Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics

This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.

Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet

In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.

Chaos control of gear system with elastomeric web based on multi-parameter multi-step method

This paper employs a multi-parameter multi-step chaos control method, which is built up on the OGY method, to stabilize desirable UPOs of a gear system with elastomeric web as a high-dimensional and non-hyperbolic chaotic system, and the analyses are carried out. Three types of relations between components of a certain control parameter combination are defined in a certain control process. Special emphasis is put on the comparison of control efficiencies of the multi-parameter multi-step method and single-parameter multi-step method. The numerical experiments show the ability to switch between different orbits and the method can be a good chaos control alternative since it provides a more effective UPOs stabilization of high-dimensional and non-hyperbolic chaotic systems than the single-parameter chaos control, and according to the relation between components of each parameter combination, the best combination for chaos control in a certain UPO stabilization process are obtained.

涉数据形态财产权益纠纷裁判方法论

数据形态财产权益既包括独立的数据本身财产权益,也包括知识产权和网络虚拟财产等数字化的“特定财产权”。处理数据行为可能同时侵害数据本身财产权益及数据承载的其他“特定财产权”,并产生民事(请求权)责任竞合。涉数据形态财产权益保护的民事案件在客体属性、权利限制、责任构成要件等法律适用方面兼具共性与差异,可在比较辨析基础上梳理类案审理思路和裁判规则。司法实践中,需要甄别不同数据形态财产权益的特征,界定数据处理行为的性质,准确适用相应的法律规范,平衡权利保护与限制的边界,明确责任竞合时的处理原则,依法保护市场主体合法权益与市场竞争秩序。

马锡五审判方式的精髓及其现代启示——以互联网为视角的分析

当前,智慧司法的创新与完善已经成为司法新业态,以云计算、大数据、人工智能等现代技术为核心的智慧法院建设如火如荼。然而,数字化背景下带来的技术风险焦虑和技术风险冲击也给司法实践带来了诸多挑战。马锡五审判方式是陕甘宁边区时期新民主主义司法制度改革的产物,在新时代继承和发展马锡五审判方式,挖掘其优良司法的精髓,并与数字司法相结合,创建“互联网+马锡五审判方式”的新机制,赋予马锡五审判方式以时代生命力。

Forecasting available parking space with largest Lyapunov exponents method

The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method.

Optimized Hybrid Block Adams Method for Solving First Order Ordinary Differential Equations

Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.

挑战与路径:司法裁判如何回应新兴权利

司法裁判领域的新兴权利,不属于法定权利类型,而是当事人就自身利益诉请法院认可的要求或主张。法官裁判新兴权利案件,面临法无明文规定之难题,这与抽象普适的成文法、不断涌现的新兴事物、积极活跃的权利观念密不可分。法官不得拒绝裁判,应致力于在解决矛盾纠纷的基础上,识别、判断及保护合理正当的新兴权利,注重司法裁判说理,及时回应公民寻求公力救济新兴权利的正当期待。由此,法官裁判案件,应准确定位新兴权利,科学运用裁判方法,追求实现个案正义。

法律解释方法在民事裁判中的运用——以弘扬社会主义核心价值观典型民事案例为例

“法无解释,不得适用。”审判实践中,法官需要通过解释法律将一般规则应用于具体个案,法律解释方法的正确选择与运用不仅是解释结果合法性与正当性的前提,也是民事裁判达至法律效果与社会效果相统一的重要保障。实践中仍存在因法律解释方法运用不当而导致裁判说理不充分、裁判结果不公正的现象。通过对弘扬社会主义核心价值观典型民事案例中法律解释方法的运用进行分析,能够更直观地发现问题并予以针对性改善,从而推动社会主义核心价值观更好融入裁判文书释法说理。

法律方法及其运用

法律方法近几年来逐渐在我国法学界和实务界引起重视,究其原因,是其对法治所具有的积极推动意义。法官只有借助于各种法律技术和法律解释方法,才能把成文法和司法有机地结合起来,从而疏通由法律规则到个案判决的转换过程。综合来看,可以将法律(解释)方法分为四类:狭义的法律解释方法、法律漏洞补充方法、不确定概念的价值补充、利益衡量。面对模糊不清的法律,一般来说,应按照文义解释、论理解释、比较法解释和社会学解释的先后排序,考虑各种狭义解释方法的运用;对于存在空缺结构的法律,需要运用法律漏洞补充方法;对于不确定的概念,则要进行价值补充;在以上各种方法的运用中,可以综合进行利益衡量。在我国当前国情下,重视法律方法的运用对于法官判案有着极其重要的推动作用。

著作权行政保护的完善

明确著作权行政保护手段的法律属性,是完善行政保护的前提,现行行政保护手段主要有行政检查、行政强制措施、行政裁决、行政处罚和行政命令等。通过在著作权法和单行法中增加行政处罚的种类、明确处罚主体和处罚行为等,可以提高执法效率并有效遏制规模化的侵权行为;通过规范行政裁决的立案条件和民事诉讼证据规则的准用,可以平衡各方利益主体的权益,而合理规范行政裁决的救济途径,则可有效提高司法效率。

