Counting commensurability classes of hyperbolic manifolds

Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about v ^v such manifolds of volume at most v, considered up to commensurability. Since the number of arithmetic ones tends to be polynomial, almost all hyperbolic manifolds are non-arithmetic in an appropriate sense. Moreover, by restricting attention to non-compact manifolds, our result implies the same growth type for the number of quasi-isometry classes of lattices in SO(n, 1). Our method involves a geometric graph-of-spaces construction that relies on arithmetic properties of certain quadratic forms.     

Modeling the power of an optical parametric generator by discrete mode summation

An analytical expression for calculating the signal output power of an optical parametric generator (OPG) configuration was developed. The model is based on Heisenberg equations in space and radiation mode theory. A simple analytical expression can be obtained by assuming that all modes within the gain bandwidth of the nonlinear crystal have the same gain and the same interaction length. Another derivation considers the gain and interaction length of each individual mode. The model predictions are in excellent agreement with the measured signal power of OPGs based on 25- and 35-mm periodically poled LiNbO₃ crystal (with effective quadratic nonlinearity of ∼14.5 pm/V) and 47-mm periodically poled LiTaO₃ crystal (with effective quadratic nonlinearity of ∼9 pm/V). In addition, a comparison was made between the summation over discrete modes approach and the traditional approach of continuous integration over the beam parameters and pump frequency. We have found that the first approach, which is developed in this paper, predicts more accurately the output power of the OPG.     

Optimal service control against worst case admission policies: A multichained stochastic game

In this paper we will consider two-person zero-sum games and derive a general approach for solving them. We apply this approach to a queueing problem. In section 1 we will introduce the model and formulate the Key-theorem. In section 2 we develop the theory that we will use in section 3 to prove the Key-theorem. This includes a general and useful result in Lemma 2.1 on the sufficiency of stationary policies.     

Characterization of optical and nonlinear properties of periodically-poled RbTiOAsO4 in the mid-infrared range via difference-frequency generation

Tunable mid-infrared coherent radiation (3.25- 3.7 μm) is generated by quasi-phase-matched difference frequency generation in a multi-grating periodically-poled RbTiOAsO₄ crystal. The spontaneous polarization and coercive field of flux-grown RbTiOAsO₄ are determined by polarization switching measurements. The nonlinear interaction enables us to explore the optical and nonlinear properties of this material in the mid-infrared range, where data is scarce. The measurements are used to derive a mid- infrared corrected dispersion equation for n_z in RbTiOAsO₄. This equation is in excellent agreement with previously published measurements of nonlinear interactions in periodically-poled RbTiOAsO₄. The measured wavelength and temperature bandwidths are ≈48 nm cm and ≈29 °C cm, respectively. A relatively high temperature tuning slope of the phase-matched idler wavelength, -1.27 nm/°C, is measured. This may be useful for realizing temperature-tuned nonlinear devices. Received: 30 March 2000 / Revised version: 9 May 2000 / Published online: 30 June 2000     

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.