The Spatial Correlation of Bent-Tail Galaxies and Galaxy Clusters

We have completed a deep radio continuum survey covering 86 square degrees of the Spitzer-South Pole Telescope deep field to test whether bent-tail galaxies are associated with galaxy clusters. We present a new catalogue of 22 bent-tail galaxies and a further 24 candidate bent-tail galaxies. Surprisingly, of the 8 bent-tail galaxies with photometric redshifts, only two are associated with known clusters. While the absence of bent-tail sources in known clusters may be explained by effects such as sensitivity, the absence of known clusters associated with most bent-tail galaxies casts doubt upon current models of bent-tail galaxies.Comment: Accepted by MNRA

Tails of probability density for sums of random independent variables

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are distributed according to the Gauss Law. In all other cases the tail for $p_{_N}(x)$ differs from the Gaussian. If the variances of random terms diverge the non-Gaussian tail is related to a Levy distribution for $p_{_N}(x)$. However, the tail is not Gaussian even if the variances are finite. In the latter case $p_{_N}(x)$ has two different asymptotics. At small and moderate values of $x$ the distribution is Gaussian. At large $x$ the non-Gaussian tail arises. The crossover between the two asymptotics occurs at $x$ proportional to $N$. For this reason the non-Gaussian tail exists at finite $N$ only. In the limit $N$ tends to infinity the origin of the tail is shifted to infinity, i. e., the tail vanishes. Depending on the particular type of the distribution of the random terms the non-Gaussian tail may decay either slower than the Gaussian, or faster than it. A number of particular examples is discussed in detail.Comment: 6 pages, 4 figure

Variable-speed tail rotors for helicopters with variable-speed main rotors

Variable tail rotor speed is investigated as a method for reducing tail rotor power, and improving helicopter performance. A helicopter model able to predict the main rotor and tail rotor powers is presented, and the flight test data of the UH-60A helicopter is used for validation. The predictions of the main and tail rotor powers are generally in good agreement with flight tests, which justifies the use of the present method in analyzing main and tail rotors. Reducing the main rotor speed can result in lower main rotor power at certain flight conditions. However, it increases the main rotor torque and the corresponding required tail rotor thrust to trim, which then decreases the yaw control margin of the tail rotor. In hover, the tail rotor may not be able to provide enough thrust to counter the main rotor torque, if it is slowed to follow the main rotor speed. The main rotor speed corresponding to the minimum main rotor power increases, if the change of tail rotor power in hover is considered. As a helicopter translated to cruise, the induced power decreases, and the profile power increases, with the profile power dominating the tail rotor. Reducing the tail rotor speed in cruise reduces the profile power to give a 37% reduction in total tail rotor power and a 1.4% reduction to total helicopter power. In high speed flight, varying the tail rotor speed is ineffective for power reduction. The power reduction obtained by the variable tail rotor speed is reduced for increased helicopter weight

Intermediate Tail Dependence: A Review and Some New Results

The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on intermediate tail dependence, and then we report new results to supplement the review. Intermediate tail dependence for elliptical, extreme value and Archimedean copulas are reviewed and further studied, respectively. For Archimedean copulas, we not only consider the frailty model but also the recently studied scale mixture model; for the latter, conditions leading to upper intermediate tail dependence are presented, and it provides a useful way to simulate copulas with desirable intermediate tail dependence structures.Comment: 25 pages, 1 figur

On Weak Tail Domination of Random Vectors

Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular weak tail domination implies strong tail domination. In particular positive answer to Oleszkiewicz question would follow from the so-called Bernoulli conjecture.Comment: 6 page