基于模算术系数解析的稀疏插值算法

稀疏多元多项式插值是利用多项式的稀疏结构及其给定的插值点信息重构黑盒函数的一种有效策略,被广泛应用于科学和工程领域。传统的基于Prony方法的稀疏插值算法,其复杂度与多项式项数和次数相关,遇到大规模问题时由于执行多个高阶代数运算而效率较低。提出一种新的求解稀疏多元多项式插值问题的算法,核心操作是利用模算术解析单变元多项式的系数,避免了传统方法必需的高阶方程组求解、高次方程求根等。该算法设定一变元为主元,将黑盒多元多项式视为该主元的单变元多项式,通过解析主元的系数多项式在不同插值点处的函数值,进而重构这些系数多项式以恢复整个多元多项式。理论分析和数值实验表明了算法的有效性和可行性。

基于二阶矩闭合模式平衡解的海浪生湍流混合系数解析估计

从次小尺度海洋运动方程和运动近各向同性假定出发,本文给出高确定性的海洋湍流二阶矩闭合方程和特征量变化方程.这组方程描述波动、涡旋和环流等较大尺度运动对海洋湍流的剪切不稳定性生成机制.同时,基于海浪破碎是湍流海面生成主要机制的认识,本文按破碎海浪统计理论给出湍流特征量变化方程的海面边界条件,包括由破碎能量损耗和卷入深度分别确定的海面动能通量和动能耗散率.根据上层海洋湍流特征量方程的平衡解和关于动能耗散率的观测资料,本文得到海浪生湍流混合系数的解析估计.所得到的海浪生湍流动能耗散率与观测资料进行了定性与定量对比,混合系数与先前Prandtl混合长度理论估计的一致性检验.

偏相关系数和偏回归系数的统计解析与意义

本研究提出了一个解析在多元线性回归时每一个自变量与因变量之间的关系的偏相关与偏回归系数的方法，包括系数的估计和每一个自变量与因变量之间的散点图的绘制。使我们能够在多元的情况下也能象一元回归一样，作出变量间关系的散点图，从而达到深入了解回归分析结果的可靠性和协助进行回归诊断的目的。

分层旋转椭球散射场准解析解级数系数的确定

推导了计算分层旋转椭球散射场准解析解级数系数的线性方程组。

边界元法线性单元插值时系数阵的解析

给出在边界元法中用线性单元进行插值分析过程中,系数阵的解析过程;文末给出了应用边界元法的常单元插值及线性单元插值分析二维弹性力学平面问题解与有限元ANSYS分析此问题解的比较,并给出了结论。

《待定系数法求二次函数解析式》的有效教学实践

在中学数学教学过程中，二次函数是其中一项非常重要的教学内容。众所周知，二次函数是初中学段与高中学段接轨的知识，对它的学习关系到初、高中的衔接。下面，本文就针对《待定系数法求二次函数解析式》的有效教学实践展开分析，以供参考。

直流配电网低电压穿越能力研究

随着装置限流和开断能力的不断提升,直流配电网实现低电压穿越的硬件条件日益完备。而对于直流配电网在低电压穿越时电压恢复稳定的条件,目前尚无较完善的暂态分析方法。为了克服传统能量函数法只能给出当前暂态稳定性的限制,该文首先分析了直流配电网各节点注入电流与端电压间的关系,据此推导了低电压穿越的稳定判据,并指出最大净注入功率可作为暂态稳定裕度。再者,进一步提出了计及多种站间控制方式的变系数解析–迭代预测算法,将整个低电压穿越的暂态过程作为一个整体考虑,且具有参数自适应能力。基于该算法设计了直流配电网低电压恢复控制策略,在保证系统低电压穿越能力的同时尽可能地少切负荷。最后为验证算法的有效性,进行了动态模型对比仿真,得到了预期的结果。

有限热源吸收式制冷机的热力学建模与分析

考虑了有限热容、有限速率传热以及工质内部耗散的影响,建立了吸收式制冷机的热力学模型。在该模型中,吸收式制冷机被等价为一个不可逆卡诺热机驱动不可逆卡诺制冷机的联合循环系统。为描述循环的内不可逆性,引入了两个内不可逆性参数I_(he)和I_r。其中,I_(he)用于描述热机循环的内不可逆性,I_r用于描述制冷循环的内不可逆性。通过对给定供热率下热机热效率和给定制冷率下两热源制冷机性能系数解析表达式的推导,并根据等价系统的定义,获得了吸收式制冷机给定制冷率下性能系数的解析表达式,利用该表达式详细地分析了各参数对性能系数的影响。所得公式和分析结论对实际系统的理解、设计以及分析具有一定的理论指导作用。

P-kernel Normal Systems in Weakly P-inversive Semigroups

In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.

