Singularities of Euler Flow? Not Out of the Blue!

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.     

研究傅里叶变换光谱超分辨率的一种新方法

应用傅里叶退卷积、自回归模型与截断奇异值分解相结合的方法，获得了比采用常规变换方法高得多的光谱分辨率。与研究光谱超分辨率的其它方法相比，用ＦＡＴ方法进行了光谱超分辨率估计，有分辨率高，谱线细锐、钪噪声能力强和无伪峰等许多优点。     

基于一级傅立叶级数的相调制法荧光寿命测量

针对纳秒量级荧光寿命的测量,提出一种改进的相调制法,提取周期性激发信号和相应的发射波形信号傅立叶级数中的一级项,按照相位法测量荧光寿命的原理求得荧光寿命τ值。据此采用易于调制的发光二极管为激发光源,充分利用实验室常用的仪器资源,设计了一种针对单指数衰减的测量系统。该系统主要由激发光源、光谱仪、示波器三部分组成,结构简单灵活、抗噪性好。对测量原理、频率的选择、系统的组成进行了详细讨论。利用该系统测量了乙醇溶液中甲酚紫(0.0033mol/L)的τ值为(4.03±0.87)ns,与采用德国PicoQuant公司TCPSC仪器测量的结果4.24ns相当。     

Nonlinear Time Series Prediction Using Chaotic Neural Networks

A nonlinear feedback term is introduced into the evaluation equation of weights of the backpropagation algorithm for neural network,the network becomes a chaotic one.For the purpose of that we can investigate how the different feedback terms affect the process of learning and forecasting,we use the model to forecast the nonlinear time series which is produced by Makey-Glass equation.By selecting the suitable feedback term,the system can escape from the local minima and converge to the global minimum or its approximate solutions,and the forecasting results are better than those of backpropagation algorithm.     

椭圆傅里叶级数展开法和椭圆光波导的截止频率

与严格马丢（Ｍａｔｈｉｅｕ）函数、有限元法等许多典型方法及一些实验测试的比较表明,本文提出的计算弱导椭圆光波导的椭圆傅里叶级数展开法具有通用、准确、高效、简便的优点。     

Conformal Quantum Effects and the Anisotropic Singularities of Scalar-Tensor Theories of Gravity

We show that the inclusion of a term C _abcd C ^abcd in the action can remove the recently described anisotropic singularity occurring on the hypersurface F () = 0 of scalar-tensor theories of gravity of the type

Properties of Physical Systems: Transient Singularities on Borders and Surface Transitive Zones

Certain alternative properties of physical systems are describable by supports of arguments of response functions (e.g. light cone, borders of media) and expressed by projectors; corresponding equations of restraints lead to dispersion relations, theorems of counting, etc. As supports are measurable, their absolutely strict borders contradict the spirit of quantum theory and their quantum evolution leading to appearance of subtractions or certain needed flattening would be considered. “Flattening” of projectors introduce transitive zones that can be examined as a specification of adiabatic hypothesis or the Bogoliubov regulatory function in QED. For demonstration of their possibilities the phenomena of refraction and reflection of electromagnetic wave are considered; they show, in particular, the inevitable appearing of double electromagnetic layers on all surfaces that formerly were repeatedly postulated, etc. Quantum dynamics of projectors proves the neediness of subtractions that usually are artificially adding and express transient singularities and zones in squeezed forms.     

A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

Fourier transform is applied to remove the time-dependent variable in the diffusion equation. Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation, which is solved by the method of fundamental solutions and the method of particular solutions. The particular solution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.     

