Orbital angular momentum density and spiral spectra of Lorentz–Gauss vortex beams passing through a single slit

Based on the Hermite–Gaussian expansion of the Lorentz distribution and the complex Gaussian expansion of the aperture function, an analytical expression of the Lorentz–Gauss vortex beam with one topological charge passing through a single slit is derived. By using the obtained analytical expressions, the properties of the Lorentz–Gauss vortex beam passing through a single slit are numerically demonstrated. According to the intensity distribution or the phase distribution of the Lorentz–Gauss vortex beam, one can judge whether the topological charge is positive or negative. The effects of the topological charge and three beam parameters on the orbital angular momentum density as well as the spiral spectra are systematically investigated respectively. The optimal choice for measuring the topological charge of the diffracted Lorentz–Gauss vortex beam is to make the single slit width wider than the waist of the Gaussian part.

The Wigner distribution function of a super Lorentz–Gauss SLG_(11) beam through a paraxial ABCD optical system

An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.

障碍物无规则运动下启发式Gauss配点参数化连续避障规划

针对障碍物无规则运动下自动驾驶车辆(SDV)的避障轨迹规划,本文提出一种结合模型约束简化和启发式非均匀Gauss配点参数化的轨迹规划算法.首先,结合SDV运动学方程和约束条件建立了SDV连续避障轨迹规划的问题;然后,在高斯伪谱法离散化算法框架下,采用Gauss配点对状态变量进行离散化;进一步,提出了启发式Gauss配点初始化策略,以此提升SDV求解速度进而实现避障实时规划;同时,对经过约束处理后的轨迹进行验证,以此保证规划轨迹的安全性;最后,在车辆模型上针对不同障碍物运动场景进行仿真测试,验证提出方法的有效性和实时性.结果显示,本文方法可以有效进行避障轨迹规划,并确保轨迹的安全性,轨迹规划平均求解耗时维持在25ms左右,显示出本文方法在实时避障规划的效能和实际应用价值.

三维Anti de Sitter空间中Lorentzian曲面的S_t^1×S_s^1-值光锥Gauss映射的奇点分类

利用Arnol'd的Legendrian理论,对三维Anti de Sitter空间中Lorentzian曲面进行了研究.引入光维高度函数概念研究了三维Anti de Sitter空间Lorentzian曲面的S1t×S1s-值、光锥Gauss映射的奇点,进行了奇点分类,揭示了类光Causs-kronecker曲率之间的关系;并研究了Lorentzian曲面的一些基本几何性质.

基于两步正则化Gauss-Newton迭代算法的ECT图像重建

电容层析成像(ECT)技术求解图像重建问题属于非线性问题,并且存在严重的不适定性。为提高图像重建精度,提出了一种基于两步正则化Gauss-Newton迭代算法的ECT图像重建方法。针对标准正则化Gauss-Newton迭代算法在图像重建中存在的不收敛问题,引入了两步迭代方法;改进了正则化矩阵,提高了解估计的精确度;考虑到Gauss-Newton算法对迭代初值的依赖性,加入了同伦算法。最后,进行仿真和静态实验,并与线性反投影(LBP)算法、Landweber算法、Tikhonov正则化算法进行对比。结果表明,该方法可有效提高图像重建精度。

Kurtosis parameters of super Lorentz-Gauss beams through a paraxial and real ABCD optical system

Based on the propagation equation of higher-order intensity moments, analytical propagation expressions for the kurtosis parameters of a super Lorentz-Gauss （SLG） SLG01 beam through a paraxial and real ABCD optical system are derived. By replacing the parameters in the expressions of the kurtosis parameters of the SLC01 beam, the kurtosis parameters of the SLG10 and SLGll beams through a paraxial and real ABCD optical system can be easily obtained. The kurtosis parameters of an SLG01 beam through a paraxial and real ABCD optical system depend on two ratios. One is the ratio of the transfer matrix element B to the product of the transfer matrix element A and the diffraction-free range of the super-Lorentzian part. The other is the ratio of the width parameter of the super-Lorentzian part to the waist of the Gaussian part. As a numerical example, the properties of the kurtosis parameters of an SLG01 beam propagating in free space are illustrated. The influences of different parameters on the kurtosis parameters of an SLG01 beam are analysed in detail.

