A generalized Weyl-Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators

By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.

RESEARCHES ON INVERSE ORDER RULE FOR WEIGHTED GENERALIZED INVERSE

The weighted generalized inverses have several important applications in researching the singular matrices,regularization methods for ill-posed problems, optimization problems and statis- tics problems.In this paper we further research inverse order rules of weighted generalizde inverse. From the view point of munerical algebra, the different methods we used in inverse order rules pro- vide beneficial means for theory and computing of generalized inverse matrices.

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

Counterexample of Local Fractional Order Chain Rule and Modified Definition of Local Fractional Order

Fractional calculus is a powerful tool for modeling nonlinear systems.It is necessary to discuss the basic properties of fractional order before solving a fractional order model.Using the formula of power function defined by local fractional derivative and the chain rule to calculate a compound function,the results are inconsistent.This shows that the chain rule of local fractional derivatives similar to classical calculus is suspicious,and fractional complex transformation based on the chain rule is also suspicious and needs further discussion.In order to overcome this inconsistency,an improved definition of local fractional derivative,which can be regarded as a fractal derivative,is proposed based on the results derived from the relationship between the mass function and the Hausdorff measure.

Decomposition Theorems for Semi-order Fuzzy Supermartingales and Submartingales

Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.

Challenges and Rules in Third Age of Space

As the space gradually becomes a multi-polar and industrialized battlefield, we human beings are entering Space 3.0. In this new era, existing international rules on space arms control can no longer effectively address increasing security risks such as arms races, armed conflicts, collisions of space objects and competition for space resources. We need more than ever to achieve consensus on space security in the new era to build new space security order.

Rule Ordering in Uvwie

One of the assumptions underlying theories of phonological derivation is that the phonological architecture of any language consists of,at least,an abstract underlying form,its surface form and conditions which derive the surface form from its underlying form.It is further assumed that the conditions are serially ordered in frameworks which subscribe to the rule ordering such as orthodox generative phonology and lexical phonology.In the present study,these issues are engaged in the case of Uvwie.In particular,the study seeks to investigate the conditions(processes and rules)which derive surface forms from their corresponding underlying forms,and the order in which they apply.Thus the study will examine the different well-motivated phonological rules attested in the derivation of Uvwie formatives,and provide evidence for the order in which the processes apply.The study employe data documented in Ekiugbo(2016),and couched its analysis within rule ordering principle of generative phonology.The study identifies six rules,which are ordered thus:nasal assimilation>glide formation>vowel elision>tone fusion>vowel lengthening>consonant elision.

O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

On the Caginalp for a Conserve Phase-Field with a Polynomial Potentiel of Order 2<i>p</i>- 1

Our aim in this paper is to study on the Caginalp for a conserved phase-field with a polynomial potentiel of order 2p - 1. In this part, one treats the conservative version of the problem of generalized phase field. We consider a regular potential, more precisely a polynomial term of the order 2p - 1 with edge conditions of Dirichlet type. Existence and uniqueness are analyzed. More precisely, we precisely, we prove the existence and uniqueness of solutions.

Zipf’s Law, Benford’s Law, and Pareto Rule

From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.

High-Order BAM, Its Modifications and Performance Analyses

Based on Tai’ s high - order bidirectional associative memory ( HOBAM) and Stmposon’ s intraconnected BAM (IBAM) , two Improved models are first presented and discussed in this paper. The improved models not only retain the advantages of both HOBAM and ISAM but overcome the shortcomings of Kosko’ s BAM also. Secondly their recall stabilities in synchronous and asyn-chronous update modes have been proven by defining corresponding energy functions which decrease as the re-call process proceeds such that the systems can ensure all the training pattern pairs to become local minima of the energy surfaces. Finally with signal - to - noise ratio (SNR) approach, we show that their storage capacities and error correction capabilities are better than that of the HOBAM.

