Nonlinear zero-sum differential game analysis by singular perturbation methods

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane

Transmitting values about education: A comparison of black teen mothers and their nonparent peers

Central to the debate about why some poor people remain poor is the enduring question of what role values play in behavior patterns as observed in chronically impoverished families and communities. Young black women who grow up in impoverished families in urban ghettos face some similar challenges to becoming competent adults who function independently in the wider society. Not all young women who fit this demographic category become young or single mothers who depend on AFDC; some who do also complete levels of education that lead to economic self-sufficiency. In order to explore the question about values and their significance among the urban poor, we examine the life histories of 50 young black women from inner-city Milwaukee, looking in particular at values and behaviors as they relate to educational competence. We analyze the perceived family values about education, the ways in which the young women's families acted on those stated values with the intention of influencing their daughters' educational outcomes, and how these values and transmission processes are related to the young women's educational attainment.

Evidence of a subenergy gap in the overdoped regime of Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7-\delta} thin films from THz Spectroscopy

We measured the terahertz (THz) complex conductivity of Ca doped YBa_{2}Cu_{3}O_{7-\delta} thin films in the frequency range of 0.1 to 3 THz (3 to 100 cm^{-1}) and at a temperature range of 20 to 300 K. The films were measured using both time domain and frequency domain THz methods. We showed evidence for the existence of a sub-gap in overdoped Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7-\delta} samples doped with 5% and 10% Ca. Evidence for the opening of this sub-gap appears as a sharp decrease in the spectrum of the real part of conductivity at frequencies equivalent to a gap energy of 1 meV and is more prominent with increased doping. This decrease in conductivity can be explained by using d-wave pairing symmetry with an imaginary part of is or id_{xy} which suggests node removal.Comment: 7 pages, 7 figure