Coherence Based Sufficient Condition for Support Recovery Using Generalized Orthogonal Matching Pursuit

In an underdetermined system,compressive sensing can be used to recover the support vector.Greedy algorithms will recover the support vector indices in an iterative manner.Generalized Orthogonal Matching Pursuit(GOMP)is the generalized form of the Orthogonal Matching Pursuit(OMP)algorithm where a number of indices selected per iteration will be greater than or equal to 1.To recover the support vector of unknown signal‘x’from the compressed measurements,the restricted isometric property should be satisfied as a sufficient condition.Finding the restricted isometric constant is a non-deterministic polynomial-time hardness problem due to that the coherence of the sensing matrix can be used to derive the sufficient condition for support recovery.In this paper a sufficient condition based on the coherence parameter to recover the support vector indices of an unknown sparse signal‘x’using GOMP has been derived.The derived sufficient condition will recover support vectors of P-sparse signal within‘P’iterations.The recovery guarantee for GOMP is less restrictive,and applies to OMP when the number of selection elements equals one.Simulation shows the superior performance of the GOMP algorithm compared with other greedy algorithms.

A New Generalized Complex Orthogonal Space-Time Block Codes

Recent research challenges in the wireless communication include the usage of diversity and efficient coding to improve data transmission quality and spectral efficiency. Space diversity uses multiple transmitting and/or receiving antennas to create independent fading channels without penalty in bandwidth efficiency. Space-time block coding is an encoding scheme for communication over Rayleigh fading channels using multiple transmitting antennas. Space-time block codes from complex orthogonal designs exist only for two transmitting antennas. This paper generalizes a new complex orthogonal space-time block code for four transmitting antennas, whose decoding complexity is very low. Simulations show that the generalized complex orthogonal space-time block code has low bit error rate, full rate and possibly large diversity.

The Related Properties of Generalized Orthogonal Group in Specific Normed Linear Spaces

Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the lp space.

GENERALIZED WEIGHTED SOBOLEV SPACES AND APPLICATIONS TO SOBOLEV ORTHOGONAL POLYNOMIALS Ⅱ

We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cτ∞(R) is dense in these spaces. As an application to Sobolev orthogonal polynomials, toe study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.

On the Generality of Orthogonal Projections and e-Projections in Banach Algebras

In this paper we develop the orthogonal projections and e-projections in Banach algebras. We prove some necessary and sufficient conditions for them and their spectrums. We also show that the sum of two generalized orthogonal projections u and v is a generalized orthogonal projection if, uv=vu=0. Our results generalize the results obtained for bounded linear operators on Hilbert spaces.

Controlling the contributions to high-order harmonic generation from different nuclei of N_2 with an orthogonally polarized two-color laser field

The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation（HHG） from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.

A Multivariate Empirical Orthogonal Function-Based Scheme for the Balanced Initial Ensemble Generation of an Ensemble Kalman Filter

The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.

THEORETICAL BASIS AND GENERAL OPTIMAL FORMULATIONS OF ISOPARAMETRIC GENERALIZED HYBRID/MIXED ELEMENT MODEL FOR IMPROVED STRESS ANALYSIS

By the modified three-field Hu-Washizu principle, this paper establishes a theoretical founda- tion and general convenient formulations to generate convergent stable generalized hybrid/mixed cle- ment (GH/ME) model which is invariant with respect to coordinate, insensitive to geometric distortion and suitable for improved stress computation. In the two proposed formulations, the stress equilibrium and orthogonality constraints are imposed through incompatible displacement and internal strain modes respectively. The proposed model by the general formulations in this paper is characterized by including as- sumed stress/strain, assumed stress, variable-node, singular, compatible and incompatible GH/ME models. When using regular meshes or the constant values of the isoparametric Jacobian Det in the assumed strain in- terpolation, the incompatible GH/ME model degenerates to the hybrid/mixed element model. Both general and concrete guidelines for the optimal selection of element shape functions are suggested. By means of the GH/ME theory in this paper, a family of new GH/ME can be and have been easily constructed. The software can also be developed conveniently because all the standard subroutines for the corresponding isoparametric displacement elements can be utilized directly.

GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS

A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation （nonlinear convection- diffusion problem） and KdV equation（single solitary and 2-solitary wave problems）, where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.

ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.

Blind CFO estimation algorithm for OFDM systems by using generalized precoding and trilinear model

This paper discusses the blind carrier frequency offset （CFO） estimation for orthogonal frequency division multiplexing （OFDM） systems by utilizing trilinear decomposition and genera- lized preceding. Firstly, the generalized precoding is employed to obtain multiple covariance matrices which are requisite for the trilinear model, and then a novel CFO estimation algorithm is proposed for the OFDM system. Compared with both the joint diagonalizer and estimation of signal parameters via rotational invariant technique （ESPRIT）, the proposed algorithm enjoys a better CFO estimation performance. Furthermore, the proposed algorithm can work well without virtual carriers. Simulation results illustrate the performance of this algorithm,

Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems

This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the conformal system. The computational results show that the conformal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical conformal grid system.

