Semi-unitary Transformation Induced Supersymmetric Partner Hulthen System

The supersymmetric partner system of Hulthen system in the s state is obtained by using a semi-unitary transformation.The physical foundation of applications of semi-unitary transformation to supersymmetric quantum mechanics is explored.

Gravitational Field of Moving Masses with Symmetrical Transformation for Relative Motion

A symmetrical transformation is constructed to analyze the gravitational interactions between two fast moving masses based on the retarded potential without resorting to general relativity. The anomalous precession of the perihelion of orbital stars or planets can be explained with the same results as given by general relativity. By introducing an effective mass for photons, the gravity-induced frequency shift and light deflection in the trajectory by the gravity are derived, which can be reduced to the results based on general relativity under special conditions. The gravity-induced time delay of radar signals and gravitational radiations from binary pulsars are analyzed. The symmetrical transformation between two moving coordinates under zero gravity will also be discussed.

Feature Extraction of Symmetrical Triangular LFMCW Signal Using Wigner-Hough Transform

Feature extraction of symmetrical triangular linear frequency modulation continuous wave （LFM- CW） signal is studied. Combined with its peculiar charaeteristics, a novel algorithm based on Wigner-Hough transform （WHT） is presented for the deteetion and parameter estimation of this type of waveform. The initial frequency and chirp rate of each segment of this wave are estimated, and the peak-value searching steps in the parameter spaee is given. Compared with Wigner-Ville distribution （WVD）, Pseudo-Wigner-Ville distri- bution （PWD） and Smoothed-Peseudo-Wigner-Ville distribution （SPWD）, WHT has proven itself to be the best method for feature extraetion of symmetrical triangular LFMCW signal. In the end, Monte-Carlo simulations under different SNRs are earried out, with validating results on this method.

Some Estimates for the Fourier Transform on Rank 1 Symmetric Spaces

Two estimates useful in applications are proved for the Fourier transform in the space L^2(X), where X a symmetric space, as applied to some classes of functions characterized by a generalized modulus of continuity.

基于轻量级对称CNN-Transformer的图像超分辨率重建方法

针对现有基于Transformer的图像超分辨率重建方法存在参数量过大和训练成本过高等问题,提出基于轻量级对称CNN-Transformer的图像超分辨率重建方法.首先,利用权值共享设计对称CNN-Transformer模块,经由通道注意模块充分融合上、下分支提取的信息,提高对局部特征和全局特征的捕获和利用.同时,通过深度可分离卷积并计算自注意跨通道的协方差矩阵,有效减少Transformer的参数量,降低计算成本和显存消耗.然后,引入HFERB(High-Frequency Enhancement Residual Block),进一步关注高频区间的纹理和细节信息.最后,探讨Transformer生成自注意时所需激活函数的选择,分析可知GELU激活函数能较好地促进特征聚合,提升网络性能.实验表明文中方法在保持轻量化的同时,能有效重建图像更多的纹理与细节.

Wavelet Synchro-squeezing Transform and Dynamic Threshold Supported Symmetrical Power Swing Technique for Modern Transmission Network

Distance relays are prone to symmetrical power swing phenomenon.To mitigate this issue,a dynamic threshold-supported algorithm is proposed.A single logic is not supposed to be secure for all cases.Thus,a supervisory algorithm,as proposed in this study,can aid in the improvement of the immunity of the relay during swing cases and be sensitive to symmetrical faults.In the developed stages,a three-phase power signal was used and processed in two different steps:(i)extraction of the effective intrinsic mode function(IMF)selected from the Kurtosis analysis using the wavelet synchro-squeezing transform,and(ii)estimation of the average Euclidean distance index using the absolute values of the decomposed IMF’s.The adaptive threshold facilitated resistance to swing situations.At the onset of a symmetrical fault,the proposed algorithm efficiently discriminated among events using a dynamic threshold.The IEEE 39-bus test system and Indian Eastern Power Grid networks were modelled using PSCAD software,and cases were generated to test the efficacy of the method.The impact of the proposed method on a large-scale wind farm was also evaluated.A comparative analysis with other existing methods revealed the security and dependability of the proposed method.

