Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree − 3

In this paper, we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k=−2,−1,…,3,4, their polynomial integrability has been characterized. Here, we have two main results. First, we characterize the polynomial integrability of those Hamiltonian systems with homogeneous potential of degree −3. Second, we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian systems with homogeneous polynomial potentials. Finally, we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential.     

4D neutral signature VSI and CSI spaces

In this paper we present a number of four-dimensional neutral signature exact solutions for which the polynomial scalar curvature invariants all vanish (VSI spaces) or are all constant (CSI spaces), which are of relevance in current theoretical physics.     

多项式拟合铁磁材料的磁滞回线曲线

确定铁磁材料的磁滞回线的绘制属于最小二乘法问题,并确定用分段三次多项式来拟合.给出三次多项式拟合,以及在求解过程中解法方程的方法,并给出了具体算法.     

嵌入随机多项式的抛物方程不确定声场快速算法

为了得到准确且高效计算起伏海洋介质中随机声场的算法,本文将随机多项式展开嵌入到宽角抛物方程声场计算模型(简称RAM模型)中,发展了一种不确定声场的快速算法。其计算结果比使用嵌入随机多项式的窄角抛物方程准确,计算时间小于作为参考的蒙特卡洛方法。在仿真算例中,随机多项式展开法对声强均值、方差、概率密度的计算准确;在一定的随机变量维度和随机多项式展开截断幂次内,其计算效率比蒙特卡洛方法至少提高一个数量级。     

Analysis of underwater mammal vocalisations using time-frequency-phase tracker

One of the most challenging applications of time-frequency representations deals with the analysis of the signal issued from natural environment. Recently, the interest for passive underwater context increased, basically due to the rich information carried out by the natural signals. Taken into account the non-linear multi-component time-frequency behaviour of such signals, their analysis is a challenging problem.In this context, the analysis of underwater mammal’s whistles is aimed to extract, accurately and adaptively, their main time-frequency components. In this paper, we define a time-frequency-phase tracker which is composed of three steps. The first one consists of modelling the short-time segments of the vocalization by a set of third order polynomial phase modulations. The second step consists in the fusion of local polynomial phase modulations according to a local phase continuity criterion. Finally, in the third step, the detected time-frequency track is used to design the time-frequency filter, in charge of extracting the samples corresponding to the detected track. This procedure is then iterated until all component of interest are extracted.Tests provided for realistic scenarios and real data taken in Bay of Biscay at September 2009 containing whistles of common dolphin Delphinus delphis illustrate the potential and the benefits of the proposed approach.     

多晶材料X射线衍射定量分析的多项式拟合法

提出了多晶材料X射线衍 (XRD)射定量分析的多项式拟合法 ,该方法将数学函数模型与计算机技术相结合 ,在建立衍射峰数学函数模型的基础上 ,利用计算机软件对谱线进行多项式全谱拟合 ,分析实验获得的XRD图谱 ,并求得各衍射峰的积分强度 ,从而精确求出混合试样中各相物质的重量分数。文章主要工作包括 3部分 :1 根据混合物的粉末衍射谱是各组成物相的粉末谱的权重叠加 ,各相的权重因子是与该相在混合物中的体积或重量分数有关的事实 ,建立全谱多项式拟合理论 ,找出各相的权重因子 ,进而求出其重量分数 ;2 数据采集与分析 ,给出了数据的处理方法及步骤 ;3 对定量分析的结果进行了比较讨论。该方法简化了数据处理的过程 ,提高了分析结果的精度 ,使粉末衍射数据处理工作变得相对容易     

用XRMF分段多项式回归法定量分析铂钯合金

在Ｘ射线荧光分析中,当工体效应严重时,工作曲线变得很复杂,仅用一条曲线来拟合,误差较大,为此,采用的分段的方法,将工作曲线分成四段,逐段拟合,取得了很好的效果。拟合工作曲线时,所使用的铂钯合金标样,由Ｘ射线微探针（ＸＲＭＦ）测试。此外,我们还用这种方法,分析了标样薄片中元素分布的均匀性水平。     

A probabilistic study of the influence of parameter uncertainty on solutions of the radiative transfer equation

The influence of uncertainty in the absorption and scattering coefficients on the solution and associated parameters of the radiative transfer equation is studied using polynomial chaos theory. The uncertainty is defined by means of uniform and log-uniform probability distributions. By expanding the radiation intensity in a series of polynomial chaos functions we may reduce the stochastic transfer equation to a set of coupled deterministic equations, analogous to those that arise in multigroup neutron transport theory, with the effective multigroup transfer scattering coefficients containing information about the uncertainty. This procedure enables existing transport theory computer codes to be used, with little modification, to solve the problem. Applications are made to a transmission problem and a constant source problem in a slab. In addition, we also study the rod model for which exact analytical solutions are readily available. In all cases, numerical results in the form of mean, variance and sensitivity are given that illustrate how absorption and scattering coefficient uncertainty influences the solution of the radiative transfer equation.     

Research on application of polynomial fitting technique in rotary kiln infrared temperature measurement system

Aiming at the linear temperature compensation algorithm’s disadvantage of temperature measurement error in rotary kiln infrared scanning temperature measurement process, this paper proposes a precise nonlinear cubic polynomial fitting temperature compensation algorithm. The proposed algorithm compensates the temperature values of scanning points on rotary kiln surface by following steps: Calculating temperature difference between the real temperature value of rotary kiln and temperature value measured by infrared scanning temperature measurement system; Fitting the temperature difference data with cubic polynomial; Using the obtained function to compensate temperature. Experimental result shows that compared with the usual linear temperature compensation algorithm, the accuracy of proposed algorithm has raised about 2.25 times when cubic polynomial is used.     