Design and Guideline Rules for the Performance Improvement of Vertically Integrated Nanogenerator

Piezoelectric nanowires have attracted much scientific interest in the last few years because of their enhanced piezoelectric coefficients at nanometer scale, with promises of efficient mechanical energy harvesters for autonomous integrated systems. This paper presents the design and, for the first time, guideline rules, based on simple analytical expressions, to improve the performance of a mechanical energy harvester integrating vertical ZnO piezoelectric nanowires. Additional simulations were carried out to account more realistically for device geometry. The authors discuss the prospects of such an approach, based on design and material improvement.

Investigation on characteristics of liquid self-diffusion in slit nanopores using simple quasicrystal model of liquid

Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantly from that in the bulk. Based on the simple quasicrystal model of liquid, analytical expressions of self-diffusion coefficient both in bulk and in slit nanopore are derived from the Stokes–Einstein equation and the modified Eyring's equation for viscosity. The local self-diffusion coefficient in different layers of liquid and the global self-diffusion coefficient in the slit nanopore are deduced from these expressions. The influences of confinement by pore walls,pore widths, liquid density, and temperature on the self-diffusion coefficient are investigated. The results indicate that the self-diffusion coefficient in nanopore increases with the pore width and approaches the bulk value as the pore width is sufficiently large. Similar to that in bulk state, the self-diffusion coefficient in nanopore decreases with the increase of density and the decrease of temperature, but these dependences are weaker than that in bulk state and become even weaker as the pore width decreases. This work provides a simple method to capture the physical behavior and to investigate the dynamic properties of liquid in nanopores.

An Analytic Solution to Well-water Level Changes under Barometric Pressure

Under barometric pressure, groundwater flow in well-aquifer systems is a kind of hydromechanical coupling problem. Applying the flux boundary conditions on borehole wall and water pressure equilibrium conditions inside and outside the borehole wall under barometric pressure （BP）, an analytic solution to well-water level changes has been proposed in this paper. The formulation shows that the BP coefficients increase with time and tend to BP constant. The Change of BP coefficients over time depends only on the ratio of transmissivity （T） to the well radius squared （ r2, ） , and has nothing to do with the change in BP. The BP constant only relates to aquifer loading efficiency （B）, and has nothing to do with the aquifer transmissivity and well radius. The BP coefficients＇ change over time in the analytic formulation is consistent with the analysis of measured data from the Nanxi wells. Based on the BP coefficient changes over time, a parameter estimation method is suggested and discussed in its application to the estimation of the aquifer BP constant （or B） and transmissivity by using the Nanxi well data.

Approximate w_φ～Ω_φ Relations in Quintessence Models

Quintessence field is a widely-studied candidate of dark energy. There is ＂tracker solution＂ in quintessence models, in which evolution of the field φ at present times is not sensitive to its initial conditions. When the energy density of dark energy is negleetable （Ωφ 〈〈 1）, evolution of the tracker solution can be well analysed from ＂tracker equation＂. In this paper, we try to study evolution of the quintessence field from ＂full tracker equation＂, which is valid for all spans of Ωφ. We get stable fixed points of we and wφ （noted as wφ and Ωφ） from the ＂full tracker equation＂, i.e., we and ωφ will always approach ωφ and Ωφ respectively. Since wφ and Ωφ are analytic functions of φ, analytic relation of φ can be obtained, which is a good approximation for the we φ relation and can be obtained for the most type of quintessence potentials. By using this approximation, we find that inequalities ωφ 〈 we and 〈ωφ are statisfied if the we （or ωφ） decreases with time. In this way, the potentiai U（φ） can be constrained directly from observations, by no need of solving the equations of motion numerically.