农作物锈病叶傅里叶变换红外光谱检测方法研究

在农作物生产中,不合理使用化学农药来防治植物病害的现象普遍存在,严重影响产品品质及食用安全,快速鉴别植物病害并采取合理的防治措施对提高农作物品质具有重要意义。利用红外光谱三级鉴别法（傅里叶变换红外光谱（FTIR）、二阶导数红外光谱（SD-IR）及二维相关红外光谱（2D-IR））对蚕豆、玉米、葱和蒜正常叶、锈病叶病斑处及病斑附近绿色部位进行了研究。结果显示,正常叶、病斑附近绿色部位及锈病叶病斑处的光谱吸收峰强度和形状存在微小差异。原始光谱中正常叶、病斑附近绿色部位及锈病叶病斑处的几个吸收强度比存在差异,蚕豆的正常叶、病斑附近绿色部位及锈病叶病斑处的吸收强度比A_{1 410}/A_{1 646}分别为0.698,0.624和0.616,A_{2 926}/A_{1 646}相应比值分别为0.665,0.638和0.552;玉米的相应比值A_{1 649}/A_{1 055}分别为0.813,0.696,0.691,A_{1 382}/A_{1 055}相应比值分别为0.552,0.478和0.465,A_{2 926}/A_{1 055}相应比值分别为0.574,0.467和0.469;葱的相应比值A_{1 382}/A_{1 061}分别为0.843,0.821和0.704,A_{2 923}/A_{1 061}相应比值分别为0.707,0.680和0.489;以上锈病叶病斑处及病斑附近绿色部位的几个峰强比均比正常叶小。二阶导数红外光谱在1 800～800 cm-1范围内,正常叶、病斑附近绿色部位及锈病叶病斑处的吸收峰的形状及强度显示明显差异。二维相关红外光谱显示,正常叶、锈病叶病斑处及病斑附近绿色部位在860～1 690 cm-1范围内自动峰和交叉峰的位置、数目及强度存在显著差异。蚕豆正常叶出现4个强自动峰,2组强的正交叉峰;病斑附近绿色部位出现5个强自动峰,4组强正交叉峰;锈病叶病斑处出现2个最强自动峰和5个中强自动峰,5组强正交叉峰;蚕豆锈病叶病斑处自动峰强度最强,而正常叶的各个自动峰的强度最低。玉米正常叶出现9个强自动峰,12组强的正交叉峰;病斑附近绿色部位出现11个强自动峰,3组最强的正交叉峰和11组中强正交叉峰;锈病叶病斑处出现6个强自动峰,3组强正交叉峰;蒜正常叶出现9个强自动峰,8组强的正交叉峰;病斑附近绿色部位出现2个最强自动峰和9个次强自动峰,10组强正交叉峰;锈病叶病斑处出现6个强自动峰,1组强正交叉峰;玉米和蒜病斑附近绿色部位的各个自动峰的强度最强,而锈病叶病斑处自动峰和交叉峰强度最弱。葱正常叶出现9个强自动峰,5组强的正交叉峰;病斑附近绿色部位出现8个强自动峰,3组强正交叉峰;锈病叶病斑处出现3个强自动峰,无正交叉峰出现。葱正常叶的各个自动峰的强度最强,而锈病叶病斑处自动峰强度最弱。结果表明,利用傅里叶变换红外光谱结合二阶导数红外光谱及二维相关红外光谱能简单、快速地鉴别研究农作物锈病叶,有望为农作物病害提供一种光谱检测方法。     

基于LASSO方法的傅里叶变换红外光谱快速定性识别方法

采用红外光谱技术对未知气体组分进行监测,需要对气体组分进行定性识别分析。基于多元线性回归模型的LASSO变量选择技术广泛应用于数据分析领域。将LASSO方法引入到红外光谱分析领域,提出一种LASSO变量选择技术结合循环线性最小二乘(LCLS)分析的定性识别方法,并开展了相关的实验对其进行验证。实验采集CO,C₂H₄,NH₃,C₃H₈,C₄H₁₀和C₆H₁₄六种单组分傅里叶变换红外(FTIR)光谱吸光度谱以及一组C₂H₄和NH₃混合组分的吸光度谱,结合实验室自建光谱数据库,先采用LASSO方法对采集的光谱进行初步定性分析,然后使用LCLS方法剔除干扰组分。实验结果表明,LASSO结合LCLS的方法能有效识别出光谱中的目标组分,即使是在干扰严重的光谱波段也可以剔除掉大部分的干扰组分。     

Mertz法傅里叶光谱计算过程的改进

叙述了常用的Ｍｅｒｔｚ法的基本原理进一步讨论了其中的计算效率问题。通过利用实序列离散傅里叶变换的性质与相位校正的具体的处理内容相结合,优化了Ｍｅｒｔｚ法的计算处理,提高了计算效率。     

Differential Groupoids and Their Application to the Theory of Spacetime Singularities

The transformation groupoid = × G, where is the total space of the generalized frame G-bundle over spacetime with a singular boundary, is not a Lie groupoid but a differential groupoid, i.e., a smooth groupoid in the category of structured spaces. We define this concept and use it to investigate spacetimes with various kinds of singularities. Any differential transformation groupoid can be represented by an algebra of operators on a bundle of Hilbert spaces defined on the groupoid fibers. This algebra reflects the structure of a given fiber even if it is a fiber over a singularity. It is also shown that any spacetime with singularities can be regarded as a noncommutative space. Its geometry is done in terms of a noncommutative algebra defined on the corresponding differential transformation groupoid. We focus on the structure of malicious singularities such as the ones appearing in the beginning and in the end of the closed Friedman universe.     