Invariants of the Riemann tensor: A classical approach

This paper describes the start of an investigation into the application of classical invariant theory to scalar polynomial invariants of the Riemann tensor. In particular, the classical methods of enumerating invariants are discussed with the aim, not achieved in this paper, of verifying Sneddon's result, obtained by explicit calculation of the invariants that the dimension of a Hilbert basis is 38.     

Polynomial Gaussian beams and topological charge conservation

We investigate polynomial Gaussian beams with rotationally symmetric Gaussian envelops and complex bivariate polynomial prefactors of finite order. A formalism for the propagation of such beams is developed, which expresses how the coefficients of the polynomial transform during propagation. This formalism is used to proof that global topological charge is conserved for this class of polynomial Gaussian beams.     

融合插值点优化的多项式结构宽带波束形成器设计方法

多项式结构设计方法是主瓣指向可调宽带波束形成器设计的一类重要方法。多项式结构的阶数是有限的,导致主瓣实际指向与期望指向之间存在偏差,因而影响了波束形成器的指向性指数。针对这一问题,该文提出了一种基于插值点优化的多项式结构宽带波束形成器设计方法。首先,引入多项式结构插值点处阵列响应的空间导数约束,以减小主瓣指向偏差;进而利用粒子群优化算法对多项式结构中的插值点进行优化,以充分利用插值点位置提供的自由度进一步提升多项式结构宽带波束形成器的性能。优化设计结果表明,与现有设计方法相比,该文提出的方法不仅降低了主瓣的指向偏差,同时也提高了指向性指数,有效改善了多项式结构宽带波束形成器的性能。     

Polynomial form of the Hilbert–Einstein action

Configuration space of general relativity is extended by inclusion of the determinant of the metric as a new independent variable. As the consequence the Hilbert–Einstein action takes a polynomial form.     

基于多项式模型法的低端数码相机的颜色特性化

近年来随着数字技术,以及彩色数字图像输入输出设备的不断发展和广泛使用,颜色在不同的设备之间精确的传递或再现成为该领域的重要课题。本论文以彩色数码相机特性化为研究内容,采用多项式转换方法,研究了多项式回归模型不同系数矩阵、不同训练样本对数码相机特性化精度的影响,得出了系数矩阵为11×3多项式模型时误差较小(2.874ΔE*ab)的结论,达到了实用水平。     

Least-Squres Polynomial Smoothing for Inductively Coupled Plasma Atomic Emission Spectra

The use of least—squres polynomial smoothing in ICP—AES is discussed and a method of points insertion into spectral scanning intervals is proposed in the present paper. Optimal FWHM/SR ratio can be obtained, and distortion of smoothed spectra can be avoided by use of the recommended method.     

A high-order finite volume method for systems of conservation laws—Multi-dimensional Optimal Order Detection (MOOD)

In this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numerical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach.     

差分吸收光谱技术测量氯气的数据处理方法研究

基于差分吸收光谱(DOAS)技术,结合自主搭建的一套小型便携式DOAS实验系统,开展了对氯气的实验测量。在处理氯气的标准截面时,比较了两种不同的高通数字滤波方法：三角函数滤波和多项式拟合滤波。实验证明采用后一处理方法能够更加准确反演出氯气的浓度。模拟计算的结果显示,采用五阶多项式处理的结果的误差较小;在不同样品池内的测量结果显示,利用该方法测量氯气的线性度达到0.996 1;实际的一条谱的反演结果显示拟合谱与测量谱基本重合,且剩余噪声谱的峰峰值最大值<5‰;给出整个实验过程中可能的误差主要来源。综合以上的实验结果表明,利用DOAS技术采用多项式拟合处理的方法可以实现对于氯气的检测。     

基于共焦显微拉曼的柑橘黄龙病无损检测研究

黄龙病危害柑橘果树日益严重,对柑橘黄龙病进行快速检测研究具有重大意义。采用拉曼光谱技术,结合偏最小二乘判别分析(PLS-DA)方法探讨快速诊断柑橘黄龙病及病情类别的可行性。获取柑橘叶片拉曼光谱并进行普通PCR鉴别分为轻度、中度、重度、缺素和正常5类。在715～1 639.5 cm-1范围内采用一阶导,基线校正(Baseline)和多项式拟合三种方法扣除光谱背景,突显叶片拉曼光谱特征峰。多项式拟合方法分别进行了2次,3次和4次拟合,与一阶导和基线校正两种扣除背景方法进行比较,结合最小二乘支持向量机(LS-SVM)和偏最小二乘判别分析(PLS-DA)建立判别模型。经比较发现,多项式拟合方法扣除光谱背景效果均好于另外两种方法,其中用2次多项式拟合的PLS-DA模型的效果最好,预测相关系数(R_P)为0.98,预测均方根误差(RMSEP)为0.67,总误判率最小为0。基线校正扣除光谱背景的LS-SVM模型效果最差,总误判率最大为40%。研究结果表明,利用拉曼光谱技术对柑橘黄龙病进行快速识别研究具有一定的可行性,为柑橘黄龙病无损检测研究提供一种新途径。     

X射线数字纹理图像的特征提取

以减少图像背景和结构纹理对特征提取的干扰为目的,提出了先去除背景和纹理,再进行特征分析的算法.该算法通过最小二乘法则拟合了类抛物线曲面函数提取数字射线图像的背景,减少了背景对图像特征的模糊,在此基础上,针对图像的结构纹理特点确定几何分布参量,定义减法运算公式消隐图像纹理,减少了纹理造成的图像灰度起伏,图像灰度级分布均匀.在平坦的图像背景中,根据数字射线图像信号点服从正态分布规律特点,设定阈值进行特征分割.