“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。

乡村社会“三治融合”的实践逻辑——基于社会基础视角的分析

通过自治、法治与德治相融合以实现乡村善治是具有中国特色的社会治理实践。借助社会基础的视角,可以深化对乡村“三治融合”实践逻辑的认识与理解。在结构转型背景下,乡村社会基础的变化会制约自治、法治与德治的作用发挥与相互融合。多地乡村通过机制创新来利用乡土熟人社会的资源,增强对个人行为的引导和约束,扩大乡村治理的社会参与,从而激活和培育了新的社会基础。凭借社会基础的支持与保障,法律和道德实施获得充分的社会助力,乡村社会内生秩序的维系和生产能力也得以增强。对于乡村“三治融合”实践探索的分析,揭示出激活和培育社会基础对实现乡村善治的重要意义,此外还需要注重法治的规范、引领与保障作用。

基于关联规则数据挖掘的Apriori算法应用分析

基于关联规则的数据挖掘主要用于发现数据集中项目之间的联系。以Apriori算法为核心,利用店铺在线订单作为数据载体,深入挖掘顾客购买商品的历史记录,探究商品之间的关联性。通过分析这些关联规则,商家可以更精准地了解顾客的购物喜好和行为模式,从而制定出更具针对性和实效性的营销策略,有效提升商品的销售业绩。

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。

“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。

粤港澳大湾区规则衔接的实践审视与路径优化

粤港澳大湾区建设具有双重意涵和定位,在经济层面旨在实现要素高效有序流动,同时型构动态综合体系化的三圈层法治秩序。《粤港澳大湾区发展规划纲要》发布五年来,规则衔接从多个维度出发,综合运用多种方式于多个领域内逐渐铺开,初步打破地区间壁垒,但仍存在未实质性打破行政壁垒、衔接缺乏融贯性、各地协同性不足,以及要素流动全链条衔接和湾区法治体系全面建构不足的问题,其根本原因为湾区间法治体系差异较大,主要原因是统筹协调不足导致规则衔接顶层设计缺失,直接原因则是体制机制不健全制约规则衔接的实效。粤港澳大湾区建设迈入纵深发展新阶段,宏观上应当以宪法为统领构筑湾区法治秩序,中观上应以全要素有序流动为具体标准构建规则衔接体系,并依托体制改革和微观机制创新达致规则衔接的根本突破。

一阶逻辑定理证明器中的无效子句删除策略

在一阶逻辑定理证明器中,子句预处理是不可或缺的步骤,而子句的消去规则是预处理中极其重要的部分。传统的基于纯文字规则的子句消去方法在理论上存在子句删除过多的问题,在算法实现上又存在子句删除不充分的情况。为了提高子句删除的精确率,在理论上,基于纯文字规则对子句进行再分类。第一类称为无效子句,该类子句不能通过等词替换与某个子句形成互补对,此类子句应完全删除;第二类为相对无效子句,该类子句无法与当前子句集中的子句形成互补对,但能进行等词替换,此类子句应在参与演绎后综合考虑是否删除。在算法实现中,考虑到子句的消去应是动态的过程,当前消去的子句会影响已判断的子句的无效性,提出一种用于判定子句无效性的递归遍历算法。将上述子句约简规则应用于证明器CSE1.5(Contradiction Separation Extension 1.5)中,以2019—2022的CADE(Conference on Automated DEduction)自动定理证明(ATP)系统竞赛中一阶逻辑问题组为测试对象。在300 s内,应用所提算法的CSE1.5_IC比原始CSE1.5总共多证明了27个问题。在两个版本证明器共同证明的所有FNE(FOF theorems without Equality)测试例中,CSE1.5_IC比CSE1.5平均每个问题多约简了28个子句,平均求解时间减少了7.07 s。实验结果表明,所提无效子句约简算法是一种有效的预处理方式,能够提高一阶逻辑子句集的约简精确率,同时能够提高自动定理证明器的证明能力和缩短证明时间。

基于间隔模型的图-库-规则-操作票自动生成方法

现有的变电站防误操作系统和调控防误操作系统中手工生成一次设备接线图、一次设备属性、防误规则,手工开列操作票的方式费时、费力,不符合用户对自动化系统的要求。提出了基于间隔模型的图—库—规则—操作票自动生成方法。建立了包含典型一次间隔和典型二次间隔的典型间隔模型,基于该模型分别介绍了一次设备接线图—库自动生成、防误规则自动生成、操作票自动生成的方法。开发了图—库—规则自动生成和操作票自动生成软件,研究成果已得到工程应用。