Tracking nonperiodic trajectories with the overtaking criterion

A tracking problem on an infinite time interval is studied, where the plant is linear with quadratic cost, and the tracked trajectory is not necessarily period. Optimal solutions with respect to the overtaking criterion are studied. Existence and uniqueness of such optimal solutions are proved and they are shown to be given by a linear feedback law which is the same as in the periodic case. A close relation between the solutions of tracking problems where the tracked trajectories are different only for very large times is established.     

An analysis of SEM techniques used to profile chemical etching on the semiconductor Hg1-xCdxTe

Various methods have been used to obtain accurate cross-sectional profiles of Hg_1-xCd_xTe devices after etching. Preliminary measurements from different etching techniques are also presented. Techniques used were scanning electron microscopy with stereo pairs and cleaved cross-sections, topography SEM (multiple detector SEM) and atomic force microscopy.     

The Nevo–Zimmer intermediate factor theorem over local fields

The Nevo–Zimmer theorem classifies the possible intermediate G-factors Y in Open image in new window , where G is a higher rank semisimple Lie group, P a minimal parabolic and X an irreducible G-space with an invariant probability measure. An important corollary is the Stuck–Zimmer theorem, which states that a faithful irreducible action of a higher rank Kazhdan semisimple Lie group with an invariant probability measure is either transitive or free, up to a null set. We present a different proof of the first theorem, that allows us to extend these two well-known theorems to linear groups over arbitrary local fields.     

High-resolution non-invasive 3D imaging of paint microstructure by synchrotron-based X-ray laminography

The characterisation of the microstructure and micromechanical behaviour of paint is key to a range of problems related to the conservation or technical art history of paintings. Synchrotron-based X-ray laminography is demonstrated in this paper to image the local sub-surface microstructure in paintings in a non-invasive and non-destructive way. Based on absorption and phase contrast, the method can provide high-resolution 3D maps of the paint stratigraphy, including the substrate, and visualise small features, such as pigment particles, voids, cracks, wood cells, canvas fibres etc. Reconstructions may be indicative of local density or chemical composition due to increased attenuation of X-rays by elements of higher atomic number. The paint layers and their interfaces can be distinguished via variations in morphology or composition. Results of feasibility tests on a painting mockup (oak panel, chalk ground, vermilion and lead white paint) are shown, where lateral and depth resolution of up to a few micrometres is demonstrated. The method is well adapted to study the temporal evolution of the stratigraphy in test specimens and offers an alternative to destructive sampling of original works of art.     

Q-switching an all-fiber laser using acousto-optic null coupler

A new method for Q-switching an all-fiber laser is presented. It is based on induced acoustic long period grating operating on a null coupler, which acts as acoustically controlled tunable output coupler. Q-switching is achieved by switching on and off the acoustic wave in a burst mode, thereby generating laser pulses that are ~400 times shorter than the acoustically controlled coupler’s rise time. Output pulse energy of 22 μJ and temporal width of ~100 ns were measured at a wavelength of 1.54 μm.     

Spacer length dependence of TGBC* and SmA phases in cholesteryl and dihydrocholesteryl-containing trimer liquid crystals

Two series of trimer liquid crystals were investigated that contain a biphenylyl central group and two cholesteryl or dihydrocholesteryl terminal mesogenic groups. Only compounds with even spacers were investigated. The dihydrocholesteryl-containing trimers show a triply intercalated smectic A (SmA) phase when the spacer lengths are greater than 8, whereas the cholesteryl-containing trimers exhibit this triply intercalated SmA phase when the spacer lengths are more than 6. With shorter spacers, a twist grain boundary C* (TGBC*) phase was found. This is revealed by the formation of a typical dotted square grid pattern upon cooling from the chiral nematic (N*) phase in the planar texture. The dots are spaced by a distance of about 1.5-1.8 µm. Upon cooling from the N* phase in the focal conic texture a striped pattern is observed with the same spacing. X-ray diffraction revealed a repeat distance for the TGBC* phase that corresponds with a monolayer ordering. The results show that the weaker interaction between the dihydrocholesteryl groups compared with cholesteryl groups or longer spacers destabilize the monolayer TGBC* phase.     

Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality

The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NP-complete, even when all variables are binary. This paper deals with integer linear minimization problems inn variables subject tom linear constraints with at most two variables per inequality, and with all variables bounded between 0 andU. For such systems, a 2-approximation algorithm is presented that runs in time O(mnU ² log(Un ² m)), so it is polynomial in the input size if the upper boundU is polynomially bounded. The algorithm works by finding first a super-optimal feasible solution that consists of integer multiples of 1/2. That solution gives a tight bound on the value of the minimum. It furthermore has an identifiable subset of integer components that retain their value in an integer optimal solution of the problem. These properties are a generalization of the properties of the vertex cover problem. The algorithm described is, in particular, a 2-approximation algorithm for the problem of minimizing the total weight of true variables, among all truth assignments to the 2-satisfiability problem.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.Research supported in part by ONR contracts N00014-88-K-0377 and N00014-91-J-1241.Research supported in part by ONR contract N00014-91-C-0026.Part of this work was done while the author was visiting the International Computer Science Institute in Berkeley, CA and DIMACS, Rutgers University, New Brunswick, NJ.