Point Transformations and Relationships among Linear Anomalous Diffusion, Normal Diffusion and the Central Limit Theorem

We present new connections among linear anomalous diffusion (AD), normal diffusion (ND) and the Central Limit Theorem (CLT). This is done by defining a point transformation to a new position variable, which we postulate to be Cartesian, motivated by considerations from super-symmetric quantum mechanics. Canonically quantizing in the new position and momentum variables according to Dirac gives rise to generalized negative semi-definite and self-adjoint Laplacian operators. These lead to new generalized Fourier transformations and associated probability distributions, which are form invariant under the corresponding transform. The new Laplacians also lead us to generalized diffusion equations, which imply a connection to the CLT. We show that the derived diffusion equations capture all of the Fractal and Non-Fractal Anomalous Diffusion equations of O’Shaughnessy and Procaccia. However, we also obtain new equations that cannot (so far as we can tell) be expressed as examples of the O’Shaughnessy and Procaccia equations. The results show, in part, that experimentally measuring the diffusion scaling law can determine the point transformation (for monomial point transformations). We also show that AD in the original, physical position is actually ND when viewed in terms of displacements in an appropriately transformed position variable. We illustrate the ideas both analytically and with a detailed computational example for a non-trivial choice of point transformation. Finally, we summarize our results.

Voltage and Current Mode Vector Analyses of Correction Procedure Application to Clarke’s Matrix—Symmetrical Three-Phase Cases

Clarke’s matrix has been applied as a phase-mode transformation matrix to three-phase transmission lines substituting the eigenvector matrices. Considering symmetrical untransposed three-phase lines, an actual symmetrical three-phase line on untransposed conditions is associated with Clarke’s matrix for error and frequency scan analyses in this paper. Error analyses are calculated for the eigenvalue diagonal elements obtained from Clarke’s matrix. The eigenvalue off-diagonal elements from the Clarke’s matrix application are compared to the correspondent exact eigenvalues. Based on the characteristic impedance and propagation function values, the frequency scan analyses show that there are great differences between the Clarke’s matrix results and the exact ones, considering frequency values from 10 kHz to 1 MHz. A correction procedure is applied obtaining two new transformation matrices. These matrices lead to good approximated results when compared to the exact ones. With the correction procedure applied to Clarke’s matrix, the relative values of the eigenvalue matrix off-diagonal element obtained from Clarke’s matrix are decreased while the frequency scan results are improved. The steps of correction procedure application are detailed, investigating the influence of each step on the obtained two new phase-mode transformation matrices.

Multi-party dense coding in non-symmetric quantum channel

A three- and an （N＋ 1）-party dense coding scheme in the case of non-symmetric Hilbert spaces of the particles of a quantum channel are investigated by using a multipartite entangled state. In the case of the （N ＋ 1）-party dense coding scheme, we show that the amount of classical information transmitted from N senders to one receiver is improved.

Numerical Evaluation of CPV Boundary Integrals with Symmetrical Quadrature Schemes

Stemming from the definition of the Cauchy principal values (CPV) integrals, a newly developed symmetrical quadrature scheme was proposed in the paper for the accurate numerical evaluation of the singular boundary integrals in the sense of CPV encountered in the boundary element method. In the case of inner element singularities, the CPV integrals could be evaluated in a straightforward way by dividing the element into the symmetrical part and the remainder(s). And in the case of end singularities, the CPV integrals could be evaluated simply by taking a tangential distance transformation of the integrand after cutting out a symmetrical tiny zone around the singular point. In both cases, the operations are no longer necessary before the numerical implementation, which involves the dull routine work to separate out singularities from the integral kernels. Numerical examples were presented for both the two and the three dimensional boundary integrals in elasticity. Comparing the numerical results with those by other approaches demonstrates the feasibility and the effectiveness of the proposed scheme.

