A 0-stable linear multistep formulas of theα-type

The-type linear multistep formulas are a generalization of the Adams-type formulas. This paper is concerned with completely characterizing theA ₀-stability of thek-step, orderk -type formulas. Specifically, all such formulas of orders 4 or less are identified and it is shown that no-type formulas of order 5 or more exist. These theorems generalize some previous results.     

4-Dimensional black holes from Kaluza-Klein theories

In this paper we consider generalizations in 4 dimensions of the Einstein-Maxwell equations which typically arise from Kaluza-Klein theories. We specify conditions such that stationary solutions lead to non-linear-models for symmetric spaces. Using both this group theoretic structure and some properties of harmonic maps we are able to generalize many of the known existence and uniqueness theorems for black holes in Einstein-Maxwell theory to this more general setting.     

Counting the microstates of a Kerr black hole in M theory

We show that an extremal Kerr black hole, appropriately lifted to M theory, can be transformed to a Kaluza-Klein black hole in M theory, or a D0-D6 charged black hole in string theory. Since all the microstates of the latter have recently been identified, one can exactly reproduce the entropy of an extremal Kerr black hole. We also show that the topology of the event horizon is not well defined in M theory.     

Complementary spectroscopic techniques to model the association of contaminant uranium with structural surfaces

Contaminant uranium poses unique problems for decontamination of former weapons processing and nuclear power facilities, as well as chemical plants, waste storage sites and former mining facilities. In addition, dealing with the possibility of intentional (i.e., a terrorist act) or accidental release of radioactive material in a populated area requires an accurate understanding of the nature of the association of such material with structural surfaces. These surfaces must also be considered in the context of repeated contamination, and the importance of atmospheric exposure, interaction with other possible contaminants, and corrosion or surface degradation due to such exposure must be taken into account. Complementary spectroscopic techniques, especially surface spectroscopies, are essential in developing models for the interaction of contaminants with surfaces and interfaces. In this review (which also presents new data on uranium association with corroding steel surfaces), we collect models of this association as determined by spectroscopic techniques, assess the important considerations in the development of more accurate models, and address some of the questions which remain.     

Spatial phase coding for incoherent optical processors

In this paper we introduce spatial phase coding of incoherent optical signals for representing signed numbers in optical processors and present an experimental demonstration of this coding technique. If a diffraction grating, such as an acousto-optic cell, modulates a stream of light, the image of the grating can be recovered from the diffracted beam. The position of the grating image, or more precisely its phase, can be used to denote the sign of the number represented by the diffracted light. The intensity of the light represents the magnitude of the number. This technique is more economical than current methods in terms of the number of information channels required to represent a number and the amount of post processing required.     

Some fractal properties of the percolating backbone in two dimensions

A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that the fractal dimensionality of the backbone isd _f ^BB =1.61±0.01, the chemical dimensionality isd _t=1.40±0.01, and the fractal dimension of the minimum pathd _min=1.15 ± 0.02 for the two-dimensional triangular lattice.     

A multiple function sonar rangefinder for divers

The rangefinder described here is a self-contained instrument for hand-held operation by a diver for searching, tracking, navigation and surveying applications. It has four modes: 1 — to measure range to a passive target directly to ± 1 m; 2 — to measure range to a passive target indirectly to ± 0.1 m; 3 — to measure range to a coded transponder to either ± 1 m or ± 0.1 m; 4 — to indicate the presence of multiple targets downrange where each target occurs in a selected range interval. The pulse echo principle is employed, with pulses typically 250 μs long. The carrier frequency of 300 kHz can be altered easily if required by changing the transducer array.     

Retrospectively gated cardiac cine imaging with temporal and spatial acceleration

Parallel imaging methods are routinely used to accelerate the image acquisition process in cardiac cine imaging. The addition of a temporal acceleration method, whereby k-space is sampled differently for different time frames, has been shown in prior work to improve image quality as compared to parallel imaging by itself. However, such temporal acceleration strategies prove difficult to combine with retrospectively gated cine imaging. The only currently published method to feature such combination, by Hansen et al. [Magn Reson Med 55 (2006) 85-91] tends to be associated with prohibitively long reconstruction times. The goal of the present work was to develop a retrospectively gated cardiac cine method that features both parallel imaging and temporal acceleration, capable of achieving significant acceleration factors on commonly available hardware and associated with reconstruction times short enough for practical use in a clinical context.Seven cardiac patients and a healthy volunteer were recruited and imaged, with acceleration factors of 3.5 or 4.5, using an eight-channel product cardiac array on a 1.5-T system. The prescribed FOV value proved slightly too small in three patients, and one of the patients had a bigemini condition. Despite these additional challenges, good-quality results were obtained for all slices and all patients, with a reconstruction time of 0.98±0.07 s per frame, or about 20 s for a 20-frame slice, using a single processor on a single PC. As compared to using parallel imaging by itself, the addition of a temporal acceleration strategy provided much resistance to artifacts.