Gravitational Lensing and Anisotropies of CBR on the Small Angular Scales

We investigate the effect of gravitational lensing, produced by linear density perturbations, for anisotropies of the Cosmic Background Radiation (CBR) on scales of arcminutes. In calculations, a flat universe ($\Omega=1$) and the Harrison-Zel'dovich spectrum ($n=1$) are assumed. The numerical results show that on scales of a few arcminutes, gravitational lensing produces only negligible anisotropies in the temperature of the CBR. Our conclusion disagrees with that of Cay\'{o}n {\it et al.} who argue that the amplification of $\Delta T/T$ on scales $\le 3'$ may even be larger than 100\%.Comment: Accepted by MNRAS. 16 pages, 2 figures, tarred, compressed and uuencoded Postscript file

Rotor-to-stator rub vibration in centrifugal compressor

One example of excessive vibration encountered during loading of a centrifugal compressor train (H type compressor with HP casing) is discussed. An investigation was made of the effects of the dynamic load on the bearing stiffness and the rotor-bearing system critical speed. The high vibration occurred at a "threshold load," but the machine didn't run smoothly due to rubs even when it had passed through the threshold load. The acquisition and discussion of the data taken in the field as well as a description of the case history which utilizes background information to identify the malfunction conditions is presented. The analysis shows that the failures, including full reverse precession rub and exact one half subharmonic vibration, were caused by the oversize bearings and displacement of the rotor center due to foundation deformation and misalignment between gear shafts, etc. The corrective actions taken to alleviate excessive vibration and the problems which remain to be solved are also presented

On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Semiclassical quantization with bifurcating orbits

Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra involving uniform approximations. As a prototype example, the method is shown to yield excellent results for photo-absorption spectra for the hydrogen atom in an electric field in a spectral range where the abundance of bifurcations would render the standard closed-orbit formula without uniform approximations useless. Our method immediately applies to semiclassical trace formulae as well as closed-orbit theory and offers a general technique for the semiclassical quantization of arbitrary systems

Random attractors for stochastic evolution equations driven by fractional Brownian motion

The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with $H\in (1/2,1)$. We would like to emphasize that we do not use the usual cohomology method, consisting of transforming the stochastic equation into a random one, but we deal directly with the stochastic equation. In particular, in order to get adequate a priori estimates of the solution needed for the existence of an absorbing ball, we will introduce stopping times to control the size of the noise. In a first part of this article we shall obtain the existence of a pullback attractor for the non-autonomous dynamical system generated by the pathwise mild solution of an nonlinear infinite-dimensional evolution equation with non--trivial H\"older continuous driving function. In a second part, we shall consider the random setup: stochastic equations having as driving process a fractional Brownian motion with $H\in (1/2,1)$. Under a smallness condition for that noise we will show the existence and uniqueness of a random attractor for the stochastic evolution equation

Simple scheme for two-qubit Grover search in cavity QED

Following the proposal by F. Yamaguchi et al.[Phys. Rev. A 66, 010302 (R) (2002)], we present an alternative way to implement the two-qubit Grover search algorithm in cavity QED. Compared with F. Yamaguchi et al.'s proposal, with a strong resonant classical field added, our method is insensitive to both the cavity decay and thermal field, and doesn't require that the cavity remain in the vacuum state throughout the procedure. Moreover, the qubit definitions are the same for both atoms, which makes the experiment easier. The strictly numerical simulation shows that our proposal is good enough to demonstrate a two-qubit Grover's search with high fidelity.Comment: manuscript 10 pages, 2 figures, to appear in Phys. Rev.

Combining Models of Approximation with Partial Learning

In Gold's framework of inductive inference, the model of partial learning requires the learner to output exactly one correct index for the target object and only the target object infinitely often. Since infinitely many of the learner's hypotheses may be incorrect, it is not obvious whether a partial learner can be modifed to "approximate" the target object. Fulk and Jain (Approximate inference and scientific method. Information and Computation 114(2):179--191, 1994) introduced a model of approximate learning of recursive functions. The present work extends their research and solves an open problem of Fulk and Jain by showing that there is a learner which approximates and partially identifies every recursive function by outputting a sequence of hypotheses which, in addition, are also almost all finite variants of the target function. The subsequent study is dedicated to the question how these findings generalise to the learning of r.e. languages from positive data. Here three variants of approximate learning will be introduced and investigated with respect to the question whether they can be combined with partial learning. Following the line of Fulk and Jain's research, further investigations provide conditions under which partial language learners can eventually output only finite variants of the target language. The combinabilities of other partial learning criteria will also be briefly studied.Comment: 28 page

Halo assembly bias and its effects on galaxy clustering

The clustering of dark halos depends not only on their mass but also on their assembly history, a dependence we term `assembly bias'. Using a galaxy formation model grafted onto the Millennium Simulation of the LCDM cosmogony, we study how assembly bias affects galaxy clustering. We compare the original simulation to `shuffled' versions where the galaxy populations are randomly swapped among halos of similar mass, thus isolating the effects of correlations between assembly history and environment at fixed mass. Such correlations are ignored in the halo occupation distribution models often used populate dark matter simulations with galaxies, but they are significant in our more realistic simulation. Assembly bias enhances 2-point correlations by 10% for galaxies with M_bJ-5logh brighter than -17, but suppresses them by a similar amount for galaxies brighter than -20. When such samples are split by colour, assembly bias is 5% stronger for red galaxies and 5% weaker for blue ones. Halo central galaxies are differently affected by assembly bias than are galaxies of all types. It almost doubles the correlation amplitude for faint red central galaxies. Shuffling galaxies among halos of fixed formation redshift or concentration in addition to fixed mass produces biases which are not much smaller than when mass alone is fixed. Assembly bias must reflect a correlation of environment with aspects of halo assembly which are not encoded in either of these parameters. It induces effects which could compromise precision measurements of cosmological parameters from large galaxy surveys.Comment: 8 pages, 4 figures, accepted for publication in MNRA

Independence Test for High Dimensional Random Vectors

This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The asymptotic distributions of the test statistic under the null and local alternative hypotheses are established as dimensionality and the sample size of the data are comparable. We apply this test to examine multiple MA(1) and AR(1) models, panel data models with some spatial cross-sectional structures. In addition, in a flexible applied fashion, the proposed test can capture some dependent but uncorrelated structures, for example, nonlinear MA(1) models, multiple ARCH(1) models and vandermonde matrices. Simulation results are provided for detecting these dependent structures. An empirical study of dependence between closed stock prices of several companies from New York Stock Exchange (NYSE) demonstrates that the feature of cross-sectional dependence is popular in stock marketsIndependence test, cross-sectional dependence, empirical spectral distribution, characteristic function, Marcenko-Pastur Law