Counting Conjugacy Classes in Out(FN)Out(F_N)

We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $N\ge 3$ the number of distinct $Out(F_N)$-conjugacy classes of fully irreducibles $\phi$ from an $R$-ball in the Cayley graph of $Out(F_N)$ with $\log\lambda(\phi)$ on the order of $R$ grows exponentially in $R$

The interaction of spherical colloidal particles with a planar surface

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Anxiety reduction via brief intervention in dentally anxious patients : a randomized controlled trial

Aim: To compare the degree of anxiety reduction in dentally anxious patients attending a Dental Access Centre where the dentist did or did not receive the patients’ assessment of dental anxiety. Methods: Patients attending two Dental Access Centres in England, completed the Modified Dental Anxiety Scale (MDAS). Those that scored high completed a state anxiety questionnaire (STAI-S) and were randomized into three groups (n=182) to test the hypothesis that patients sharing assessment information about their dental anxiety to members of the dental team has beneficial effects on their state anxiety. Group 1 were controls (n=60), Group 2 gave their MDAS to the receptionist who passed it onto the dentist unknown to the patient (n=62) and Group 3 handed their MDAS to the dentist (n=60). After their appointment they repeated the STAI-S. Results and conclusion: Patients in Group 3 were less anxious (by more than STAI-S 3 scale units) on leaving the surgery than those from the other groups especially if they entered into a discussion with the dentist about their concerns (by more than 5 scale units). Brief assessment of dental anxiety shared by the patient with the dentist collaboratively has the potential to reduce anxiety on completion of the appointment. Dental anxiety is common, has a multifactorial aetiology, and is far from being homogenous, as individuals seem to differ in the origins, age of onset and manifestations of their dental fears (Locker et al., 2001b); (Milgrom et al., 1988). Previous negative experiences are a major factor in the development of dental anxiety (Kleinknect et al., 1973); (Bernstein et al., 1979); (de Jongh et al., 1995); (Locker et al., 1999); (Ost and Hugdahl, 1985). For some individuals, their fear of dentistry may be associated with concurrent anxiety disorders, or more general psychopathology (Locker, 2003); (Locker et al., 2001a).PreprintPeer reviewe

D-branes and the Noncommutative Torus

We show that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world-volume theories. This gives strong evidence that they are well-defined quantum theories. It also gives a physical derivation of the identification proposed by Connes, Douglas and Schwarz of Matrix theory compactification on the noncommutative torus with M theory compactification with constant background three-form tensor field.Comment: harvmac, 5 pp. Minor error fixe

A Cartan-Hadamard type result for relatively hyperbolic groups

In this article, we prove that if a finitely presented group has an asymptotic cone which is tree-graded with respect to a precise set of pieces then it is relatively hyperbolic. This answers a question of M. Sapir.Comment: 33 pages, 2 figure

Neighboring suboptimal control for vehicle guidance

The neighboring optimal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied (neighboring suboptimal control). This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. Neighboring suboptimal control is applied to the lunar launch problem. Two approaches, single optimization and multiple optimization for calculating the gains are used, and the gains are tested in a guidance simulation with a mismatch in the acceleration of gravity. Both approaches give acceptable results, but multiple optimization keeps the perturbed path closer to the nominal path