Density estimates for a random noise propagating through a chain of differential equations

We here provide two sided bounds for the density of the solution of a system of n differential equations of dimension d, the first one being forced by a non-degenerate random noise and the n−1 other ones being degenerate. The system formed by the n equations satisfies a suitable Hörmander condition: the second equation feels the noise plugged into the first equation, the third equation feels the noise transmitted from the first to the second equation and so on … , so that the noise propagates one way through the system. When the coefficients of the system are Lipschitz continuous, we show that the density of the solution satisfies Gaussian bounds with non-diffusive time scales. The proof relies on the interpretation of the density of the solution as the value function of some optimal stochastic control problem.     

Spectroscopic analysis of asymmetric top free radicals——Application to pure rotational spectra of NO_2 in the ground vibronic state

Several key problems involved in the analyses of spectra of asymmetric top molecules, i.e., the effective Hamiltonian, the representation and basis vector, identification of energy levels, the selection rules, the relative intensity, and Zeeman tuning rate, were elucidated systematically. Introducing the high-order centrifugal distortion terms into the effective Hamiltonian, the precision for calculation has been improved substantially, which allows us to analyze the high-lying rotational transitions. A global analysis of all available spectra of 14N16O2 in the ground vibronic state has been made to obtain a set of molecular constants of 14N16O2 in the ground vibronic state which is the most precise and extensive so far. Using the improved parameters, some FIR LMR lines left unassigned hitherto have been identified successfully.     

Numerical limit analysis bounds for ductile porous media with oblate voids

The paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by [Gologanu et al., 1994] and [Gologanu et al., 1997] for porous media with oblate voids.     

Dual extremum principles for geometrically exact finite strain beams

Both necessary and sufficient conditions for the existence of two complementary-dual extremum principles for geometrically exact finite strain (one-dimensional) beam models are investigated by means of two different approaches. One is based on the results published by Gao and Strang, and the other relies on the approach proposed by Noble and Sewell. While the former is limited to beam models restricted to moderate large deformations, the latter is valid for arbitrarily large deformations (and strains). The numerical implementation of the complementary-dual extremum principles can lead to simple true global upper bounds of the error of the approximate solutions.     

Characteristic polynomial theory of two-stage phase shifting algorithms

Two-stage phase shifting algorithms make possible to directly recover the sum or the difference of the optical phase of two different fringe patterns. These algorithms can be built by combining the known phase shifting algorithms in a non-linear way. In this work, we associate a two-dimensional characteristic polynomial to each two-stage phase shifting algorithm. This enables us to qualitatively compare their behaviour against the main systematic error sources, by means of an analysis protocol like that used for phase shifting algorithms. We show that this tool allows to understand the propagation of properties from precursor phase shifting algorithms to new evaluation algorithms built from them. As an experimental application, a wavefront distortion evaluation in differential phase-shifting interferometry is presented.     

Tails of waiting times and their bounds

Tails of distributions having the form of the geometric convolution are considered. In the case of light-tailed summands, a simple proof of the famous Cramér asymptotic formula is given via the change of probability measure. Some related results are obtained, namely, bounds of the tails of geometric convolutions, expressions for the distribution of the 1st failure time and failure rate in regenerative systems, and others. In the case of heavy-tailed summands, two-sided bounds of the tail of the geometric convolution are given in the cases where the summands have either Pareto or Weibull distributions. The results obtained have the property that the corresponding lower and upper bounds are tailed-equivalent. This revised version was published online in June 2006 with corrections to the Cover Date.     

autoDIAS: a python tool for an automated distortion/interaction activation strain analysis

The distortion/interaction activation strain (DIAS) analysis is a powerful tool for the investigation of energy barriers. However, setup and data analysis of such a calculation can be cumbersome and requires lengthy intervention of the user. We present autoDIAS, a python tool for the automated setup, performance, and data extraction of the DIAS analysis, including automated detection of fragments and relevant geometric parameters. © 2019 Wiley Periodicals, Inc.     

ON THE ZEROS OF A CLASS OF POLYNOMIALS AND RELATED ANALYTIC FUNCTIONS

In this paper we prove some interesting extensions and generalizations of Enestrom- Kakeya Theorem concerning the location of the zeros of a polynomial in a complex plane. We also obtain some zero-free regions for a class of related analytic functions. Our results not only contain some known results as a special case but also a variety of interesting results can be deduced in a unified way by various choices of the parameters.     

广角镜头桶形畸变的二元二次多项式修正法

为了修正广角镜头的桶形畸变,提出了一种基于二元二次多项式的修正方法,阐述了其图像的像素坐标校正和像素灰度恢复方法。该方法首先用模板对广角镜头进行对准相对标定,然后用二元二次多项式拟合畸变图像与非畸变图像像素坐标之间的规律,最后把该方法应用于某广角镜头拍摄的图像,并采用最小二乘法对校正效果进行评价。结果表明:在不考虑视觉系统具体参数的情况下,该方法能够有效地对广角镜头桶形畸变进行修正。