Inference for Spatial Autoregressive Models with Infinite Variance Noises

A self-weighted quantile procedure is proposed to study the inference for a spatial unilateral autoregressive model with independent and identically distributed innovations belonging to the domain of attraction of a stable law with index of stability α, α ∈ (0, 2]. It is shown that when the model is stationary, the self-weighted quantile estimate of the parameter has a closed form and converges to a normal limiting distribution, which avoids the difficulty of Roknossadati and Zarepour (2010) in deriving their limiting distribution for an M-estimate. On the contrary, we show that when the model is not stationary, the proposed estimates have the same limiting distributions as those of Roknossadati and Zarepour. Furthermore, a Wald test statistic is proposed to consider the test for a linear restriction on the parameter, and it is shown that under a local alternative, the Wald statistic has a non-central chisquared distribution. Simulations and a real data example are also reported to assess the performance of the proposed method.     

On the stationary distribution of self-sustained oscillators around bifurcation points

A double expansion in powers of the damping coefficient and noise intensity is shown to be a powerful method for obtaining the stationary distribution of systems that after rescaling become weakly damped conservative ones. Systems undergoing Hopf bifurcations belong to this class. As an illustrative example, the generalized van der Pol oscillator is considered around its bifurcation point. A calculation is carried out up to third order in both the noise intensity and the bifurcation parameter (damping coefficient).     

A comparison between transitions induced by random and periodic fluctuations

It is shown that a certain class of nonlinear systems possesses a unique and stable stationary state when subjected to periodic dichotomous modulations of an external parameter. This result enables us to define a probability density for the system and to characterize its shape and support. We compare this probability density with the one obtained in the case that the external parameter fluctuates randomly like a Markovian dichotomous noise and discuss various fluctuation-induced transition phenomena. The effects of these two types of fluctuations are quite dissimilar: the random fluctuations give rise to a richer behavior. The results are applied to the Freedericksz transition in nematic liquid crystals.Fellow of the University of Texas at Austin.     

Schrödinger uncertainty relation for a quantum oscillator in a thermostat

We introduce the Schrödinger correlator as the holistic characteristic of two types of fluctuation correlations in quantum dynamics and in statistical thermodynamics. We are the first to derive it using methods of thermofield dynamics for the coordinate-momentum variables of a quantum oscillator in a thermostat. We show that the obtained value ensures that the Schrödinger uncertainty relation becomes an equality at all temperatures. We find that the thermal equilibrium for the quantum oscillator has the sense of the thermal correlated coherent state and can be adequately described by a wave function with temperature-dependent amplitude and phase.     

一种改进的SAR图像边缘检测方法

针对Ration边缘提取算法对弱边缘检测效果差，边缘定位精度低的缺点，提出了一种改进算法用于检测微弱边缘，并给出具有FCAR特性的阀值选取办法，实际应用中，将两种方法结合为一种综合处理方法，对真实SAR图像的处理结果表明，该综合处理方法具有较高检测正确率及较好的边缘定位精度。     

一种测量较微弱信号的尝试

本文利用数字锁相放大器原理，提出了改善信噪比的尝试方法。     

A Wiener-Wintner theorem for 1/f power spectra

Wiener's generalized harmonic analysis (GHA) provides a theory of harmonic analysis for subspaces of tempered functions not accessible to the L¹,L², and Fourier series theories; and it does it in a way that is usually more quantitative than that provided by the theory of distributions. On the other hand, GHA does not yield an adequate spectral analysis of large classes of functions, including nonstationary processes and, in particular, 1/f noise. In this paper we adapt GHA to deal with 1/f noise by extending the Wiener-Wintner theorem to the case of 1/f power spectra.     

Highway traffic noise prediction using method fully compliant with ISO 9613: comparison with measurements

In this study, we introduce outdoor sound simulation that is fully compliant with ISO 9613 yet with some complementary methods that enhance its applicability; for example, calculation of sound attenuation due to undulating terrain in octave bands, geometric divergence in the near-field of the source, and short-term wind effects. Using the method, we have carried out highway traffic noise prediction and measurement for 12 sites with representative road shapes and structures. In the prediction, the sound power level for a road segment was estimated by the method suggested in ASJ Model-1998 with experimental corrections to the overall noise level and spectrum. Comparing results between predicted and measured noise levels show good correspondence at direct, diffracted and reflected sound fields within 30m from the center of the near side lane.     

Existence and Smoothness of the Density for Spatially Homogeneous SPDEs

In this paper, we extend Walsh’s stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns out to be equivalent to Dalang’s one. Then we study existence and regularity of the density of the probability law for the real-valued mild solution to a general second order stochastic partial differential equation driven by such a noise. For this, we apply the techniques of the Malliavin calculus. Our results apply to the case of the stochastic heat equation in any space dimension and the stochastic wave equation in space dimension d=1,2,3. Moreover, for these particular examples, known results in the literature have been improved.      

Passive and active interior noise control of box structures using the structural intensity method

This paper presents passive and active vibro-acoustic noise control methods for attenuating the interior noise level in box structures which can be an analogy of cabins of vehicle and aircraft. The structural intensity (SI) approach is adopted to identify the predominant vibration panels and interior noise sources for box structures. In the study, the finite element method is used to determine the structural vibration and structural intensity in the box surfaces. According to structural intensity vectors plot and structural intensity stream lines presentation, the possible effective control positions where the dampers may be attached and the active control forces may act to reduce vibration and interior noise, are identified. From the study, it can be demonstrated that the structural intensity approach and stream line presentation are possible methods for identifying the vibro-acoustic interior noise source and predominant panels which may be modified to reduce the interior noise level. The structural intensity methodology, passive and active noise control results can be extended to the further study of the vibration and interior noise control of actual cabins of vehicles and aircraft.