Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established

A strong triangle inequality in hyperbolic geometry

For a triangle in the hyperbolic plane, let $\alpha,\beta,\gamma$ denote the angles opposite the sides $a,b,c$, respectively. Also, let $h$ be the height of the altitude to side $c$. Under the assumption that $\alpha,\beta, \gamma$ can be chosen uniformly in the interval $(0,\pi)$ and it is given that $\alpha+\beta+\gamma c + h$ holds approximately 79\% of the time. To accomplish this, we prove a number of theoretical results to make sure that the probability can be computed to an arbitrary precision, and the error can be bounded

Optimization of payload mass placement in a dual keel space station

In order to keep a Space Station in a stable low-Earth orbit, angular momentum storage and translational attitude control systems will have to be used. In order to minimize the size of these attitude control systems, the induced gravity gradient torque effects will have to be minimized. This can be done by minimizing the cross-products of inertia of the Station through the management of payload placement with the Station geometry. A derived and automated methodology is presented which utilizes mathematical nonlinear programming techniques. An optimal arrangement of a set of five payloads on a Dual Keel Space Station was found that minimized the cross products of inertia and thus the required controllability resources

Using Whole-Group Metabolic Rate and Behaviour to Assess the Energetics of Courtship in Red-Sided Garter Snakes

Reproductive effort is an important aspect of life history as reproductive success is arguably the most important component of fitness. Males tend to compete for access to females and, in the process, expend their energetic capital on mate searching, maleemale competition and courtship rather than directly on offspring. Red-sided garter snakes, Thamnophis sirtalis parietalis, are an exceptional model for studying energetic costs of courtship and mating as they fast during the spring mating season, which segregates the cost of energy acquisition from the cost of courtship and mating. However, measuring an individual male\u27s metabolic rate during courtship is complicated by the fact that male courtship behaviour in redsided garter snakes is dependent on both the detection of a female sexual attractiveness pheromone and on facilitated courtship (i.e. vigorous courtship is only exhibited in the presence of other males). Thus, traditional techniques of placing a mask over the head of individuals would prevent male courtship behaviour, and single animals placed in a flow-through chamber would not yield ecologically realistic levels of courtship, which are only seen in the context of a mating aggregation in this species. Because of these difficulties, we placed groups of males in a flow-through metabolic chamber together with a single female whose respiratory gases were vented outside the chamber to yield a whole-group metabolic rate during competitive courtship. We also measured the standard metabolic rates (SMR) of the males individually for comparison with active metabolic rates. Conservative estimates of peak group metabolic rates during courtship are 10e20 times higher than resting group metabolic rate, which was 1.88 times higher than SMR. These measurements, coupled with the fact that these males are aphagous during the breeding, indicates that costs of courtship may be high for males and has implications for the male mating tactics in this system

Stability of the interface of an isotropic active fluid

We study the linear stability of an isotropic active fluid in three different geometries: a film of active fluid on a rigid substrate, a cylindrical thread of fluid, and a spherical fluid droplet. The active fluid is modeled by the hydrodynamic theory of an active nematic liquid crystal in the isotropic phase. In each geometry, we calculate the growth rate of sinusoidal modes of deformation of the interface. There are two distinct branches of growth rates; at long wavelength, one corresponds to the deformation of the interface, and one corresponds to the evolution of the liquid crystalline degrees of freedom. The passive cases of the film and the spherical droplet are always stable. For these geometries, a sufficiently large activity leads to instability. Activity also leads to propagating damped or growing modes. The passive cylindrical thread is unstable for perturbations with wavelength longer than the circumference. A sufficiently large activity can make any wavelength unstable, and again leads to propagating damped or growing modes.Comment: 12 pages, 12 figure