宋代的法律方法论——以《名公书判清明集》为中心的考察

宋代名公们的断案模式大致属于法律论证模式,经常运用的法律方法主要有演绎论证、类比论证以及价值衡量等。与西方法律论证方法相比,这些论证方法虽然形式方面不及西方的逻辑,但却有着"学理的基本,而没有形式的累赘"。由于中国传统思维方式带有整体性特点,因此,中国传统的法律思维模式也带有整体性特点,具体表现为整体论的法律观、整体论的司法观以及整体论的法律方法论。这种整体性的思维模式与西方的分析性思维模式相比,并不显得落后,也不是"不合逻辑的"。

司法裁判正当性来源的法理追问

公民不愿服从裁判的现实使得有必要追问司法裁判正当性的来源,而传统的理论对这一问题已经丧失了解释力。比如,神意论已经随着人类认识能力的提高淡出了历史舞台;民主立法论之于裁判正当性,不是文不对题,就是大而不当。程序正义对于维系裁判的正当性不可或缺,具有某种“通过程序的正当化”的功能,但程序正义充其量只是提供了裁判操作的空间。法律方法从技术上关切实质正义。程序正义与法律方法是兼容互助的,程序正义为法律方法的运用提供了制度化的形式公正空间,法律方法从技术层面上论证着裁判的实质公正,弥合了程序正义的内在空洞性。

量刑方法论——从对传统观念的检讨与批判谈起

对犯罪人裁量决定刑罚是刑事审判中重要的环节,事关对司法活动公平与正义的评价。而正确把握量刑的方法,对做到“罚当其罪”和“罪刑相适应”至关重要。从传统观念的检讨与批判谈起,论述量刑的理念、原则、方法和因素,并在量刑的步骤和方法上提出见解。

基于多步裁定法评估编队超视距空战效能

提出了评估编队歼击机超视距空战效能的多步裁定法。用损失交换比和剩余飞机数量作为效能指标,将最优火力分配与空空反导弹引入到多步裁定模型中。考虑了电子对抗与飞机生存力,计算了歼击机领先发射概率、空空导弹击毁概率和发射次数。算例表明,领先发射一方超视距空战效能通常较高,滞后发射一方若采用最优火力分配、空空反导弹、电子对抗及提高飞机生存力等措施也可提高超视距空战效能。此模型计算简便,合理有效。

司法方法论的若干问题思考——以规范与事实之间的关系为视角

司法方法,即司法适用的方法,主要是指司法裁判方法。司法适用过程,是将法律与事实有机结合,确定案件处理的司法效果过程。在这个过程中,如何判断规范与事实之间的关系;判断两者的相互一致性或符合性的程度;根据事实与法律的有机联系,确定案件的司法效果的推理方式;以及对这一司法效果结论的论证等,无疑是司法方法论的基本问题。正确认识司法方法与法律方法之间的关系,是法律方法研究的重要课题。

目标分配在超视距空战效能中的应用研究

将目标分配引入到两步裁定法的效能研究之中。首先根据空战态势评估双方战机的易损性;然后根据易损性确定双方战机的先敌发射率;继而综合先敌发射率和导弹杀伤概率等因素来确定空战中每一架战机个体的被毁伤概率,结合约束条件得到超视距空战模型。给出一种基于Memetic算法的目标分配求解方法,该算法分别用离散差分进化算法和邻域搜索算法来进行全局和局部搜索。在收敛速度方面同离散差分进化算法进行了比较,最后通过仿真验证了该方法的合理性和有效性。

重提马锡五审判方式的时代意蕴

马锡五审判方式在民事审判的实践和立法中历经起伏。重提马锡五审判方式,应主要从当下的时代意蕴去思考。重提马锡五审判方式反映了社会对于司法正当性的需求,而司法需求又有阶段性、适域性、异存性的特点。把握司法需求要考虑其所处法治时代的特征:熟人社会时代向熟人社会、陌生人社会并存时代的演进;法律创制主导时代向法律创制、法律改进、司法并重时代的演进。司法改革要从司法本身和司法之外对待司法正当性。

《民事诉讼法》第六十四条第一款及相关规定的解释方法——从中国民事审判方式改革的实践出发

《民事诉讼法》第64条和《关于民事诉讼证据的若干规定》第2条是关于举证责任的规定。中国民事审判方式改革实践过程中,恰逢外国举证责任理论的引进。外国理论与中国实践的结合,悄然引发了举证责任解释方法的摇摆不定,直接导致司法实践的迷惑。理论的产生有其本土起源,举证责任作为民事诉讼的脊梁,这种先天特性,决定了其解释方法首先要从中国本土出发,从中国民事审判方式改革的背景入手。

规范出发型民事审判思维方法在借款担保纠纷中的具体运用

"审判思维方法"是作为法律直接实施者的法官为达到裁判案件之目的,在案件审判思维活动中所凭借的途径、手段和办法。科学的审判思维方法有助于促进公正和高效司法,有助于法官素质的提升和法学研究的深入,更有助于保障民主政治和市场经济的发展。笔者倡导在我国构建系统的从规范出发的民事审判思维方法,并通过借款担保合同纠纷案例具体解析此种思维方法在实务中的运用。