Suitable region of dynamic optimal interpolation for efficiently altimetry sea surface height mapping

The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compared with the linear optimal interpolation(LOI)method,the DOI method can improve the accuracy of gridded ADT locally but with low computational efficiency.Consequently,considering both computational efficiency and accuracy,the DOI method is more suitable to be used only for regional applications.In this study,we propose to evaluate the suitable region for applying the DOI method based on the correlation between the absolute value of the Jacobian operator of the geostrophic stream function and the improvement achieved by the DOI method.After verifying the LOI and DOI methods,the suitable region was investigated in three typical areas:the Gulf Stream(25°N-50°N,55°W-80°W),the Japanese Kuroshio(25°N-45°N,135°E-155°E),and the South China Sea(5°N-25°N,100°E-125°E).We propose to use the DOI method only in regions outside the equatorial region and where the absolute value of the Jacobian operator of the geostrophic stream function is higher than1×10^(-11).

Research on Interpolation Method for Missing Electricity Consumption Data

Missing value is one of the main factors that cause dirty data.Without high-quality data,there will be no reliable analysis results and precise decision-making.Therefore,the data warehouse needs to integrate high-quality data consistently.In the power system,the electricity consumption data of some large users cannot be normally collected resulting in missing data,which affects the calculation of power supply and eventually leads to a large error in the daily power line loss rate.For the problem of missing electricity consumption data,this study proposes a group method of data handling(GMDH)based data interpolation method in distribution power networks and applies it in the analysis of actually collected electricity data.First,the dependent and independent variables are defined from the original data,and the upper and lower limits of missing values are determined according to prior knowledge or existing data information.All missing data are randomly interpolated within the upper and lower limits.Then,the GMDH network is established to obtain the optimal complexity model,which is used to predict the missing data to replace the last imputed electricity consumption data.At last,this process is implemented iteratively until the missing values do not change.Under a relatively small noise level(α=0.25),the proposed approach achieves a maximum error of no more than 0.605%.Experimental findings demonstrate the efficacy and feasibility of the proposed approach,which realizes the transformation from incomplete data to complete data.Also,this proposed data interpolation approach provides a strong basis for the electricity theft diagnosis and metering fault analysis of electricity enterprises.

Integer multiple quantum image scaling based on NEQR and bicubic interpolation

As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been studied.In this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral multiple.Firstly,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules.Then,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic modules.Finally,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these pixels.Through simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.

Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

Comparison of Methods for Nitrate Interpolation in Wells in Aguascalientes, Mexico

The accuracy of interpolation models applied to groundwater depends, among other factors, on the interpolation method chosen. Therefore, it is necessary to compare different approaches. For this, different methods of interpolation of nitrate concentrations were contrasted in sixty-seven wells in an aquifer in Aguascalientes, Mexico. Four general interpolation methods were used in ArcGIS 10.5 to make the maps: IDW, Kriging, Natural Neighbor and Spline. In the modeling, only method type was varied. The input parameters (location, temporality, and nitrate concentration) were the same in the four interpolations;despite this, different maximum and minimum values were obtained for each interpolation method: for IDW, 0.2 to 22.0 mg/l, for Kriging, 3.5 to 16.5 mg/l, for Natural Neighbor, 0.3 to 21.7 mg/l and for Spline −30.8 to 37.2 mg/l. Finally, an assessment of the maps obtained was conducted by comparing them with the Official Mexican Standard (OMS), where 24 of the 67 wells were found outside the 10 mg/l that the OMS establishes as maximum permissible limit for human consumption. Taking as a starting point the measured values of nitrates (0.25 to 22.12 mg/l), as well as the spatial distribution of the interpolated values, it was determined that the Krigging method best fitted the data measured in the wells within the studied aquifer.

