Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

A class of compact dwarf galaxies from disruptive processes in galaxy clusters

Dwarf galaxies have attracted increased attention in recent years, because of their susceptibility to galaxy transformation processes within rich galaxy clusters. Direct evidence for these processes, however, has been difficult to obtain, with a small number of diffuse light trails and intra-cluster stars, being the only signs of galaxy disruption. Furthermore, our current knowledge of dwarf galaxy populations may be very incomplete, because traditional galaxy surveys are insensitive to extremely diffuse or compact galaxies. Aware of these concerns, we recently undertook an all-object survey of the Fornax galaxy cluster. This revealed a new population of compact members, overlooked in previous conventional surveys. Here we demonstrate that these 'ultra-compact' dwarf galaxies are structurally and dynamically distinct from both globular star clusters and known types of dwarf galaxy, and thus represent a new class of dwarf galaxy. Our data are consistent with the interpretation that these are the remnant nuclei of disrupted dwarf galaxies, making them an easily observed tracer of galaxy disruption.

Compact tiled display with uniform illumination

The demand for more pixels is beginning to be met as manufacturers increase the native resolution of projector chips. Tiling several projectors still offers a solution to augment the pixel capacity of a display. However, problems of color and illumination uniformity across projectors need to be addressed as well as the computer software required to drive such devices. We present the results obtained on a desktop-size tiled projector array of three D-ILA projectors sharing a common illumination source. A short throw lens (0.8:1) on each projector yields a 21-in. diagonal for each image tile; the composite image on a 3×1 array is 3840×1024 pixels with a resolution of about 80 dpi. The system preserves desktop resolution, is compact, and can fit in a normal room or laboratory. The projectors are mounted on precision six-axis positioners, which allow pixel level alignment. A fiber optic beamsplitting system and a single set of red, green, and blue dichroic filters are the key to color and illumination uniformity. The D-ILA chips inside each projector can be adjusted separately to set or change characteristics such as contrast, brightness, or gamma curves. The projectors were then matched carefully: photometric variations were corrected, leading to a seamless image. Photometric measurements were performed to characterize the display and are reported here. This system is driven by a small PC cluster fitted with graphics cards and running Linux. It can be scaled to accommodate an array of 2×3 or 3×3 projectors, thus increasing the number of pixels of the final image. Finally, we present current uses of the display in fields such as astrophysics and archaeology (remote sensing).

A compact superconducting magnet for magnetic resonance microscopy

Magnetic resonance microscopy (MRM) depends on the use of high field, superconducting magnet systems for its operation. The magnets that are conventionally used are those that were initially designed for chemical structural analysis work. A novel, compact magnet designed specifically for MRM is presented here, and while preserving high field, high homogeneity conditions, has a length less than one-third that of conventional systems. This enables much better access to samples, an important consideration in many MRM experiments. As the homogeneity of a magnet is strongly dependent on its length, novel geometries and optimization techniques are required to meet the requirements of MRM in a compact system. An important outcome of the stochastic optimization performed in this work, is that the use used of a thin superconducting solenoid surrounded by counterwound disk windings provides a mechanism for drastic length reductions over conventional magnet designs. (C) 1998 American Institute of Physics.

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

The fornax spectroscopic survey: the number of unresolved compact galaxies

We describe a sample of 13 bright (18.5 < B-J < 20.1), compact galaxies at low redshift (0.05 < z < 0.21) behind the Fornax Cluster. These galaxies are unresolved on UK Schmidt sky survey plates, and so they would be missing from most galaxy catalogs compiled from this material. The objects were found during initial observations of The Fornax Spectroscopic Survey. This project is using the Two-degree Field spectrograph on the Anglo-Australian Telescope to obtain spectra for a complete sample of all 14,000 objects, stellar and nonstellar, with 16.5 < B-J < 19.7, in a 12 deg(2) area centered on the Fornax Cluster of galaxies. The surface density of compact galaxies with magnitudes 16.5 < B-J < 19.7 is 7 +/- 3 deg(-2), representing 2.8% +/- 1.6% of all local (z < 0.2) galaxies to this limit. There are 12 +/- 3 deg(-2) with 16.5 < B-J < 20.2. They are luminous (-21.5 < M-B < -18.0, for H-o = 50 km s(-1) Mpc(-1)), and most have strong emission lines (H alpha equivalent widths of 40-200 Angstrom) and small sizes typical of luminous H II galaxies and compact narrow emission line galaxies. Four out of 13 have red colors and early-type spectra, and so they are unlikely to have been detected in any previous surveys.

Designs for an asymmetric gradient set and a compact superconducting magnet for neural magnetic resonance imaging

Imaging of the head and neck is the most commonly performed clinical magnetic resonance imaging (MRI) examination [R. G. Evans and J. R. G. Evans, AJR 157, 603 (1991)]. This is usually undertaken in a generalist MRI instrument containing superconducting magnet system capable of imaging all organs. These generalist instruments are large, typically having a bore of 0.9-1.0 m and a length of 1.7-2.5 m and therefore are expensive to site, somewhat claustrophobic to the patient, and offer little access by attending physicians. In this article, we present the design of a compact, superconducting MRI magnet for head and neck imaging that is less than 0.8 m in length and discuss in detail the design of an asymmetric gradient coil set, tailored to the magnet profile. In particular, the introduction of a radio-frequency FM modulation scheme in concert with a gradient sequence allows the epoch of the linear region of the gradient set to be much closer to the end of the gradient structure than was previously possible. Images from a prototype gradient set demonstrate the effectiveness of the designs. (C) 1999 American Institute of Physics. [S0034-6748(99)04910-2].

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Risk management for scuba diving operators on Australia's Great Barrier Reef

Australia's Great Barrier Reef is one of the world's most popular scuba diving destinations. Unfortunately, a series of recent diving injuries and deaths has tarnished the region's safety record. In particular, media attention surrounding the disappearance of American divers Thomas and Eileen Lonergan has focused attention on dive operators' legal responsibilities and the consequences of failing to discharge their duty of care to customers. This paper briefly examines the relevant Australian law for recreational diving operations, and reviews risk management strategies that may reduce or prevent the occurrence of future problems. (C) 2000 Elsevier Science Ltd. All rights reserved.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

Compact stellar systems in the Fornax Cluster: Super-massive star clusters or extremely compact dwarf galaxies?

We describe a population of compact objects in the centre of the Fornax Cluster which were discovered as part of our 2dF Fornax Spectroscopic Survey. These objects have spectra typical of old stellar systems, but are unresolved on photographic sky survey plates. They have absolute magnitudes - 13 < M-B