Remarks on the extension of the Ricci flow

We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.Comment: 9 pages, to appear in Journal of Geometric Analysi

The Ranger 4 Flight Path and Its Determination from Tracking Data

The ranger iv flight path and its determination from tracking dat

Linking Ultracold Polar Molecules

We predict that pairs of polar molecules can be weakly bound together in an ultracold environment, provided that a dc electric field is present. The field that links the molecules together also strongly influences the basic properties of the resulting dimer, such as its binding energy and predissociation lifetime. Because of their long-range character these dimers will be useful in disentangling cold collision dynamics of polar molecules. As an example, we estimate the microwave photoassociation yield for OH-OH cold collisions.Comment: 4 pages 2 figure

Information and Multi-Period Optimal Income Taxation with Government Commitment

The optimal income taxation problem has been extensively studied in one- period models. When consumers work for many periods, this paper analyzes what information, if any, that the government learns about abilities in one period can be used in later periods to attain more redistribution than in a one- period world. liken the government must commit itself to future tax schedules, the gains cane from relaxing self-selection constraints by intertemporal nonstationarity. The effect of nonstationarity is analogous to that of randomization in one-period models. In a model with two ability classes it is shown that the key use of information is that only a single lifetime self-selection constraint for each type of consumer must be imposed. Sane necessary and sufficient conditions for randomization or nonstationarity are given. The planner can make additional use of the information when individual and social rates of time discounting differ. In this case, the limiting tax schedule is a nondistorting one if the government has a lower discount rate than individuals.

SP mountain data analysis

An analysis of synthetic aperture radar data of SP Mountain was undertaken to demonstrate the use of digital image processing techniques to aid in geologic interpretation of SAR data. These data were collected with the ERIM X- and L-band airborne SAR using like- and cross-polarizations. The resulting signal films were used to produce computer compatible tapes, from which four-channel imagery was generated. Slant range-to-ground range and range-azimuth-scale corrections were made in order to facilitate image registration; intensity corrections were also made. Manual interpretation of the imagery showed that L-band represented the geology of the area better than X-band. Several differences between the various images were also noted. Further digital analysis of the corrected data was done for enhancement purposes. This analysis included application of an MSS differencing routine and development of a routine for removal of relief displacement. It was found that accurate registration of the SAR channels is critical to the effectiveness of the differencing routine. Use of the relief displacement algorithm on the SP Mountain data demonstrated the feasibility of the technique

Ringdown frequencies in black holes formed from precessing black-hole binaries

We present a simple formula for the effective ringdown frequencies of the gravitational-wave signal of a precessing black-hole binary in the coprecessing frame. This formula requires only knowledge of the quasi-normal mode frequencies of the system and the value of the precession angle β during ringdown. Such a formula will be useful in modeling precessing systems. We also provide a comprehensive description of the oscillations in the ringdown frequency in an inertial frame where the spin of the final black hole is in the z-direction. These oscillations arise due to the superposition of the prograde and retrograde frequencies. Our understanding of these oscillations can be used to extract the ratio of the amplitudes of the prograde and retrograde frequencies from numerical data. Alternatively, knowledge of this ratio of the amplitudes can be used to produce a simple model of the time-domain oscillations in the ringdown frequency

Study made of explosive cutting in simulated space environments

Study indicates the feasibility of explosive cutting and establishes techniques applicable to in-space cutting operations. Results show no degradation of the explosive and that work hardening of the target material is limited to the cut edge

Local light-ray rotation

We present a sheet structure that rotates the local ray direction through an arbitrary angle around the sheet normal. The sheet structure consists of two parallel Dove-prism sheets, each of which flips one component of the local direction of transmitted light rays. Together, the two sheets rotate transmitted light rays around the sheet normal. We show that the direction under which a point light source is seen is given by a Mobius transform. We illustrate some of the properties with movies calculated by ray-tracing software.Comment: 9 pages, 6 figure

A study of the regional economic development impact of a university led entrepreneurship education programme for small business owners

The health and performance of the small- and medium-sized enterprise (SME) sector is crucial to regional and national economies of most developed countries (Jones, Macpherson and Thorpe, 2010; Thorpe, Cope, Ram and Pedler, 2009). In recognition of this, Higher Education Institutions (HEIs) have been supported through government policy to provide training programmes for SMEs aimed at developing a higher level of skills that will support small business growth (European Commission, 2003; Lambert Review, 2003; Leitch Review of Skills, 2006; DIUS, 2007, 2008; Zhang and Hamilton, 2010). In this paper we explore the relationship between entrepreneurship education and regional development by examining a programme delivered by a higher education institution for growth-oriented small business owners. We concern ourselves with addressing the overarching questions: What is the impact of HEI and SME engagement on entrepreneurship education? And How does HEI/SME engagement impact on a regional economy? To deal with these questions a qualitative approach to the research was adopted to examine the situations of five SME owner/managers over a five year period. Findings show that entrepreneurship education delivered a range of economic benefits to SMEs and the region. Moreover, through engaging owner/managers have the opportunity to interact with others and this supports the growth and development of the business