A Hybrid Method Using HAVOK Analysis and Machine Learning for Predicting Chaotic Time Series

The prediction of chaotic time series systems has remained a challenging problem in recent decades. A hybrid method using Hankel Alternative View Of Koopman (HAVOK) analysis and machine learning (HAVOK-ML) is developed to predict chaotic time series. HAVOK-ML simulates the time series by reconstructing a closed linear model so as to achieve the purpose of prediction. It decomposes chaotic dynamics into intermittently forced linear systems by HAVOK analysis and estimates the external intermittently forcing term using machine learning. The prediction performance evaluations confirm that the proposed method has superior forecasting skills compared with existing prediction methods.     

Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing

The precise mechanisms connecting the cardiovascular system and the cerebrospinal fluid (CSF) are not well understood in detail. This paper investigates the couplings between the cardiac and respiratory components, as extracted from blood pressure (BP) signals and oscillations of the subarachnoid space width (SAS), collected during slow ventilation and ventilation against inspiration resistance. The experiment was performed on a group of 20 healthy volunteers (12 females and 8 males; BMI =22.1±3.2 kg/m2; age 25.3±7.9 years). We analysed the recorded signals with a wavelet transform. For the first time, a method based on dynamical Bayesian inference was used to detect the effective phase connectivity and the underlying coupling functions between the SAS and BP signals. There are several new findings. Slow breathing with or without resistance increases the strength of the coupling between the respiratory and cardiac components of both measured signals. We also observed increases in the strength of the coupling between the respiratory component of the BP and the cardiac component of the SAS and vice versa. Slow breathing synchronises the SAS oscillations, between the brain hemispheres. It also diminishes the similarity of the coupling between all analysed pairs of oscillators, while inspiratory resistance partially reverses this phenomenon. BP–SAS and SAS–BP interactions may reflect changes in the overall biomechanical characteristics of the brain.     

New Eigenmodes of Propagation in Quadratic Graded Index Media and Complex Fractional Fourier Transform

By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.     

A Model of Interacting Navier–Stokes Singularities

We introduce a model of interacting singularities of Navier–Stokes equations, named pinçons. They follow non-equilibrium dynamics, obtained by the condition that the velocity field around these singularities obeys locally Navier–Stokes equations. This model can be seen as a generalization of the vorton model of Novikov that was derived for the Euler equations. When immersed in a regular field, the pinçons are further transported and sheared by the regular field, while applying a stress onto the regular field that becomes dominant at a scale that is smaller than the Kolmogorov length. We apply this model to compute the motion of a pair of pinçons. A pinçon dipole is intrinsically repelling and the pinçons generically run away from each other in the early stage of their interaction. At a late time, the dissipation takes over, and the dipole dies over a viscous time scale. In the presence of a stochastic forcing, the dipole tends to orientate itself so that its components are perpendicular to their separation, and it can then follow during a transient time a near out-of-equilibrium state, with forcing balancing dissipation. In the general case where the pinçons have arbitrary intensity and orientation, we observe three generic dynamics in the early stage: one collapse with infinite dissipation, and two expansion modes, the dipolar anti-aligned runaway and an anisotropic aligned runaway. The collapse of a pair of pinçons follows several characteristics of the reconnection between two vortex rings, including the scaling of the distance between the two components, following Leray scaling tc−t.     

A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks

Measuring the predictability and complexity of time series using entropy is essential tool designing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the parameters of the methods. To overcome these difficulties, this study proposes a new method for estimating the entropy of a time series using the LogNNet neural network model. The LogNNet reservoir matrix is filled with time series elements according to our algorithm. The accuracy of the classification of images from the MNIST-10 database is considered as the entropy measure and denoted by NNetEn. The novelty of entropy calculation is that the time series is involved in mixing the input information in the reservoir. Greater complexity in the time series leads to a higher classification accuracy and higher NNetEn values. We introduce a new time series characteristic called time series learning inertia that determines the learning rate of the neural network. The robustness and efficiency of the method is verified on chaotic, periodic, random, binary, and constant time series. The comparison of NNetEn with other methods of entropy estimation demonstrates that our method is more robust and accurate and can be widely used in practice.     

Discussion of Some Problems About Nonlinear Time Series Prediction Using v-Support Vector Machine

Some problems in using v-support vector machine (v-SVM) for the prediction of nonlinear time series are discussed. The problems include selection of various net parameters, which affect the performance of prediction, mixture of kernels, and decomposition cooperation linear programming v-SVM regression, which result in improvements of the algorithm. Computer simulations in the prediction of nonlinear time series produced by Mackey-Glass equation and Lorenz equation provide some improved results.     

一种基于傅里叶变换的分析载波条纹的新方法

针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。