Q estimation using multifrequency point average method based on the Taylor series expansion with a different order

The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic data.In this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order Taylor series expansion of the amplitude attenuated factor.Moreover,the multifrequency point average(MFPA)method is introduced to obtain a stable Q estimation.The model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation accuracy.In addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex models.When the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each other.In contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average values.In conclusion,the MFPA method has superior stability and practicability for the Q estimation.

A Perturbative-Based Generalized Series Expansion in Terms of Non-Orthogonal Component Functions

In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, the contribution of a given component function, at each point, in the time domain or frequency in the Fourier domain, is assumed to be perturbed by contributions from the other component functions in the set. In the case of orthogonal basis functions, the formulation reduces to the non-perturbative case approximate series expansion. Application of the series expansion is demonstrated in the context of two non-orthogonal component function sets. The technique is applied to a series of non-orthogonalized Bessel functions of the first kind that are used to construct a compound function for which the coefficients are determined utilizing the proposed approach. In a second application, the technique is applied to an example associated with the inverse problem in electrophysiology and is demonstrated through decomposition of a compound evoked potential from a peripheral nerve trunk in terms of contributing evoked potentials from individual nerve fibers of varying diameter. An additional application of the perturbative approximation is illustrated in the context of a trigonometric Fourier series representation of a continuous time signal where the technique is used to compute an approximation of the Fourier series coefficients. From these examples, it will be demonstrated that in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results.

Mean-field and high temperature series expansion calculations of some magnetic properties of Ising and XY antiferromagnetic thin-films

In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a mean-field and high temperature series expansion （HTSE） combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff （mean）, ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk （∞）.

SERIES PERTURBATIONS APPROXIMATE SOLUTIONS TO N-S EQUATIONS AND MODIFICATION TO ASYMPTOTIC EXPANSION MATCHED METHOD

A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.

Application of Fourier Series Expansion Method with PMLs to the Microcavities on Two-Dimensional Photonic Crystals

By using a Fourier series expansion method combined with Chew＇s perfectly matched layers （PMLs）, we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Compared with the results by the method without PML and finite-difference time-domain （FDTD） based on supercell approximation, it can be shown that by the present method with PMLs, the resonant frequency and the quality factor values can be calculated satisfyingly and the characteristics of the micro-cavity can be obtained by changing the size and permittivity of the point defect in the micro-cavity.

HAUSDORFF DIMENSION OF SOME KIND OF ALTERNATING OPPENHEIM SERIES EXPANSION

For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.

Determinantal Expressions and Recursive Relations for the Bessel Zeta Function and for a Sequence Originating from a Series Expansion of the Power of Modified Bessel Function of the First Kind

In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.

AN ASYMPTOTIC EXPANSION FORMULA OF KERNEL FUNCTION FOR QUASI FOURIER-LEGENDRE SERIES AND ITS APPLICATION

Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.

Real Time Implementation of Series Expansion Based Digital Controller for Magnetic Levitation System

This paper addresses a digital controller for a real time magnetic levitation system using series expansion of pulse transfer function, which achieves desired closed loop response. The proposed digital controller designed, based on series expansion of pulse transfer function by solving a linear equation using the method of least squares, which improves the transient performance and step tracking capability of the compensated system. The designed algorithm used for the control input is not iterative, so the calculation is very fast. The proposed control scheme has successfully applied on maglev system and also validated through the simulation and hardware experimental results.

Note on Barenblatt power series solution to Boussinesq equation

To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.

Further Discussion on the Calculation of Fourier Series

Fourier series is an important mathematical concept. It is well known that we need too much computation to expand the function into Fourier series. The existing literature only pointed that its Fourier series is sine series when the function is an odd function and its Fourier series is cosine series when the function is an even function. And on this basis, in this paper, according to the function which satisfies different conditions, we give the different forms of Fourier series and the specific calculation formula of Fourier coefficients, so as to avoid unnecessary calculation. In addition, if a function is defined on [0,a], we can make it have some kind of nature by using the extension method as needed. So we can get the corresponding form of Fourier series.

CHARACTERISTIC FUNCTIONS OF BILINEAR TIME SERIES MODEL

Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.

Numerical Solution of Differential Equations by Direct Taylor Expansion

A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.

Series Solution of a Trapped Ultracold Ion in a Raman—Type Configuration

The Raman interaction of a trapped ultracold ion with two traveling wave lasers is studied analytically by series expansion technique without the need of rotating wave approximation and the limitations of both the Lamb–Dicke limit and the weak excitation regime. As an example, a scheme for the preparation of Schr?dinger-cat states in such a process is proposed beyond the weak excitation regime.

Series Representation of Power Function

This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.

