer effects three basic areas, the cooling rate of the crystal, the bulk flow and the bulk temperature of the melt. The shield is installed above the melt to inhibit the heat transfer from the melt to the cooling crystal, allowing the crystal to grow 40% faster. Radiation is the primary mode of heat transfer in the furnace where the temperature to grow silicon crystals is around 1773K. The governing equations are the three-dimensional Navier Stokes equations in cylindrical coordinates for laminar flow, with the buoyancy term present, and the energy equation. The boundary conditions at the free surface of the melt are nonlinear due to the presense of the radiation. Instead of introducing the stream function to facilitate the solution, the Svanberg vorticity parameter, w/r, was introduced. The resulting equations were solved by an iterative process to yield the velocity distribution in the melt. Then these equations were used to solve the unsteady state energy equation. The radiation view factors were calculated by using a program called CONFACII. The temperature values thus obtained were used for the buoyancy terms in the Navier Stokes equations