Comparison of Spatial Interpolation Methods of Precipitation Data in Central Macedonia, Greece

The purpose of this paper is to investigate the spatial interpolation of rainfall variability with deterministic and geostatic inspections in the Prefecture of Kilkis (Greece). The precipitation data where recorded from 12 meteorological stations in the Prefecture of Kilkis for 36 hydrological years (1973-2008). The cumulative monthly values of rainfall were studied on an annual and seasonal basis as well as during the arid-dry season. In the deterministic tests, the I.D.W. and R.B.F. checks were inspected, while in the geostatic tests, Ordinary Kriging and Universal Kriging respectively. The selection of the optimum method was made based on the least Root Mean Square Error (R.M.S.E.), as well as on the Mean Error (M.E.), as assessed by the cross validation analysis. The geostatical Kriging also considered the impact of isotropy and anisotropy across all time periods of data collection. Moreover, for Universal Kriging, the study explored spherical, exponential and Gaussian models in various combinations. Geostatistical techniques consistently demonstrated greater reliability than deterministic techniques across all time periods of data collection. Specifically, during the annual period, anisotropy was the prevailing characteristic in geostatistical techniques. Moreover, the results for the irrigation and seasonal periods were generally comparable, with few exceptions where isotropic methods yielded lower (R.M.S.E.) in some seasonal observations.

Quantum color image scaling based on bilinear interpolation

As a part of quantum image processing, quantum image scaling is a significant technology for the development of quantum computation. At present, most of the quantum image scaling schemes are based on grayscale images, with relatively little processing for color images. This paper proposes a quantum color image scaling scheme based on bilinear interpolation, which realizes the 2^(n_(1)) × 2^(n_(2)) quantum color image scaling. Firstly, the improved novel quantum representation of color digital images(INCQI) is employed to represent a 2^(n_(1)) × 2^(n_(2)) quantum color image, and the bilinear interpolation method for calculating pixel values of the interpolated image is presented. Then the quantum color image scaling-up and scaling-down circuits are designed by utilizing a series of quantum modules, and the complexity of the circuits is analyzed.Finally, the experimental simulation results of MATLAB based on the classical computer are given. The ultimate results demonstrate that the complexities of the scaling-up and scaling-down schemes are quadratic and linear, respectively, which are much lower than the cubic function and exponential function of other bilinear interpolation schemes.

OPTIMAL BIRKHOFF INTERPOLATION AND BIRKHOFF NUMBERS IN SOME FUNCTION SPACES

This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

Missing interpolation model for wind power data based on the improved CEEMDAN method and generative adversarial interpolation network

Randomness and fluctuations in wind power output may cause changes in important parameters(e.g.,grid frequency and voltage),which in turn affect the stable operation of a power system.However,owing to external factors(such as weather),there are often various anomalies in wind power data,such as missing numerical values and unreasonable data.This significantly affects the accuracy of wind power generation predictions and operational decisions.Therefore,developing and applying reliable wind power interpolation methods is important for promoting the sustainable development of the wind power industry.In this study,the causes of abnormal data in wind power generation were first analyzed from a practical perspective.Second,an improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)method with a generative adversarial interpolation network(GAIN)network was proposed to preprocess wind power generation and interpolate missing wind power generation sub-components.Finally,a complete wind power generation time series was reconstructed.Compared to traditional methods,the proposed ICEEMDAN-GAIN combination interpolation model has a higher interpolation accuracy and can effectively reduce the error impact caused by wind power generation sequence fluctuations.

Interpolation Technique for the Underwater DEM Generated by an Unmanned Surface Vessel

High-resolution underwater digital elevation models(DEMs)are important for water and soil conservation,hydrological analysis,and river channel dredging.In this work,the underwater topography of the Panjing River in Shanghai,China,was measured by an unmanned surface vessel.Five different interpolation methods were used to generate the underwater DEM and their precision and applicability for different underwater landforms were analyzed through cross-validation.The results showed that there was a positive correlation between the interpolation error and the terrain surface roughness.The five interpolation methods were all appropriate for the survey area,but their accuracy varied with different surface roughness.Based on the analysis results,an integrated approach was proposed to automatically select the appropriate interpolation method according to the different surface roughness in the surveying area.This approach improved the overall interpolation precision.The suggested technique provides a reference for the selection of interpolationmethods for underwater DEMdata.