Quinoa Expansion in Peruvian Departments and Land Use Change before the Health Crisis

National and international policies have promoted quinoa consumption, influencing the expansion of the crop, and generating changes in land use. In this article, we analyzed the evolution of quinoa cultivation in Peru both at the national and departmental levels. Time series analysis vas used to. Between 1951 and 2019, the evolution of the quinoa-harvested areas in Peru has gone through various stages, first in regression until 1990, and then it has experienced a growth rate of 10%. Puno is still by far the department where the crop is most widespread. Taking into account the geographical and technological conditions, this highland area is less likely to maintain the rate of expansion than the Peruvian coast, which will imply great challenges for Andean farmers who have maintained the traditional crop throughout the period.

一种基于蒙特卡洛方法的配电网概率可靠性快速计算方法

配电网的概率可靠性能够弥补传统可靠性指标的期望值仅从均值角度衡量系统可靠性的不足,但随着配电网规模扩大以及数据量的剧增,能够同时兼顾计算准确性与计算速度的概率可靠性计算方法是亟待研究的。为此,提出一种基于蒙特卡洛方法的配电网概率可靠性快速计算方法,利用改进三点估计法以及三阶多项式正态变换,在保留输入变量相关性的同时有效缩减输入样本点规模,并采用级数展开得到概率可靠性。首先采用改进三点估计法,在独立标准正态空间内选取样本点,再通过三阶多项式正态变换将其转换为原始变量空间的样本点;接着采用序贯蒙特卡洛方法,在考虑孤岛划分的情况下对样本点进行可靠性计算;最后通过Edgeworth级数展开,得到可靠性指标的概率分布。对改进的IEEE-RBTS Bus6的F4馈线进行算例分析,结果表明:该文所提方法与传统蒙特卡洛方法的配电网系统可靠性计算结果之间仅存在2.195%的最大偏差,而该文所提方法计算时间仅为传统蒙特卡洛方法的1.05%,证明该文所提方法在保证较高精度的同时可以显著提升计算速度。

基于叠前方位各向异性的火山岩裂缝预测——以松辽盆地南部LFS地区为例

利用叠前方位道集地震数据进行各向异性参数反演是目前裂缝预测的主要方法之一,其中RÜGER近似方程和傅里叶级数展开式2种算法应用较为广泛,RÜGER近似方程中的各向异性梯度与傅里叶级数展开式的二阶项均可以表征裂缝强度。应用2种方程在单层界面、实钻井裂缝层分别对比了计算方法的适用性,并在实际火山岩发育区对比了裂缝空间预测结果。单界面模型2种方程预测裂缝强度存在量纲差异,RÜGER近似方程裂缝强度值域大于傅里叶级数展开式计算结果,RÜGER近似方程计算裂缝方位存在多解性,可能为垂直裂缝方向;井上裂缝层应用2种方法计算裂缝方位和强度结果基本一致;在松辽盆地南部LFS地区火山岩地层应用2种方法分别预测裂缝发育情况,傅里叶级数二阶项相比方位各向异性梯度,与电成像测井解释裂缝强度吻合稍好,且预测裂缝方位与成像测井解释方位相同。研究认为,在火山岩领域傅里叶级数方程预测裂缝方法更适于推广应用。

TimeGAN-Informer长时机场能见度预测

能见度的预测对机场的业务决策、保障飞机的安全起降具有重要的意义。针对现有能见度预测模型预测时间较短的问题,提出一种基于TimeGAN Informer(Time Generative Adversarial Network-Informer)的机场能见度预测方法。利用2018—2022年气象和污染物数据,通过相关系数法和递归特征消除法提取出能见度的主要影响因素,使用TimeGAN时间序列生成对抗网络对数据进行扩充,并将Informer长时间序列预测模型应用于能见度预测。结果显示:当预测步长为1 d、2 d、3 d时,TimeGAN Informer的绝对误差(Mean Absolute Error,MAE)分别为2.42、3.13、3.57,比Informer分别降低了0.29、0.27、0.28,比长短时记忆网络(Long Short-Term Memory,LSTM)分别降低了0.28、0.49、0.63;均方根误差(Root Mean Square Error,RMSE)分别为3.03、3.7、4.09,比Informer分别降低了0.38、0.22、0.24,比长短时记忆网络(LSTM)分别降低了0.3、0.5、1.04;百分误差小于30%的分别占测试样本集的78.07%、70.68%、63.84%。尽管随着步长的增加预测效果变差,但在预测步长为3 d时,多数样本的预测误差仍小于30%,实现了对机场区域较为准确的长时能见度预测。

可对角化矩阵特征值分解扰动问题的快速求解方法

针对特征值扰动计算的传统方法收敛速度慢的问题,提出了一种求解特征值扰动问题的快速迭代算法.首先,通过矩阵变换将初始矩阵的特征值扰动问题转化为对角矩阵的特征值扰动问题.然后,提出了一种快速迭代算法求解扰动参数,同时对算法的收敛性进行分析,并将其与基于摄动级数展开法导出的方法进行对比.再次,采用逐一求解特征值并进行矩阵降阶的策略,有效降低运算量.最后,通过2个算例分别展示算法的计算过程及其在结构模态参数追踪方面的应用效果.