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].

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.

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.

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.

Conservation Laws and Soliton Solutions for Generalized Seventh Order KdV Equation

With the assistance of the symbolic computation system Maple,rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonlinear evolution equation by using a direct algebraic method.From the compatibility conditions that guaranteeing the existence of conserved densities,an integrable unnamed seventh order KdV-type equation is found.By introducing some nonlinear transformations,the one-,two-,and three-solition solutions as well as the solitary wave solutions are obtained.

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.

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.

Infinite Sequence of Conservation Laws and Analytic Solutions for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation in Fluids

在这份报纸，为在液体的一个概括可变系数的第五顺序的 Korteweg-de Vries 方程的能量守恒定律的一个无限的序列基于 B 被构造 ? cklund 转变。Hirota 双线性的形式和符号的计算被使用获得三种答案。可变系数能影响典型的线的保存密度，联系流动，和外观。soliton 结构上的波浪数字的效果也被讨论并且 soliton 结构打字，例如，双 periodic soliton，平行 soliton 和 soliton 建筑群，被介绍。

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.

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.

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.

论未来刑法学的十大着力点

刑法教义学是随着刑法的立法和司法不断向前发展的,在我国法治现代化的建设中,刑法理论对法治现实的指导意义得以彰显。本文根据我国刑法教义学的理论研究现状,对未来刑法学研究的十个重点问题进行了论述。这十个问题既包括刑法方法论等理论问题,也包括正当防卫、单位犯罪和共同犯罪等刑法总论问题和法定犯、财产犯和秩序犯等刑法各论问题,基本上涵盖了刑法理论的各个重要内容,对于我国刑法教义学的未来发展起到了路线图的作用。

数据产权刑法保护模式的构建

数据产权是一种具有财产权属性的新型权利,该权利与虚拟财产权和知识产权具有明显差异。数据产权属于刑法保护的公法益范畴,其应归属于市场经济秩序法益之中。现行刑法有关财产犯罪、知识产权犯罪和数据犯罪的规定均无法实现对数据产权的全面保护。刑法对数据产权的保护应以促进数据流通为主要目标,且应当覆盖数据处理的各流程阶段。对侵犯数据产权行为进行刑法规制时,应对“未经同意”获取数据行为审慎入罪。应增设妨害数据流通管理秩序罪,对“情节严重的”妨害数据流通管理秩序行为予以刑法规制。

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。

“平台”与我国县域基层法治秩序的生成——浙江海宁社会治理实践的观察

基层社会治理“平台”是我国县域范围构建具有中国特色法治秩序的重要实践形式。在提升县域基层社会治理水平的过程中,平台被打造成一个由不同政府机构、不同社会组织与社会成员通过协调、协商、议论等方式博弈以解决与民生密切相关的各种类型问题的工作机制,客观上已经助力生成了法治秩序不可或缺的不同主体之间展开话语交流的公共空间。在浙江海宁,平台被用于促进实现公众与企业合法权利、改造和规范行使公共权力、保障社会稳定与居民安居乐业,以公开促公正公平,有效提升了法律在基层的实施能力。在法治建设正在寻求新的突破之际,有关平台建设的实践具有一定的可借鉴的普遍意义。

“以规则为基础的国际秩序”之批判

“以规则为基础的国际秩序”的产生可以追溯到以美国为主导的自由主义国际秩序的兴起,并因其政治属性而受到诸多国家推崇。理论上,“以规则为基础的国际秩序”存在效力的不确定性、适用范围的模糊性以及制度霸权的特征。实践中,“以规则为基础的国际秩序”所展现出的是一种双重的评判标准。南海仲裁裁决以及我国加入世界贸易组织时的替代国条款,这两个实例都揭示了“以规则为基础的国际秩序”中的制度霸权与压制异己属性。推崇规则之治实为意图不遵守国际法,削弱国际法在国际秩序中的权威。中国倡导“以国际法为基础的国际秩序”,并在国内法治建设过程中将国际法纳入考量,在参与全球治理实践中积极践行国际法之治。

习近平法治思想中的“大变局”应对方略论

“大变局”应对方略是习近平法治思想立足于“百年未有之大变局”的科学论断,针对积极应对世界大变局的现实需要所彰显之实效导向型共识。其作为一种凸显执行性遵守之行动整合的共同准则与依据,往往围绕建立健全涉外法治体系和营造国际法治新秩序这两种应对方略而具体展开。法治体系应对方略主要表征为建立健全涉外法治体系的原则表达、目标设定与核心要素,法治秩序应对方略则主要表征为营造国际法治新秩序的目标设定、方案要义与路径导向。基于此,全面梳理习近平法治思想中的“大变局”应对方略样态,能够为涉外法治工作的有效推动提供系统的类型化指引。