Two Families of Multipoint Root-Solvers Using Inverse Interpolation with Memory

In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.

The QCD Ground State Chiral Tetrahedron Symmetry

We propose that the exotic meson tetraquark ud~dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, dd~ and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The ud~dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũdd~ for the electrons and ud~dd~ for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state ud~dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.

基于高倍过采样与加窗插值FFT的电力谐波分析

为提高谐波分析精度,分析了信号加窗引起的信噪比损失以及AD转换产生的量化误差,阐述了过采样技术提高信噪比的原理。在此基础上,提出了基于高倍过采样和加窗插值快速傅里叶变换(fast Fourier transform, FFT)的谐波分析方法。该方法充分利用AD转换器的潜力,以尽量高的采样速率进行AD采样,同时通过均值滤波避免高倍过采样引起的采样数据量激增问题。详细研究了所提谐波分析方法对信号中谐波分量幅值和相位的影响,并给出了简洁实用的谐波幅值和相位校正方法。仿真表明,所提方法可在不增加系统成本的前提下改善加窗插值FFT的抗噪声能力,提高谐波分析精度。

考虑自由液面影响的多凸体结构浮态计算方法

针对液舱内自由液面对浮态和稳性的影响,文中提出了一种新的多凸体组合结构浮态算法。该方法将浮体和液舱分解成多个四面体单元,通过分析每个四面体与水面/液面的相对位置关系来确定浮体的浮力和浮心以及液舱液体的重心。该方法还提出了一种改进的双重迭代法用来确定多凸体组合结构的浮态:内层迭代法模拟浮体的升沉运动,得到浮体外的水面方程和液舱内的液面方程;通过外层迭代法模拟浮体的旋转运动。两种迭代方法交替进行,直至浮体的重力作用线和浮力作用线之间的距离满足精度要求,同时重力等于浮力。自编程序对某半潜船和某半潜式海洋平台的多种典型工况进行了浮态计算,同时也考虑了自由液面影响。此外利用Maxsurf建模进行了对比分析,还利用AUTOCAD进行了精度验证。对照结果表明:该研究提出的算法可以考虑自由液面对浮态的影响,原理清晰,收敛性好;算法无论对传统的单凸体结构(例如单体船),还是多凸体结构(例如多体船、漂浮式海洋平台等)均更容易取得准确解,且计算效率更高;算法可以实现“搭积木”式的建模方式,多工况建模时可以极大地减小工作量;算法无需依赖国外第三方图形平台(比如AUTOCAD、CATIA),可为我国相关工业软件的国产化打下良好的基础。

中国舞蹈艺术的审美文化观——内外部相融的舞蹈研究方法论探讨

舞蹈创作和批评研究既包括“生命体”身体意识和时空关系的内部规律探讨,也要阐释舞蹈与人类其他社会实践的外部规律联系,内外部结合的方法论很有意义。舞蹈分析与动作分析并非相同概念。舞蹈创作和研究从业者除了提升动作分析理论,还应密切关注新的编舞走向和跨学科的舞蹈研究趋势。20世纪八九十年代以来,西方舞蹈学者的舞蹈分析框架,融入了文化研究,揭示出仅作动作分析或内部研究的局限性;中国舞蹈学者的元素分析、形态分析也与舞蹈文化密切相关。在全球在地化和全媒体时代,作为一种方法论,舞蹈艺术的“审美文化观”将舞蹈创作到批评视为审美文化活动,承袭了古今中西文化汇通的中国美学、文学、理论界和舞蹈学的相关研究,自律论、他律论与通律论相辅相成,重视具体的真实的人本体,一方面强调侧重内部研究的“跨媒介性”视角,另一方面也倡导将内外部打通的“跨文化”观,尝试既在审美中看舞蹈文化,也在文化中看舞蹈审美,是一种具有“中国式现代化”路径的文艺观和方法论。“点线面体”充分融合的审美文化四面体图式,基于艾布拉姆斯“四要素”三角和格里斯沃尔德“文化菱形”理论基础,融入拉班动作分析四面体思路,并与中国人文社科学术界倡导多年的“审美文化”研究相通。