Existence Theorem of the Multipliers on Riemannian Symmetric Space SL(3,H)/SP(3)

Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, and we have gain the same result. Key words Riemannian symmetric space SL(3,H)/SP(3) - multipliers - spherical Fourier transform - invariant differential operator CLC number O 152.5 - O 186.12 Biography: LIAN Bao-sheng (1973-), male, Master, research direction: Li group and Lie algebra.

Power Network Asymmetrical Faults Analysis Using Instantaneous Symmetrical Components

Although the application of Symmetrical Components to time-dependent variables was introduced by Lyon in 1954, for many years its application was essentially restricted to electric machines. Recently, thanks to its advantages, the Lyon transformation is also applied to power network calculation. In this paper, time-dependent symmetrical components are used to study the dynamic analysis of asymmetrical faults in a power system. The Lyon approach allows the calculation of the maximum values of overvoltages and overcurrents under transient conditions and to study network under non-sinusoidal conditions. Finally, some examples with longitudinal asymmetrical faults are illustrated.

Two-Fold and Symmetric Repeatability Rates for Comparing Keypoint Detectors

The repeatability rate is an important measure for evaluating and comparing the performance of keypoint detectors.Several repeatability rate measurementswere used in the literature to assess the effectiveness of keypoint detectors.While these repeatability rates are calculated for pairs of images,the general assumption is that the reference image is often known and unchanging compared to other images in the same dataset.So,these rates are asymmetrical as they require calculations in only one direction.In addition,the image domain in which these computations take place substantially affects their values.The presented scatter diagram plots illustrate how these directional repeatability rates vary in relation to the size of the neighboring region in each pair of images.Therefore,both directional repeatability rates for the same image pair must be included when comparing different keypoint detectors.This paper,firstly,examines several commonly utilized repeatability rate measures for keypoint detector evaluations.The researcher then suggests computing a two-fold repeatability rate to assess keypoint detector performance on similar scene images.Next,the symmetric mean repeatability rate metric is computed using the given two-fold repeatability rates.Finally,these measurements are validated using well-known keypoint detectors on different image groups with various geometric and photometric attributes.

Finding the Maximal Eigenpair for a Large, Dense, Symmetric Matrix based on Mufa Chen's Algorithm

A hybrid method is presented for determining maximal eigenvalue and its eigenvector(called eigenpair)of a large,dense,symmetric matrix.Many problems require finding only a small part of the eigenpairs,and some require only the maximal one.In a series of papers,efficient algorithms have been developed by Mufa Chen for computing the maximal eigenpairs of tridiagonal matrices with positive off-diagonal elements.The key idea is to explicitly construet effective initial guess of the maximal eigenpair and then to employ a self-closed iterative algorithm.In this paper we will extend Mufa Chen's algorithm to find maximal eigenpair for a large scale,dense,symmetric matrix.Our strategy is to first convert the underlying matrix into the tridiagonal form by using similarity transformations.We then handle the cases that prevent us from applying Chen's algorithm directly,e.g.,the cases with zero or negative super-or sub-diagonal elements.Serval numerical experiments are carried out to demonstrate the efficiency of the proposed hybrid method.

Elastodynamics of axi-symmetric deformation in magneto-micropolar generalized thermoelastic medium

The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transform techniques are used to solve the problem. Various types of sources are taken to illustrate the utility of the approach. Integral transforms are inverted by using a numerical technique to obtain the components of stresses, temperature distribution, and induced electric and magnetic fields. The expressions of these quantities are illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i.e., Lord and Shulman （L-S theory） and Green and Lindsay （G-L theory）. Some particular interesting cases are also deduced from the present investigation.