Influence of Pipe-Diameter on Water Hammer Phenomenon

The influence of parameters pertaining to the confinant structure on water hammer had been less studied than those relative to the fluid. One of them is the inner pipe-diameter, a basic structural-parameter that makes its influence in essential hydraulic topics such as head loss, in pipelines. In this paper, the objective is to analyze the inner-diameter influence on water hammer phenomenon. An analytical algorithm for solving the unsteady-one-dimensional water hammer model had been applied. It had allowed estimating the instantaneous head at any point of a single pipeline. The model was solved by mean of the Laplace＇s Transformed application and the anti-transforming procedure into the complex field. To determinate the influence of internal-diameter conduit on the pressure oscillation, four distinct inside-diameter values were introduced into the solution, successively. The first overpressure-peak at each case was tabulated along with the corresponding inner^liameter and a mathematical relation had been founded. The obtained results show a close dependence between both, over-pressure peaks and internal-pipe diameter. It was founded that this dependence is given in terms of a non-linear relation between them. It was further founded that the wave frequency is sensitive to the variation of the pipe-diameter.

Theoretical model of double-walled carbon nanotube pullout from a composite matrix

A micromechanical model of double-walled carbon nanotube (DWCNT) pullout from a composite matrix is presented with the interfacial residual stress and van der Waals (vdW) forces taken into consideration.The interfacial residual stress induced by thermal expansion coefficient (TEC) mismatch is introduced via thermo-elastic constitutive relations.The influence of vdW interactions between two layers of DWCNT on the interfacial stress distributions of DWCNT and matrix is analyzed.The analytical expressions of interfacial shear stress and the axial stresses of DWCNT and matrix are derived,respectively.Furthermore,the influences of temperature change,interfacial friction coefficient,DWCNT aspect ratio,DWCNT volume fraction and the relative modulus between DWCNT and matrix are illustrated and discussed.

Fourier coefficients of Zygmund functions and analytic functions with quasiconformal deformation extensions

An open problem is to characterize the Fourier coefficients of Zygmund functions.This problem was also explicitly suggested by Nag and later by Teo and Takhtajan-Teo in the course of study of the universal Teichmu¨ller space.By a complex analysis approach,we give a characterization for the Fourier coefficients of a Zygmund function by a quadratic form.Some related topics are also discussed,including those analytic functions with quasiconformal deformation extensions.

The parametric symmetry and numbers of the entangled class of 2×M×N system

We present in the work two intriguing results in the entanglement classification of a pure and true tripartite entangled state of 2 × M × N under stochastic local operation and classical communication: (i) the internal symmetric properties of the nonlocal parameters in the continuous entangled class; (ii) the analytic expression for the total numbers of the true and pure entangled class 2 × M × N states. These properties help better understand the nature of the 2 × M × N entangled system.

Tunable time delay in active fiber Bragg grating coupler

Slowing down velocity and controlling time delay of optical pulses in fiber have many potential applications in optical com-munication systems,and a number of theoretical and experimental studies have been done.In this paper,the transmission spectrum and reflective spectrum of active fiber Bragg grating(FBG)couplers are studied,and the analytic expressions of dispersion and time delay are obtained.By changing the detuning and gain coefficient,different dispersions and time delays in active fiber Bragg grating coupler are obtained.The results show that different detunings and gain coefficients can result in various time delays,and thus tunable time delay could be achieved by changing signal frequency or gain coefficient.

TESTING FOR OUTLIERS IN TIME SERIES USING WAVELETS

One remarkable feature of wavelet decomposition is that the waveletcoefficients are localized, and any singularity in the input signals can only affect the waveletcoefficients at the point near the singularity. The localized property of the wavelet coefficientsallows us to identify the singularities in the input signals by studying the wavelet coefficients atdifferent resolution levels. This paper considers wavelet-based approaches for the detection ofoutliers in time series. Outliers are high-frequency phenomena which are associated with the waveletcoefficients with large absolute values at different resolution levels. On the basis of thefirst-level wavelet coefficients, this paper presents a diagnostic to identify outliers in a timeseries. Under the null hypothesis that there is no outlier, the proposed diagnostic is distributedas a χ_1~2. Empirical examples are presented to demonstrate the application of the proposeddiagnostic.

Darboux Transformation and N-soliton Solution for Extended Form of Modified Kadomtsev–Petviashvili Equation with Variable-Coefficient

The extended form of modified Kadomtsev–Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation.Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation.