Some New Transformation Formulas for q-Series through the Bailey Transform

In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also obtain some new terminated identities. Furthermore, we establish a companion identity to the Rogers-Ramanujan identity labelled by number (23) on Slater’s list.

REFINEMENTS OF TRANSFORMATION INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS

In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.

Comprehensive Reliability Allocation Method for CNC Lathes Based on Cubic Transformed Functions of Failure Mode and Effects Analysis

Reliability allocation of computerized numerical controlled（CNC）lathes is very important in industry.Traditional allocation methods only focus on high-failure rate components rather than moderate failure rate components,which is not applicable in some conditions.Aiming at solving the problem of CNC lathes reliability allocating,a comprehensive reliability allocation method based on cubic transformed functions of failure modes and effects analysis（FMEA）is presented.Firstly,conventional reliability allocation methods are introduced.Then the limitations of direct combination of comprehensive allocation method with the exponential transformed FMEA method are investigated.Subsequently,a cubic transformed function is established in order to overcome these limitations.Properties of the new transformed functions are discussed by considering the failure severity and the failure occurrence.Designers can choose appropriate transform amplitudes according to their requirements.Finally,a CNC lathe and a spindle system are used as an example to verify the new allocation method.Seven criteria are considered to compare the results of the new method with traditional methods.The allocation results indicate that the new method is more flexible than traditional methods.By employing the new cubic transformed function,the method covers a wider range of problems in CNC reliability allocation without losing the advantages of traditional methods.

New Generalized Transformation Method and Its Application in Higher-Dimensional Soliton Equation

A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.

Combining Cubic Spline Interpolation and Fast Fourier Transform to Extend Measuring Range of Reflectometry

The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.

DEFORMATION DUE TO TIME HARMONIC SOURCES IN MICROPOLAR THERMOELASTIC MEDIUM POSSESSING CUBIC SYMMETRY WITH TWO RELAXATION TIMES

The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.

Improvement of Orbit Prediction Algorithm for Spacecraft Through Simplified Precession-Nutation Model Using Cubic Spline Interpolation Method

For the on-orbit flight missions,the model of orbit prediction is critical for the tasks with high accuracy requirement and limited computing resources of spacecraft.The precession-nutation model,as the main part of extended orbit prediction,affects the efficiency and accuracy of on-board operation.In this paper,the previous research about the conversion between the Geocentric Celestial Reference System and International Terrestrial Reference System is briefly summarized,and a practical concise precession-nutation model is proposed for coordinate transformation computation based on Celestial Intermediate Pole(CIP).The idea that simplifying the CIP-based model with interpolation method is driven by characteristics of precession-nutation parameters changing with time.A cubic spline interpolation algorithm is applied to obtain the required CIP coordinates and Celestial Intermediate Origin locator.The complete precession nutation model containing more than 4000 parameters is simplified to the calculation of a cubic polynomial,which greatly reduces the computational load.In addition,for evaluating the actual performance,an orbit propagator is built with the proposed simplified precession-nutationmodel.Compared with the orbit prediction results obtained by the truncated series of IAU2000/2006 precession-nutation model,the simplified precession-nutation model with cubic spline interpolation can significantly improve the accuracy of orbit prediction,which implicates great practical application value in further on-orbit missions of spacecraft.

Denoising of hyperspectral imagery by cubic smoothing spline in the wavelet domain

The acquired hyperspectral images （HSIs） are inherently attected by noise wlm Dano-varylng level, which cannot be removed easily by current approaches. In this study, a new denoising method is proposed for removing such kind of noise by smoothing spectral signals in the transformed multi- scale domain. Specifically, the proposed method includes three procedures： 1 ） applying a discrete wavelet transform （DWT） to each band; 2） performing cubic spline smoothing on each noisy coeffi- cient vector along the spectral axis; 3 ） reconstructing each band by an inverse DWT. In order to adapt to the band-varying noise statistics of HSIs, the noise covariance is estimated to control the smoothing degree at different spectra｜ positions. Generalized cross validation （GCV） is employed to choose the smoothing parameter during the optimization. The experimental results on simulated and real HSIs demonstrate that the proposed method can be well adapted to band-varying noise statistics of noisy HSIs and also can well preserve the spectral and spatial features.

Structure evolution of cubic boron nitride under spark plasma sintering

Cubic boron nitride(CBN) micro powders and mixture of CBN micro powders with Al or Ti powders were fast heated at 1 300,1 400,1 450,1 500℃,and then kept for 5 min under spark plasma sintering (SPS).The obtained powders were analyzed with XRD.The results show that,simple CBN kept cubic structure after heated at 1 300℃;when the temperature rose to 1 400℃,some CBN was transformed into hexagonal structured boron nitride(hBN).As for CBN micro powders mixed with aluminum or titanium micro powders,the onset transforming temperature of CBN to hBN get raised.This results indicated that the structural transformation of boron nitride begun from the surface of CBN crystal particle,different coexist elements affect the surface situation of CBN particles.As the stabilities of CBN crystal particle surface improved,the onset structural transform temperature of CBN was also increased.

Causes and solutions of overshoot and undershoot and end swing in Hilbert-Huang transform

There are overshoot and undershoot phenomenon and end swing phenomenon in the cubic spline fitting in Hil- bert-Huang transform. The two problems influence data quality of the empirical mode decomposition seriously. The cubic spline fitting has been analysed, and the causes of producing the overshoot and undershoot phenomenon and the end swing phenomenon have been pointed out in this paper. Two new methods of cubic spline fitting and sine spline fitting and the new technique of handling the end points of the original data curve can completely re- move the overshoot and undershoot phenomenon and the end swing phenomenon on the condition of unchanging original data, and have the advantages of the continuous fitting functions and its continuous one order derivative, the simple and convenient calculations, the small calculation amount and the easy work on it.

Solitons for the cubic-quintic nonlinear Schrdinger equation with varying coefficients

In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger （CCQNLS） equations through the generalized Darboux transformation （DT）. A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed：（i） the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; （ii） hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; （iii） hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.

四向加权香农熵最大化导向的自动阈值分割方法

灰度图像的灰度直方图可以呈现出无峰、单峰、双峰或多峰的形态特征,但传统熵阈值分割方法大多仅适合处理具有单峰或双峰形态特征的灰度图像。为了提高熵阈值分割方法的分割精度和分割适应性,提出一种四向加权香农熵最大化导向的自动阈值分割方法 FWSE(Four-directional Weighted Shannon Entropy)。首先用新设计的方向性Prewitt卷积核在4个方向进行多尺度乘积变换(MPT),以获得一系列方向性MPT图像;再基于三次样条插值函数和曲率最大化准则自动计算出每个方向的最优MPT图像;其次在每个方向上通过内外轮廓图像对最优MPT图像的像素进行重新取样,以获取重构的灰度直方图,并在此基础上计算相应的香农熵;最后以4个方向的加权香农熵最大化为准则选取最佳分割阈值。与新近的3种阈值分割方法以及2种非阈值分割方法在4幅合成图像和100幅真实世界图像上进行实验,结果显示:在合成图像上,FWSE方法的平均马修斯相关系数(MCC)达到了0.999;在真实世界图像上,FWSE方法与其他5个分割方法的平均MCC分别是0.974、0.927、0.668、0.595、0.550和0.525。这表明FWSE方法具有更高的分割精度和更灵活的分割适应性。

晶相设计钌基纳米催化剂提高CO_(2)甲烷化活性

金属纳米颗粒在许多化学反应中表现出优异的催化性能,因而广泛用于能源和环境等催化领域.形貌是影响其催化行为的关键因素之一,它通过改变金属纳米颗粒表层原子排列结构,进而调控化学反应过程中的物质吸附、催化机理和反应动力学.此外,由于金属存在多种晶相结构,其纳米颗粒暴露的表面结构也可通过改变晶相得以实现.该调控策略可使得纳米颗粒具有独特的表面结构,并展现出不同的催化性能.因此,金属纳米颗粒的晶相设计为优化金属催化剂的催化性能提供了一种有效方式.Ru基纳米催化剂对CO_(2)甲烷化反应具有较好的活性和选择性,且密堆积的Ru(0001)晶面被证明是hcp相Ru纳米催化剂的活性中心,而(10-11)面对CO_(2)甲烷化反应的贡献较小.因此,开发具有更丰富密堆积fcc-(111)表面的Ru基纳米催化剂,有望大幅提高CO_(2)甲烷化的活性.本文首先通过密度泛函理论计算和微观动力学模拟,研究了fcc相Ru纳米催化剂的密堆积(111)晶面上CO_(2)加氢反应的催化机理.结果表明,与hcp-(0001)相比,该密堆积的fcc-(111)表面因能促进CO_(2)的吸附活化,而具有更好的CO_(2)甲烷化反应活性.制备了具有完全暴露fcc-(111)晶面的二十面体Ru金属纳米颗粒,并将其负载于惰性载体氧化铝上,结果表明,CO_(2)甲烷化活性比传统六方密堆积相(hcp)的钌基催化剂高5‒8倍,证实了fcc相催化剂具有更高的甲烷化催化性能.同时,在较高的反应温度下,fcc-晶相的Ru基催化剂在初始反应阶段甲烷化反应活性逐渐下降,但其CO_(2)甲烷化活性仍远高于hcp-相催化剂.原位X射线衍射和环境透射电镜等结果表明,在反应温度高于250°C条件下,fcc-晶相的金属催化剂发生部分晶相转变.该相变主要发生于Ru金属纳米颗粒的聚集体,并伴随着金属粒子的团聚和粒径的增长;然而,单颗粒分散的Ru纳米粒子在相同条件下仍能维持其fcc-晶相,从而确保了其较高的甲烷化活性.此外,原位红外结果进一步证实了CO_(2)甲烷化在Ru基纳米催化剂上通过氢化生成HCOO*中间体的反应路径,以及Ru纳米颗粒在反应过程中的动态结构演化.综上,金属纳米颗粒的晶相设计是调控表面原子结构及其催化反应性能的有效手段.通过对Ru基纳米催化剂的晶相设计,可以显著提升其在CO_(2)甲烷化反应中的催化活性.然而,潜在的高温晶相转变可导致催化剂活性的部分失活.总之,晶相设计通过对金属纳米粒子表面原子结构的调变,为高效催化剂的设计开发和反应机理的深入研究提供了新的机遇.