Characteristics of paraxial propagation of a super Lorentz-Gauss SLG_(01) mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss（SLG） 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.

考虑Gauss移动热源瞬态效应的传热结构拓扑优化

针对热源位置随时间发生变化的结构热传导问题,考虑Gauss移动热源进行瞬态热传导拓扑优化设计.分别以整个时间历程内传热结构散热弱度最小化与区域温度最大值最小化为设计目标,体积分数为约束条件,采用伴随变量法推导目标函数与约束条件的敏度信息,借助移动渐进线法更新设计变量,研究了不同Gauss热源移动路径与移动速度对拓扑优化结果的影响.结果表明,瞬态拓扑结构相较于稳态结果具有明显时变性,同时最佳传热构型受到热源加热时间和移动速度及路径的多重影响.

修正的Gauss-Weierstrass积分算子在Orlicz空间内的指数加权逼近

本文研究修正的Gauss-Weierstrass积分算子在指数加权Orlicz空间内的逼近问题.通过在指数加权Orlicz空间内建立逼近问题的相关引理,并结合Orlicz空间内的光滑模,Korovkin定理及相关分析技巧得出了该算子在指数加权Orlicz空间内的逼近正定理以及相关逼近性质.

基于Gauss过程分数位回归模型的锂电池SOH估计

为了提升锂电池使用安全性,延缓其寿命退化,提出了一种Gauss过程分位数回归模型的锂电池健康状态(SOH)方法。该模型结合了准Gauss过程回归与非平稳时间序列分析以及分位数回归的优点,可有效处理健康特征数据非线性及时变性问题,具有模型参数的自适应调节能力,从而提升SOH估计的精确性和鲁棒性;通过美国国家航空航天局的电池数据集,基于不同温度的数据验证了所提出模型的有效性。结果表明:该模型的SOH估计结果的平均绝对误差(MAE)、均方根误差(RMSE)和平均绝对百分比误差(MAPE)分别为0.002 8、0.003 8、0.003 4,模型运行时间为0.008 1 s,与灰狼优化Guass过程回归模型以及文献中3种典型模型估计对比,其RMSE结果精度分别提高了0.0199、0.0030、0.019 6、0.002 0,证明所提出模型具有较好的鲁棒性和估计结果的高精确性。

Cartan-Hadamard流形上关于Lorentz范数的Trudinger-Moser不等式

本文研究了Cartan-Hadamard流形上带Lorentz范数的Trudinger-Moser不等式.利用了相关格林函数的逐点估计以及O’Neil不等式,我们得到了该不等式的最佳常数,推广了相应欧氏空间上的结果.

VALUE DISTRIBUTION PROPERTIES FOR GAUSS MAPS OF IMMERSED HARMONIC SURFACES RAMIFIED OVER HYPERSURFACES

In this paper,we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(m),which is the case where the generalized Gauss mapΦis ramified over a family of hypersurfaces{Q_(j)}_(j=1)^(q)in P^(m-1)(C)located in the N-subgeneral position.In addition,we investigate the Gauss curvature estimate for the K-quasiconformal harmonic surfaces immersed in R^(3)whose Gauss maps are ramified over a family of hypersurfaces located in the N-subgeneral position.

Nonparaxial propagation of a super-Lorentz-Gauss SLGmode beam

Based on the vectorial Rayleigh-Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz-Gauss （SLG） SLGo1 mode beam in free space. The far field expression and the scalar paraxial result are treated with special cases of the general formulae. According to the obtained analytical representation, the nonparaxial propagation properties of the SLG01 mode beam are illustrated and analysed with numerical examples. This research provides an approach to investigate the propagation of the SLG01 mode beam within the framework of the nonparaxial regime.

