The quadratic isoperimetric inequality for mapping tori of free group automorphisms II: The general case

If F is a finitely generated free group and \phi is an automorphism of F then the mapping torus of \phi admits a quadratic isoperimetric inequality. This is the third and final paper in a series proving this theorem. The first two were math.GR/0211459 and math.GR/0507589.Comment: 73 page

Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity

We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimiser of the wave energy $\mathcal H$ subject to the constraint $\mathcal I=2\mu$, where $\mathcal I$ is the wave momentum and $0< \mu \ll 1$. Since $\mathcal H$ and $\mathcal I$ are both conserved quantities a standard argument asserts the stability of the set $D_\mu$ of minimisers: solutions starting near $D_\mu$ remain close to $D_\mu$ in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Korteweg-deVries equation (for strong surface tension) or a nonlinear Schr\"{o}dinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as $\mu \downarrow 0$Comment: Corrected version. To appear in Proceedings of the Royal Society of Edinburgh: Section

Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations

We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.Comment: arXiv admin note: text overlap with arXiv:1411.247

A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

Toward a unified PNT, Part 1: Complexity and context: Key challenges of multisensor positioning

The next generation of navigation and positioning systems must provide greater accuracy and reliability in a range of challenging environments to meet the needs of a variety of mission-critical applications. No single navigation technology is robust enough to meet these requirements on its own, so a multisensor solution is required. Known environmental features, such as signs, buildings, terrain height variation, and magnetic anomalies, may or may not be available for positioning. The system could be stationary, carried by a pedestrian, or on any type of land, sea, or air vehicle. Furthermore, for many applications, the environment and host behavior are subject to change. A multi-sensor solution is thus required. The expert knowledge problem is compounded by the fact that different modules in an integrated navigation system are often supplied by different organizations, who may be reluctant to share necessary design information if this is considered to be intellectual property that must be protected

Spiritual Conversations

How can the Keesler Air Force Base Chapel provide spiritual care for airmen who are spiritual but who are not religious? The Department of Defense challenges the chapel to promote the spiritual health of all airmen while the chapel mostly provides religion-based services. The chapel\u27s efforts, therefore, ignore airmen who do not fit into a particular religion. The problem will be addressed by suggesting that the chapel incorporate a spiritual conversations gathering into the existing religion-based services. The chapel needs to embrace spiritual-but-not-religious airmen by offering a spiritual conversations gathering and conducting an annual spirituality survey. The purpose of this dissertation is to provide an understanding of how to respond to postmodern spirituality and to help motivate Christian chaplains to view themselves as missionaries so that they embrace the spiritual-but-not-religious students. Accomplishing a spirituality survey and leading a spiritual conversations gathering are the primary ways to embrace the spiritual-but-not-religious students. Such efforts may uncover new forms of spiritual care that, if implemented, will motivate airmen to turn toward the chapel for their spiritual care. Chapter 1 describes the problem and claim, illustrates the problem with a narrative, and presents contextual factors such as demographics, structure, timelines, and symbols. Chapter 2 desc1ibes the spiritual-but-not-religious student airmen, influenced by postmodern culture. Based on a 2007 student spirituality survey, spiritual-but-not-religious airmen are not interested in chapel participation. Chapter 3 reveals that the chapel\u27s spiritual care efforts are funneled solely through traditional religious programs, ignoring those who are spiritual-but-not-religious. Chapter 4 provides biblical guidance for a spiritual conversations gathering. Chapter 5 briefly outlines a history of the church\u27s adaptation to culture. Chapter 6, the concluding chapter, suggests that a spiritual conversations gathering is a way to adapt to the spiritual-but-not-religious airmen

Fathers of school phobic children

Thesis (M.S.)--Boston Universit

Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

GNSS signals can be blocked and reflected by nearby objects, such as buildings, walls, and vehicles. They can also be reflected by the ground and by water. These effects are the dominant source of GNSS positioning errors in dense urban environments, though they can have an impact almost anywhere. Non- line-of-sight (NLOS) reception occurs when the direct path from the transmitter to the receiver is blocked and signals are received only via a reflected path. Multipath interference occurs, as the name suggests, when a signal is received via multiple paths. This can be via the direct path and one or more reflected paths, or it can be via multiple reflected paths. As their error characteristics are different, NLOS and multipath interference typically require different mitigation techniques, though some techniques are applicable to both. Antenna design and advanced receiver signal processing techniques can substantially reduce multipath errors. Unless an antenna array is used, NLOS reception has to be detected using the receiver's ranging and carrier-power-to-noise-density ratio (C/N0) measurements and mitigated within the positioning algorithm. Some NLOS mitigation techniques can also be used to combat severe multipath interference. Multipath interference, but not NLOS reception, can also be mitigated by comparing or combining code and carrier measurements, comparing ranging and C/N0 measurements from signals on different frequencies, and analyzing the time evolution of the ranging and C/N0 measurements

Environmental Context Detection for Adaptive Navigation using GNSS Measurements from a Smartphone

The signals available for navigation depend on the environment. To operate reliably in a wide range of different environments, a navigation system is required to adopt different techniques based on the environmental contexts. In this paper, an environmental context detection framework is proposed, building the foundation of a context adaptive navigation system. Different land environments are categorized into indoor, urban, and open-sky environments based on how Global Navigation Satellite System (GNSS) positioning performs in these environments. Indoor and outdoor environments are first detected based on the availability and strength of GNSS signals using a hidden Markov model. Then the further classification of outdoor environments into urban and open-sky is investigated. Pseudorange residuals are extracted from raw GNSS measurements in a smartphone and used for classification in a fuzzy inference system alongside the signal strength data. Practical test results under different kinds of environments demonstrate an overall 88.2 percent detection accuracy

An existence theory for three-dimensional periodic travelling gravity-capillary water waves with bounded transverse profiles

An existence theory for three-dimensional periodic travelling gravity-capillary water waves with bounded transverse profile