基于三次样条插值法的柱面近场测量欠采样修正算法研究

为解决暗室近场测试效率低的问题,本文针对天线近场测量中高效测量方法进行了研究,提出了一种柱面近场欠采样恢复算法。该算法利用高精度的三次样条插值(cubic spline interpolation,CSI)法对未采样的点进行恢复,可减少采样点数,提高测试速度。此外,在柱面近场欠采样恢复CSI求解过程中充分利用系数矩阵的正定、对称等优良特性,使线性方程组的计算量从O(n^(3))降为O(n),大大提高了CSI的计算效率。最后使用插值后的近场幅度和相位结合柱面近远场变换理论求得天线远场方向图。为验证所提出算法的有效性,试验测试了天线样机,试验结果与理论分析一致。

Ramanujan's cubic transformation and generalized modular equation

We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.

基于小波双三次插值提高光学遥感图像空间分辨率的研究

为了尽可能的保持光学遥感图像的原始信息 ,提高图像的空间分辨率 ,有利于对图像的细节信息进行观察分析 ,本文提出了小波双三次插值方法 ,并将其应用于提高光学遥感图像空间分辨率 .实验结果表明 ,该算法得到了比全小波插值和小波双线性插值更高的峰值信噪比和更好的图像细节效果 ,是一种适合提高光学遥感图像分辨率的有效算法 .

电力系统周期性数据大比率压缩算法

针对电力系统大量周期性实时数据,提出了一种新的数据压缩与解压缩算法。针对周期性数据循环内与循环间信息不均衡性,基于三次样条插值方法进行重采样以实现整周期采样,克服电网频率波动的影响,消除循环内与循环间信息的耦合,更有效去除循环间数据的冗余性,实现大压缩比。分析了该重采样方法的误差,利用基于提升格式的小波分解对数据等相位点序列分别进行分解与重构,实现数据压缩与解压缩。利用实际测取的电力生产过程中的周期性数据对所提出的算法进行验证,试验结果表明,在相同的压缩比下,重采样之后进行压缩的数据的信噪比优于直接压缩数据的信噪比。

三阶多项式相位信号参数估计

三阶多项式相位信号常用于描述复杂运动目标的雷达回波,但其未知参数多,参数估计实现起来比较困难。针对此问题,本文提出了一种分两步的三阶多项式相位信号参数估计方法:首先利用Radon变换提取三阶多项式相位信号在三次相位变换后对应的直线,从而得到相位参数的初始值估计;然后将初始值代入最大似然估计函数并利用单纯形法对其进行优化得到精确估计结果。给出了单分量和多分量情况下的参数估计流程。仿真结果表明,本文算法估计性能达到CRB界,且起始工作信噪比门限低。

基于三次样条函数算法的逆阿贝尔变换

等离子体有关参数的径向分布 ,在等离子体研究中十分有意义的。只要等离子体具有轴对称和光性薄的性质 ,那么利用 Abel逆变换便可以从所测量得到的某种物理量 ,沿测量方向的积分求出径向分布值。激光等离子体实验中的轴对称的 X光体发射强度分布及通过多通道方法可测量电子密度和温度分布 ,需要采用逆阿贝尔 ( Abel)变换。本文采用三次样条函数近似方法计算逆 Abel变换 ,并对两种有代表性的分布进行了计算 ,数值模拟结果表明 :此方法反演的精度高 ,计算也比较简便 ,程序实现很容易。