Triple reverse order law for the Drazin inverse

In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.

The Reverse Order Law for Moore-Penrose Inverse of Closed Operators

In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].

A tentative model for the explanation of B?th law using the order parameter of seismicity in natural time

Using the order parameter of seismicity defined in natural time, we suggest a simple model for the expla- nation of Bath law, according to which a mainshock differs in magnitude from its largest aftershock by approximately 1.2 regardless of the mainshock magnitude. In addition, the validity of Bath law is studied in the Global Centroid Moment Tensor catalogue by using two different aftershock definitions. It is found that the mean of this difference, when considering all the pairs mainshock-largest aftershock, does not markedly differ from 1.2 and the corresponding distributions do not depend on the mainshock＇s magnitude threshold in a statistically significant manner. Finally, the analysis of the cumulative distribution functions provides evidence in favour of the proposed model.

REVERSE ORDER LAW FOR GROUP INVERSE OF PRODUCT OF MATRICES ON SKEW FIELDS

Let Kn×n be the set of all n×n matrices and Krn×n the set {A∈Kn×n|rankA=r} on askew field K. Zhuang [1] denotes by A# the group inverse of A∈Kn×n which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.

ON THE REVERSE ORDER LAW (AB)~D=B^DA^D

By using the ranks of matrices, necessary and sufficient conditions are presented for the two term reverse order law (AB) D=B DA D to hold.

Experimental researches for scaling laws of low-order structure function in boundary layer

Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of upstream velocity(u'),longitudinal velocity(v')and ponderance of vorticity(dv'/dx)at Reθ=2167 in different wall distance and verify the anomaly of the scaling exponents of high-order structure functions with the increasing order of the moments,discuss the scaling of non-integer moments of order between+2 and-1.The difference of scaling exponents of low-order structure functions between the experimental data and Kolmogorov's,SL's(She & Leveque)prediction increases as the moment order decreases toward-1,which shows that the anomaly is manifested in low-oeder moments as well.However,for same order structure functions,the scaling exponents of v' and dv'/dx are not changeable in different wall distance.

A scaling law of high-order harmonic generation

Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation （HHG）, a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ）, and the intensity I of the laser field change simultaneously to kEb, λ/k, and k3I, respectively. The characteristics of the HHG spectrum remain unchanged, while the harmonic yield is enhanced k3 times. That HHG obeys the same scaling law with above-threshold ionization is a solid proof of the fact that the two physical processes have similar physical mechanisms. The variation of integrated harmonic yields is also discussed.

Mixed-Type Reverse Order Laws for Generalized Inverses over Hilbert Space

In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.

Extended trajectory shaping guidance law considering a first-order autopilot lag

To satisfy the terminal position and impact angel constraints,an optimal guidance problem was discussed for homing missiles. For a stationary or a slowly moving target on the ground,an extended trajectory shaping guidance lawconsidering a first-order autopilot lag（ ETSG L-C FAL） was proposed. To derive the ETSG L-C FAL,a time-to-go- nth power weighted objection function was adopted and three different derivation methods were demonstrated while the Schwartz inequality method was mainly demonstrated.The performance of the ETSG L-C FAL and the ETSG L guidance laws was compared through simulation.Simulation results showthat although a first-order autopilot is introduced into the ETSG L-C FAL guidance system,the position miss distance and terminal impact angle error induced by the impact angle is zero for different guidance time.

Order of Precedence Between Local Laws of Cities with Subordinate Districts and Regulations of Provincial Governments Clarifying Premises for Discussion Based on the Characteristics of Laws

The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of China(Legislation Law) has led to two divergent views. One holds that "the local laws of cities with subordinate districts should take precedence over the regulations of provincial governments," while the other supports the exact opposite. This is a value judgment issue in legislation. To reach a solution, we need to clarify the premises based on the characteristics of the laws in question so that a basic common ground can be established for discussion. The first premise for traditional legislation is that a law should be based on experience as well as logic; the second is that the experience of authority subjects, plus the three aspects of logic should outweigh the experience of social subjects, plus the three aspects of logic. With respect to postmodern legislation, the first premise is that experience should override logic, and the second is that the experience of the authority subject should take precedence over that of social subject, with no requirements for logical consistency. Since Legislation Law fal s into the category of postmodern legislation, according to the premises, the argument that the local laws of cities with subordinate districts should take precedence enjoys wider acceptance, but the view is logically challenged in terms of conceptual consistency, system consistency and principle consistency. More studies must be conducted to facilitate the discussion.

Cavitating/non-cavitating flows simulation by third-order finite volume scheme and power-law preconditioning method

Equations of steady inviscid and laminar flows are solved by means of a third-order finite volume （FV） scheme. For this purpose, a cell-centered discretization technique is employed. In this technique, the flow parameters at the cell faces are computed using a third-order weighted averages procedure. A fourth-order artificial dissipation is used for stability of the solution. In order to achieve the steady-state situation, four-step Runge-Kutta explicit time integration method is applied. An advanced progressive preconditioning method, named the power-law preconditioning method, is used for faster convergence. In this method, the preconditioning matrix is adjusted automatically from the velocity and/or pressure flow-field by a power-law relation. Attention is directed towards accuracy and convergence of the schemes. The results presented in the paper focus on steady inviscid and laminar flows around sheet-cavitating and fully-wetted bodies including hydrofoils and circular/elliptical cylinder. Excellent agreements are obtained when numerical predictions are compared with other available experimental and numerical results. In addition, it is found that using the power-law preconditioner significantly increases the numerical convergence speed.

