Phase operators, phase states and vector phase states for SU(3) and SU(2,1)

This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and infinite-dimensional representations of A(k,2) are constructed for k < 0 and k > 0 or = 0, respectively. Phase operators associated with A(k,2) are defined and temporally stable phase states (as well as vector phase states) are constructed as eigenstates of these operators. Finally, we discuss a relation between quantized phase states and a quadratic discrete Fourier transform and show how to use these states for constructing mutually unbiased bases

Sterilization of liquids by filtration and certification of probability

Sterilization of liquids by hydrosol filtratio

A transport properties of a moderately dense lennard-jones gas

First and second order density corrections to transport coefficients of moderately dense ga

Wiener Reconstruction of Large-Scale Structure from Peculiar Velocities

We present an alternative, Bayesian method for large-scale reconstruction from observed peculiar velocity data. The method stresses a rigorous treatment of the random errors and it allows extrapolation into poorly sampled regions in real space or in k-space. A likelihood analysis is used to determine the fluctuation power spectrum, followed by a Wiener Filter (WF) analysis to obtain the minimum-variance mean fields of velocity and mass density. Constrained Realizations (CR) are then used to sample the statistical scatter about the WF mean field. The WF/CR method is applied as a demonstration to the Mark III data with 1200 km/s, 900 km/s, and 500 km/s resolutions. The main reconstructed structures are consistent with those extracted by the POTENT method. A comparison with the structures in the distribution of IRAS 1.2Jy galaxies yields a general agreement. The reconstructed velocity field is decomposed into its divergent and tidal components relative to a cube of +/-8000 km/s centered on the Local Group. The divergent component is very similar to the velocity field predicted from the distribution of IRAS galaxies. The tidal component is dominated by a bulk flow of 194 +/- 32 km/s towards the general direction of the Shapley concentration, and it also indicates a significant quadrupole.Comment: 28 pages and 8 GIF figures, Latex (aasms4.sty), submitted to ApJ. Postscript version of the figures can be obtained by anonymous ftp from: ftp://alf.huji.ac.il/pub/saleem

3D freeform surfaces from planar sketches using neural networks

A novel intelligent approach into 3D freeform surface reconstruction from planar sketches is proposed. A multilayer perceptron (MLP) neural network is employed to induce 3D freeform surfaces from planar freehand curves. Planar curves were used to represent the boundaries of a freeform surface patch. The curves were varied iteratively and sampled to produce training data to train and test the neural network. The obtained results demonstrate that the network successfully learned the inverse-projection map and correctly inferred the respective surfaces from fresh curves

On the Complexity of Local Search for Weighted Standard Set Problems

In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in Johnson et al., [JPY88]. We show that for most of these problems, computing a locally optimal solution is already PLS-complete for a simple neighborhood of size one. For the local search versions of weighted SetPacking and SetCover, we derive tight bounds for a simple neighborhood of size two. To the best of our knowledge, these are one of the very few PLS results about local search for weighted standard set problems

The measurements of vehicle glow on the Space Shuttle

From the combined data set of glow observations on STS-3, STS-4 and STS-5 some of the properties of the shuttle glow were observed. Comparison of the STS-3 (240 km) and STS-5 (305 km) photographs show that the intensity of the glow is about a factor of 3.5 brighter on the low altitude (STS-3) flight. The orbiter was purposely rotated about the x axis in an experiment on STS-5 to observe the dependence of the intensity on the angle of incidence between the spacecraft surface normal and the velocity vector. For a relatively large angle between the velocity vector and the surface normal there is an appreciable glow, provided the surface is not shadowed by some other spacecraft structure. As the angle becomes less the glow intensifies. The grating experiments (STS-4 photography only, STS-5 image intensifier photography) provided a preliminary low resolution spectra of the spacecraft glow. Accurate wavelength calibrations of the STS-5 instrument permitted measuring of the spectrum and intensity of the Earth's airglow

Renormalization of Multiple qq-Zeta Values

In this paper we shall define the renormalization of the multiple $q$-zeta values (M$q$ZV) which are special values of multiple $q$-zeta functions $\zeta_q(s_1,...,s_d)$ when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (math.NT/0606076v3) on the renormalization of Euler-Zagier multiple zeta values. We show that our renormalization process produces the same values if the M$q$ZVs are well-defined originally and that these renormalizations of M$q$ZV satisfy the $q$-stuffle relations if we use shifted-renormalizations for all divergent $\zeta_q(s_1,...,s_d)$ (i.e., $s_1\le 1$). Moreover, when \qup our renormalizations agree with those of Guo and Zhang.Comment: 22 pages. This is a substantial revision of the first version. I provide a new and complete proof of the fact that our renormalizations satisfy the q-stuffle relations using the shifting principle of MqZV