Gauss求积公式的直接构造研究

研究从数值积分公式的代数精度概念出发,通过直接对涉及的非线性代数方程组进行分析,即无需用到正交多项式的单根特性,获得了求积系数ai的计算公式和Gauss求积公式存在性及其构造,并以推论的方式获得了正交多项式的单根特性。

A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

基于Gauss分布的抛掷爆破爆堆形态HHO-LSSVM预测模型

露天煤矿抛掷爆破爆堆形态是影响抛掷爆破–拉斗铲倒堆工艺系统作业效率和生产成本的重要因素。为了提高露天煤矿抛掷爆破爆堆形态预测的精确度,进一步优化抛掷爆破设计并降低矿山抛掷爆破剥离成本,依据黑岱沟露天煤矿抛掷爆破实测数据进行实例分析,采用熵值法–灰色关联度方法研究抛掷爆破效果影响指标与最远抛掷距离、松散系数和有效抛掷率的权重及关联度,孔距和剖面宽与抛掷爆破效果评价指标的关联程度较低,选取最小抵抗线、排距、炸药单耗、台阶高度、采空区下口宽、坡面角、采空区上口宽作为预测模型输入参数。引入高斯(Guass)分布模型模拟爆堆剖面曲线,通过1~8阶高斯分布模型对爆堆剖面曲线模拟分析,确定阶数为5时模拟精度与效率达到最优,利用训练完成的HHO–LSSVM预测5阶Guass分布模型15个参数作为预测输出的爆堆形态的控制参数,并采用Gauss分布模型结合HHO–LSSVM算法预测爆堆形态,与LSSVM、粒子群算法(PSO)优化最小二乘支持向量机和遗传算法(GA)优化BP神经网络模型进行精度对比,同时将本文所建立模型的预测爆堆形态与真实爆堆形态进行对比。结果表明:利用5阶高斯分布模拟的爆堆曲线误差平方和(S)参数趋于稳定为25.69,决定系数(R^(2))与调整后的决定系数(R^(2)_(A))分别为0.9992和0.9990,均方根误差(R)为0.5146;HHO–LSSVM对于5阶Gauss分布控制参数的预测误差大部分在1%左右,且误差没有超过5%,与LSSVM、PSO、GA–BP算法模型相比精度较高;以E5–8、E5–9及E5–10剖面为例,预测爆堆形态与真实爆堆形态误差R^(2)和均方根误差R分别为0.9987和0.6142、0.9992和0.4931、0.9992和0.5052,预测爆堆形态接近真实爆堆形态。

On the Implementation of the Method of Derivation of Lorentz Transformations Used by Einstein

The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and identify the cause of the incorrect implementation of the method. The cause is related to the incorrect proof of the equality φ(v)=1for the unknown function φ(v)arising in the process of derivation of the Lorentz transformations. We develop proof of the equality φ(v)=1and eliminate the cause of the incorrect implementation of the method of derivation of the Lorentz transformations used by Einstein.

二元Gauss-Weierstrass算子线性组合的一致逼近

通过介绍二元Gauss-Weierstrass算子线性组合,并借助K-泛函、光滑模二者之间的关系,首先对二元Gauss-Weierstrass算子的基本性质进行了分析,其次证明了该算子的有界性,最后构建了二元Gauss-Weierstrass算子线性组合在一致逼近意义下的一致逼近性质,并给出了逼近误差的估计。

利用Gauss-Newton算法探究电极数对EIT重建图像质量的影响

电阻抗成像(electrical impedance tomography,EIT)技术是一种安全无创、廉价便捷的新型成像技术,通过测量边界电压重建物体组织内部的电导率分布。为了更进一步提升EIT重建图像的质量,通过Gauss-Newton算法分析不同电极数、不同有限元数对EIT重建图像质量的影响,并利用相关系数评估EIT重建图像的质量。仿真结果表明,若保持有限元数不变,电极数越多,EIT重建图像的质量越好;同时,若电极数保持不变,有限元数越多,目标物体轮廓形状更接近于真实值,但是EIT重建图像的质量略差;仿真分析为设计EIT成像系统提供了参考基础,为选取EIT系统电极数、有限元数以及提升EIT重建图像质量提供了参考。

基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化

基于一种求解最优控制问题的新方法—Gauss伪谱法(Gauss Pseudospectral Method-GPM),研究了高超声速飞行器滑翔式再入的快速轨迹优化问题。针对远程多约束条件下滑翔式再入轨迹优化问题的难点,提出了基于GPM的串行分段优化策略,包括三个方面:(1)构造了设计变量初值生成器,获得近似最优解作为优化初值;(2)提出从可行解到最优解的串行优化策略;(3)引入平衡滑翔条件构造动态分段点,将再入轨迹分为初始下降段和滑翔段分别求解。以某高超声速再入飞行器为对象进行轨迹优化计算,仿真结果验证了本文的轨迹优化方法具有较高的精度和计算效率。