配电变压器三相不平衡附加损耗量化分析

配电网变压器三相不平衡附加损耗的计算由于缺乏对铁耗等的全面分析而精度不高。考虑到损耗治理依赖于精确有效的损耗数据,故提出计及铁耗变化的配电变压器三相不平衡附加损耗计算方法。利用磁动势平衡方程式来分析励磁磁动势和主磁通的产生过程,以建立励磁电流与一、二次侧相电流的关系。根据配电变压器的绕组联结方式建立正序、负序和零序等值电路模型,给出三相不平衡下的附加损耗计算方法。仿真测试结果表明,与现有方法相比,所提附加损耗计算方法能够量化反映三相不平衡对变压器损耗产生的影响,在不同负荷率和不同励磁阻抗参数条件下均具有更低的计算误差。

基于空间域图像生成和混合卷积神经网络的配电网故障选线方法

传统的配电网故障选线方法大多基于一维零序电流序列构建故障诊断模型,单一的诊断模型往往限制了故障特征的深层挖掘。为了提高故障选线的准确率,提出一种基于空间域图像和混合卷积神经网络的配电网故障选线方法。首先,利用优化的降噪光滑模型对零序电流信号进行降噪处理,减少外界环境的电磁干扰。其次,利用对称希尔伯特变换将一维时域信号转成二维空间域图像,图像的颜色、形状和纹理特征能够充分反映当前系统的运行状态。最后,将一维时域信号和二维空间域图像同步作为混合卷积神经网络的输入,充分挖掘系统的故障特征,利用Sigmoid函数实现故障选线。在辐射状配电网、IEEE-13节点模型、IEEE-34节点、StarSim仿真平台上模型上进行了实验验证。实验结果表明,该选线方法可以有效克服传统方法过度依赖主观特征选择、抗噪性能差等问题,能够在高阻接地、采样时间不同步、两点接地故障等极端情况下可靠地筛选出故障线路。

CuΣ15晶界结构低能化转变的微观机制研究

采用分子动力学模拟方法对CuΣ15晶界的结构转变过程进行了系统研究,发现在单轴拉伸作用下CuΣ15[112](512)晶界会向Σ11[112](131)晶界发生低能化结构转变。位错演化和原子运动轨迹分析表明,该结构转变过程主要在两种肖克莱不全位错b_(1)=1/6[211]和b_(3)=1/6[121]的共同作用下完成。首先b_(1)位错从与Σ15晶界六边形结构单元的5和6号原子处形核并发射,此后其在{111}面上滑移导致内禀型堆垛层错的形成;b_(3)位错随后在与b_(1)同样位置形核并发射,引起{111}面上原子二次重排,从而导致堆垛层错消失。在上述位错作用下,CuΣ15晶界中原本组成六边形结构单元的5和6号原子脱离晶界区域,沿{111}面进入晶粒内而变为体相原子,剩余4个原子则重新排列形成四边形结构单元;CuΣ15晶界由此逐步完成向Σ11晶界的结构低能化转变。

Fractional Action-Like Variational Problem and Its Noether Symmetries for a Nonholonomic System

For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are studied,based on the fractional action-like approach for dynamics modeling proposed by El-Nabulsi.Firstly,the fractional action-like variational problem is established,and the fractional action-like Lagrange equations of holonomic system and the fractional action-like differential equations of motion with multiplier for nonholonomic system are given;secondly,according to the invariance of fractional action-like Hamilton action under infinitesimal transformations of group,the definitions and criteria of fractional action-like Noether symmetric transformations and quasi-symmetric transformations are put forward;finally,the fractional action-like Noether theorems for both holonomic system and nonholonomic system are established,and the relationship between the fractional action-like Noether symmetry and the conserved quantity is given.

Complementarity Properties of the Lyapunov Transformation over Symmetric Cones

The well-known Lyapunov＇s theorem in matrix theory/continuous dynamical systems as- serts that a square matrix A is positive stable if and only if there exists a positive definite matrix X such that AX＋XA^＊ is positive definite. In this paper, we extend this theorem to the setting of any Euclidean Jordan algebra V. Given any element a E V, we consider the corresponding Lyapunov transformation La and show that the P and S-properties are both equivalent to a being positive. Then we characterize the R0-property for La and show that La has the R0-property if and only if a is invertible. Finally, we provide La with some characterizations of the E0-property and the nondegeneracy property.