ON A GENERALIZED GEOMETRIC CONSTANT AND SUFFICIENT CONDITIONS FOR NORMAL STRUCTURE IN BANACH SPACES

In this paper, we introduce a new geometric constant C;（a, X） of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized Garc′?a-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.

Jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems

Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.

基于反射系数谱的配电电缆局部缺陷识别定位

传统配电电缆在局部缺陷识别与精准定位上灵敏度较差,位置范围识别受到限制,为解决现有技术在配电电缆缺陷诊断上存在的不足,提出一种基于反射系数谱的配电电缆局部缺陷识别定位方法。首先依据电缆分布参数模型,获得配电电缆完好状态与存在局部缺陷段的反射系数谱,然后利用广义正交积分法,将反射系数谱的虚部从频域转换到空间域,建立积分诊断图,得到具有直观性的定位图谱,根据积分诊断图实现配电电缆局部缺陷的识别与精准定位,方法适用于同时存在多处电缆缺陷的情况。最后,在实验室50 m长的配电电缆上制作老化与破损两种缺陷,用于验证所提方法的有效性。仿真和实验结果表明,该方法对不同缺陷情况均具有较高的识别精度,定位误差小于0.15 m。

利用非均匀正交激光选择谐波发射短量子路径

理论研究了谐波发射的量子路径在非均匀正交激光场下的调控机制.结果表明,在适当的双色激光偏振角和非均匀参数的组合下,不仅谐波截止能量有明显增大;谐波发射的短量子路径可以被单独选择出来对谐波连续区起到贡献作用.并且,该方案在长脉宽激光下依然适用.最后,利用谐波连续区可以获得脉宽在50 as的孤立阿秒脉冲.

风电叶片涡流发生器的作用与参数设计

为抑制叶片表面流动分离,提升叶片气动性能,提出在叶片表面安装涡流发生器的设计方案。以DU97-W-300叶片段设置涡流发生器为研究对象,采用正交实验设计方法,探究该叶片段涡流发生器高度、长度、安装角、弦向安装位置、间距、节距对叶片气动性能的影响,从而确定涡流发生器参数设计基本规律。研究结果表明:影响叶片气动性能大小的涡流发生器参数依次为涡流发生器间距、节距、长度、高度、弦向安装位置、安装角;最优涡流发生器参数组合规律为高度0.75ξ(ξ为叶片边界层厚度)、长度1.60ξ、安装角20.0°、弦向安装位置10%叶片弦长、间距1.60ξ、节距0.80ξ,可以使该叶片最大升力系数增大40%,最大失速攻角增大9.5°。

6G新型时延多普勒通信范式:OTFS的技术优势、设计挑战、应用与前景

在未来的通信网络中,被广泛期待的第6代移动通信系统(The Sixth Generation of Mobile Communications System,6G)技术将面临诸多挑战,其中包括在高速移动场景下的超高可靠通信问题。正交时频空间(Orthogonal Time Frequency Space,OTFS)调制技术克服了传统通信系统在高速移动环境下多径和多普勒效应的影响,为实现6G超高可靠通信提供了新的可能性。该文首先介绍了OTFS的基本原理、数学模型、干扰与优势分析。然后,归纳分析了OTFS技术在同步、信道估计、信号检测技术上的研究现状。接着,从车联网、无人机、卫星通信、海洋通信4个典型应用场景分析了OTFS的应用趋势。最后,从降低多维匹配滤波器、相位解调和信道估计、硬件实现的复杂度和提高对时频资源的高度利用4个角度探讨了未来研究OTFS需要克服的困难和挑战。

基于机器学习的OTFS系统信道估计与信号检测研究进展

OTFS调制可以在高速移动场景下有效对抗ICI,能提供比传统的OFDM更显著的性能增益,充分提升高多普勒扩展场景下的通信系统频谱效率,改善通信系统质量,近年来得到广泛研究。OTFS系统的研究重点和难点在于信道估计与信号检测。人工智能已经成为一种有效的信息处理手段,在各行业都得到了广泛的应用。而机器学习是人工智能中的重要分支,通过将机器学习与OTFS技术相结合,可以有效解决信道估计与信号检测中的问题,提高系统性能、稳定性和可靠性。对目前基于机器学习的OTFS系统的信道估计与信号检测算法进行了较为全面的调研、分析、对比和归纳,进而梳理出技术挑战,并就未来的技术发展趋势进行了探讨。

基于Q-POD的脉动背压下压气机流场特性

针对一台自由活塞发动机(FPEG)匹配的电动压气机,研究了脉动背压条件下压气机的瞬态特性,并将脉动背压和稳定背压工况进行对比,揭示了压气机内部不同形成机理的非定常特征.采用四重本征正交模态分解(Q-POD)法,对压气机非定常流场进行了降阶重构.基于局部熵产率,对分解后的四重流场结构逐一分析,量化并定位了压气机非定常流动中的不可逆损失.结果表明:有/无脉动背压的熵产差异在叶轮中接近17%,在压壳中仅为1%.叶轮中的大尺度结构扰动耗散熵产占主导,扩压器中直接湍流耗散熵产占比超过92%.脉动背压通过改变压气机中大尺度相干结构进而影响瞬时流场结构.大尺度涡结构在环形通道内周向发展是造成扩压器中不可逆损失的主要因素.