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

Development of high energy density primary batteries Fourth quarterly report, 22 Mar. - 21 Jun. 1966

High energy density primary batteries for space flight applications - electrolyte systems, cell systems, and positive electrode constructio

Electronic structure of single-crystalline Mgx_xAl1−x_{1-x}B2_2 probed by x-ray diffraction multipole refinements and polarization-dependent x-ray absorption spectroscopy

X-ray diffraction multipole refinements of single-crystalline Mg$_x$Al$_{1-x}$B$_2$ and polarization-dependent near-edge x-ray absorption fine structure at the B 1$s$ edge reveal a strongly anisotropic electronic structure. Comparing the data for superconducting compounds ($x= 0.8$, 1.0) with those for the non-superconductor ($x=0$) gives direct evidence for a rearrangement of the hybridizations of the boron $p_z$ bonds and underline the importance of holes in the $\sigma$-bonded covalent $sp^2$ states for the superconducting properties of the diborides. The data indicate that Mg is approximately divalent in MgB$_2$ and suggest predominantly ionic bonds between the Mg ions and the two-dimensional B rings. For AlB$_2$ ($x=0$), on the other hand, about 1.5 electrons per Al atom are transferred to the B sheets while the residual 1.5 electrons remain at the Al site which suggests significant covalent bonding between the Al ions and the B sheets. This finding together with the static electron deformation density points to almost equivalent electron counts on B sheets of MgB$_2$ and AlB$_2$\@, yet with a completely different electron/hole distribution between the $\sigma$ and $\pi$ bonds

Development of high energy density primary batteries First quarterly report, 22 Jun. - 21 Oct. 1965

Electrode and electrolyte studies for lithium- copper fluoride batterie

Flood trends along the Rhine: the role of river training

Several previous studies have detected positive trends in flood flows in German rivers, among others, at Rhine gauges over the past six decades. The presence and detectability of the climate change signal in flood records has been controversially discussed, particularly against the background of massive river training measures in the Rhine. In the past the Rhine catchment has been heavily trained, including the construction of the Rhine weir cascade, flood protection dikes and detention basins. The present study investigates the role of river training on changes in annual maximum daily flows at Rhine gauges starting from Maxau down to Lobith. In particular, the effect of the Rhine weir cascade and of a series of detention basins was investigated. By homogenising the original flood flow records in the period from 1952 till 2009, the annual maximum series were computed that would have been recorded had river training measures not been in place. Using multiple trend analysis, relative changes in the homogenised time series were found to be from a few percentage points to more than 10 percentage points smaller compared to the original records. This effect is attributable to the river training measures, and primarily to the construction of the Rhine weir cascade. The increase in Rhine flood discharges during this period was partly caused by an unfavourable superposition of the Rhine and Neckar flood waves. This superposition resulted from an acceleration of the Rhine waves due to the construction of the weir cascade and associated channelisation and dike heightening. However, at the same time, tributary flows across the entire Upper and Lower Rhine, which enhance annual maximum Rhine peaks, showed strong positive trends. This suggests the dominance of another driver or drivers which acted alongside river training

Development of high energy density primary batteries 200 watt hours per pound total battery weight minimum Final report, 10 Jun. 1964 - 9 Jun. 1965

High energy density lithium-anode primary cells developed with energy-to-weight ratios over 200 watt hours per poun