紫外可见波长溶液标准物质的研制

以紫外可见区无吸收的高氯酸溶液作为空白基体,利用稀土元素钬和钕在紫外可见光区丰富的光谱特征吸收,研制一种可以覆盖200~900nm的紫外可见区的波长溶液标准物质。采用对峰值点附近进行3次样条插值进行数据处理,并以插值后的峰值数据作为峰值波长,分辨力可到小数点后两位。经过均匀性和稳定性检验,由9家实验室采用高精度紫外可见分光光度计对该标准物质进行协同定值,并进行不确定度评定。结果表明,该标准物质均匀性良好,在25℃下保存稳定性在1年以上。该标准物质可应用于光谱光度测量仪器的波长校准和期间核查等。

一种基于四平面的图像插值算法

针对现有图像插值算法存在的不足,提出了四平面插值算法,根据待插入点周围的4个像素点结合周边的像素点,从4个平面中选择一个作为插值平面,对于不符合平面插值的情况,则利用双线性插值,规避了用同一个插值公式对所有像素进行插值存在的不足,实验结果和数据分析表明了本方法的有效性。

基于双线性插值的单目标检测算法

针对已有算法对于空中小目标检测效果差、精度低、漏检等问题,提出一种基于双线性插值的单目标检测算法。对主干网络进行设计,再根据特征图的特点,使用不同的方法进行特征融合。在特征融合的过程中使用双线性插值算法进行上采样。对算法的先验框进行设计,使算法的先验框尺寸与数据集目标框尺寸更加契合。实验结果表明,提出算法的平均检测精度对比SSD提升了10.29%,算法计算量对比Faster-RCNN减少了82.18%。

具有系数相关性的可变分数时延滤波器设计方法

针对可变分数时延滤波器设计中的复杂度问题提出一种设计方法,将时域插值与泰勒级数展开相结合对Farrow结构进行系数配置,推导出相应的滤波器系数相关公式。该方法设计出的滤波器具有系数相关性,可使近一半滤波器系数独立,并得到低复杂度的滤波器实现结构。从复杂度、幅频响应及群时延、误差方面进行理论推导和仿真验证,分析结果表明,所提方法能有效降低可变分数时延滤波器的复杂度和计算成本。

考虑地震动空间相关性及大震震源效应的烈度场插值方法

地震发生后,利用强震动观测数据快速生成合理的等震线图是地震烈度速报中的一项关键技术。基于震源参数及烈度衰减规律生成的烈度等震线过于规则,无法反映局部烈度分布特征;而直接采用观测数据通过插值生成的等震线无法合理反映大震的震源效应。为此,提出一种考虑地震动空间相关性及大震震源效应的烈度场融合克里金插值方法,利用点到点之间的距离来考虑烈度的空间相关性,利用点到源之间的距离来考虑大震的震源效应。首先,在克里金插值方法的框架下,使用粒子群优化算法实现半变异函数的快速自动拟合;其次,通过两种自变量不同的半变异函数拟合实现了对空间相关性和震源效应的考虑;最后,使用日本和中国地震数据的插值结果验证方法的合理性。结果表明,融合克里金插值方法获得的烈度等震线图形状规则,能反映出一次地震的震源效应,且对台站稀疏的情况有较好的适应性,满足地震烈度速报的要求。该方法可为地震烈度速报及地震烈度等震线的绘制提供技术支持。