论监察“责令候查”措施的功能定位、构设维度和价值目标

责令候查措施作为2024年修改的《监察法》增设的监察强制措施,旨在通过轻微限制被调查人的人身自由以保障监察程序的顺利进行。在监察制度中,应将责令候查措施定位为一种非羁押性监察强制措施和监察调查手段,从完善监察强制措施体系、实现监察调查权和保障被调查人权利三个维度进行制度构设,并以加强人权保障、推进程序顺畅和优化流程衔接作为其应然价值目标。

新型占取、大空间与战争类型的转变——施米特基于空间结构要素的新国际法秩序构想

施米特反对普遍主义抽象国际法和世界一体化,他以具体秩序范式下占取、空间秩序和战争类型三个概念为基础,阐释了现代国际法秩序的诞生和危机,随后又以之为线索,提示了新国际法秩序的三种构建路径。首先,以考察陆海之外天空的控制及影响为前提,探讨了两种新型占取场域——工业和宇宙空间,寄望于通过新型占取达成新的空间结构均衡。其次,在国家和世界一体化之间,提出新政治实体和国际法主体——大空间概念。大空间之间的力量均衡构筑起新的空间结构均衡,促成新的大空间多元秩序。最后,强调实际敌人和政治性概念,以敌意理论转变的深刻理解为前提,期望在新型敌友划分中具体而明确地区分敌友。

从“经济基础”到“经济秩序”:埃利希对马克思法律思想的继承与批判

尽管马克思本人没有直接建构一种完整的法社会学理论,但他的思想对法社会学产生了深远影响。作为现代法社会学的创始人之一,埃利希的思想与唯物史观之间存在着复杂而又深刻的关系。虽然其“活法”思想与唯物史观的基本原理十分相似,埃利希亦高度赞扬了马克思的理论贡献,但为了规避阶级分析方法,突出法律的能动作用,他使用了“经济秩序”而非“经济基础”来描述经济和法律的关系。埃利希认为,法律作为维护社会秩序的重要规范,对经济秩序的形成和发展具有重要作用,保护了社会大众而非仅仅统治阶级的利益。不难看出,埃利希用“经济秩序”取代“经济基础”的努力从一开始就建立在对马克思的“误读”之上。马克思看到了法律对经济基础的反作用,更重要的是,私法作为法律体系的重要组成部分,向来与经济基础密切相关。因此,只要身处唯物史观的分析框架下,资产阶级法律便无法摆脱其阶级“烙印”。

一种改进的Power-Law检测器在突发信号检测中的应用

根据短时突发通信信号的特点,提出了一种改进的基于高阶谱的power-law检测器。该方法利用高斯噪声和通信信号的高阶统计量存在较大差异的特点,对传统power-law检测器进行了改进。仿真结果表明,基于高阶谱的power-law检测器对短时突发通信信号的检测效果优于传统的基于DFT的power-law检测器。

基于扩展高阶滑模扰动观测器的PMSM终端滑模控制

针对永磁同步电机采用传统滑模控制存在转速误差收敛速度慢以及抖振严重的问题,提出了一种基于扩展高阶滑模扰动观测器的PMSM终端滑模控制。首先,设计了一种自适应趋近律与积分终端滑模,二者结合设计出自适应积分终端滑模速度控制器,提高了系统误差全局收敛速度并削弱抖振。其次,为提高观测器观测精度与动态响应速度,设计了一种扩展高阶滑模扰动观测器以实现控制器的外部扰动补偿。最后,通过仿真结果对比,来证实本文所提方法有效抑制了系统抖振,提高了系统误差收敛速度和鲁棒性。

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Extended optimal guidance law with impact angle and acceleration constriants

The extended optima straints of miss distance and Schwartz inequality. To reduce guidance law with terminal conmpact angle is derived by the terminal acceleration and eliminate gravity disturbance absolutely, the object function, which designs the weight of control command to be the power function of time-to-go＇s reciprocal, is given. And the gravity is considered when building the state equation. Based on the parsing express of the guidance command change with varying time and adjoint system analysis method, the command characteristics and the non-dimensional miss distance of the guidance law are analyzed, a design principle of guidance order coefficients is discussed. Finally, based on the requirement of engineering, the method to calculate the guidance condition and maximal required acceleration of the guidance law is given. The simulation demonstrates that not only the guidance law can satisfy the terminal position and impact angle constraints, but also the terminal acceleration can be converged toward zero, which will support a good situation for the terminal angle of attacking control.

Adaptive fuzzy synchronization for a class of fractional-order neural networks

In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as synchronization errors, are employed to approximate the unknown nonlinear functions. Based on the fractional Lyapunov stability criterion, an adaptive fuzzy synchronization controller is designed, and the stability of the closed-loop system, the convergence of the synchronization error, as well as the boundedness of all signals involved can be guaranteed. To update the fuzzy parameters, fractional-order adaptations laws are proposed. Just like the stability analysis in integer-order systems, a quadratic Lyapunov function is used in this paper. Finally, simulation examples are given to show the effectiveness of the proposed method.

法域协调视角下生成式人工智能产物涉知识产权问题研究——以ChatGPT为例

人类情感的表达是人类器官独有的自然反应,而并非是某种规则的产物。作品的认定应当包含作者的情感表达。现阶段的生成式人工智能并不具备情感表达能力,只是智能化程度更高的弱人工智能产品。其自身无法承担侵权责任,其生成物并不属于作品。随着科技的不断发展,带有情感的生成式强人工智能产品终有一天会被设计并投入使用,应对相关法律提前进行完善,以满足生成式强人工智能自身能够承担责任的需要。为了保证法律完善的顺利进行,应当坚持政策导向,并遵守法秩序统一性原则。具体完善路径包括:第一,肯定生成式强人工智能作为作者与被侵权人的主体地位;第二,应当明确生成式强人工智能在刑法上的地位,肯定其既可能成为刑法的犯罪主体,也能成为刑法中的被害人;第三,为生成式强人工智能设置专属的处罚方式。