Automatic structures for subsemigroups of Baumslag–Solitar semigroups

This paper studies automatic structures for subsemigroups of Baumslag–Solitar semigroups (that is, semigroups presented by 〈x,y∣(yx ^m ,x ⁿ y)〉 where $m,n \in\mathbb {N}$ ). A geometric argument (a rarity in the field of automatic semigroups) is used to show that if m>n, all of the finitely generated subsemigroups of this semigroup are (right-) automatic. If m<n, all of its finitely generated subsemigroups are left-automatic. If m=n, there exist finitely generated subsemigroups that are not automatic. An appendix discusses the implications of these results for the theory of Malcev presentations. (A Malcev presentation is a special type of presentation for semigroups embeddable into groups.)     

Green index in semigroups: generators, presentations, and automatic structures

The Green index of a subsemigroup T of a semigroup S is given by counting strong orbits in the complement S?T under the natural actions of T on S via right and left multiplication. This partitions the complement S?T into T-relative -classes, in the sense of Wallace, and with each such class there is a naturally associated group called the relative Schützenberger group. If the Rees index |S?T| is finite, T also has finite Green index in S. If S is a group and T a subgroup then T has finite Green index in S if and only if it has finite group index in S. Thus Green index provides a common generalisation of Rees index and group index. We prove a rewriting theorem which shows how generating sets for S may be used to obtain generating sets for T and the Schützenberger groups, and vice versa. We also give a method for constructing a presentation for S from presentations of T and the Schützenberger groups. These results are then used to show that several important properties are preserved when passing to finite Green index subsemigroups or extensions, including: finite generation, solubility of the word problem, growth type, automaticity (for subsemigroups), finite presentability (for extensions) and finite Malcev presentability (in the case of group-embeddable semigroups).     

Inside the D-stable matrices

Let $\text{DS}{}_{\mathrm{n}}\text{(}\text{F}\text{)}$ denote the set of n×nD-stable matrices with entries from $\text{F}\text{?}\text{C}$. A characterization of the interior of $\text{DS}{}_{\mathrm{n}}\text{(}\text{F}\text{)}$ considered as subset of the topological space $\text{F}$ⁿ², is given for the cases $\text{F}\text{=}\text{R}\text{and}\text{C}$.     

Enhanced material classification using turbulence-degraded polarimetric imagery

An enhanced material-classification algorithm using turbulence-degraded polarimetric imagery is presented. The proposed technique improves upon an existing dielectric/metal material-classification algorithm by providing a more detailed object classification. This is accomplished by redesigning the degree-of-linear-polarization priors in the blind-deconvolution algorithm to include two subclasses of metals--an aluminum group classification (includes aluminum, copper, gold, and silver) and an iron group classification (includes iron, titanium, nickel, and chromium). This new classification provides functional information about the object that is not provided by existing dielectric/metal material classifiers. A discussion of the design of these new degree-of-linear-polarization priors is provided. Experimental results of two painted metal samples are also provided to verify the algorithm's accuracy.     

Cavitation clouds created by shock scattering from bubbles during histotripsy

Histotripsy is a therapy that focuses short-duration, high-amplitude pulses of ultrasound to incite a localized cavitation cloud that mechanically breaks down tissue. To investigate the mechanism of cloud formation, high-speed photography was used to observe clouds generated during single histotripsy pulses. Pulses of 5-20 cycles duration were applied to a transparent tissue phantom by a 1-MHz spherically focused transducer. Clouds initiated from single cavitation bubbles that formed during the initial cycles of the pulse, and grew along the acoustic axis opposite the propagation direction. Based on these observations, we hypothesized that clouds form as a result of large negative pressure generated by the backscattering of shockwaves from a single bubble. The positive-pressure phase of the wave inverts upon scattering and superimposes on the incident negative-pressure phase to create this negative pressure and cavitation. The process repeats with each cycle of the incident wave, and the bubble cloud elongates toward the transducer. Finite-amplitude propagation distorts the incident wave such that the peak-positive pressure is much greater than the peak-negative pressure, which exaggerates the effect. The hypothesis was tested with two modified incident waves that maintained negative pressure but reduced the positive pressure amplitude. These waves suppressed cloud formation which supported the hypothesis.     

The quality improvement process in telecommunications

Describes the quality improvement process recommended by Bellcore, and discusses the methodology developed for its implementation. The process is based on five principles: quality is conformance to valid requirements; the provider is responsible for quality and must demonstrate conformance; the way to achieve quality is prevention rather than inspection; the performance standard is defect-free work; and a major measurement of quality improvement is a reduction in the cost of quality. Steps for implementing quality are outlined. The cost of quality and its analysis are discussed. The application of the basic principles to the operation of network elements, the systems that provide services, the logistic systems, and administrative or white collar processes is examined, and the role of quality improvement is discussed for each of them     

The Charge-Energy-Mass Spectrometer for 0.3-300 keV/e Ions on the AMPTE CCE

The CHEM spectrometer on the CCE spacecraft is designed to measure the mass and charge-state compositions as well as the energy spectra and pitch-angle distributions of all major ions from H through Fe with energies from 0.3 to 300 keV/charge and a time resolution of less than 1 min in the Earth's magnetosphere and magnetosheath. It has the sensitivity and resolution to detect artificially injected Li ions. Complementing the hot-plasma composition experiment and the medium-energy particle analyzer, this experiment will provide essential information on outstanding problems related to dynamical processes of space plasmas and of suprathermal ions. The instrument uses a combination of electrostatic deflection, post acceleration, and time of flight versus energy measurements to determine the ionization state Q, mass M, and energy E of the ambient-ion population. Pitch angle and anisotropy measurements are made utilizing the spinning motion of the CCE spacecraft. Isotopes of hydrogen and helium are resolved as are individual elements up to neon and dominant elements up to iron. Because of the intrinsically low instrument background achieved by using fast coincidence techniques combined with electrostatic deflection, the instrument has a large dynamic range and can identify rare elements and ions even in the presence of high-intensity radiation background. To increase significantly the information returned from the experiment within the allocated telemetry, an intelligent on-board data system which is part of the CHEM instrument performs fast M versus M/Q classifications.     

The spinning Astrid-2 satellite used for modeling the Earth's mainmagnetic field

The Swedish micro-satellite Astrid-2 was successfully launched into a near polar orbit in December 1998. Despite the fact that the primary science mission was auroral research, the magnetic instrument was designed to accomplish high-resolution and high-precision vector field magnetic measurements, and therefore mapping of the Earth's magnetic field was possible. The spacecraft spins about a highly stable axis in space. This fact and the globally distributed data make the magnetic measurements well suited for the estimate of a magnetic field model at the spacecraft altitude (about 1000 km). This paper describes the initial analysis of the Astrid-2 magnetic data. As a result of the study of a single day (February 7, 1999), magnetically fairly quiet, it was possible to in-flight adjust the calibration of the magnetometer and find a magnetic field model fitting the scalar component of the measurements to better than 5 nT_rms for latitudes equatorward of 50°. Several methods for field modeling are discussed in this paper under the assumption that the direction of the spin axis in inertial space is nearly constant, and this assumption is corroborated by the observations. The approximate inertial orientation of the magnetometer could then be determined simultaneously with the instrument intrinsic calibration and the estimate of main field model coefficients