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.

LOCAL SOLVABILITY OF THE CAUCHY PROBLEM OF A FIFTH-ORDER NONLINEAR DISPERSIVE EQUATION

The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.

A realistic model for complex networks with local interaction, self-organization and order

In this paper, a new mechanism for the emergence of scale-free distribution is proposed. It is more realistic than the existing mechanism. Based on our mechanism, a model responsible for the scale-free distribution with an exponent in a range of 3-to-5 is given. Moreover, this model could also reproduce the exponential distribution that is discovered in some real networks. Finally, the analytical result of the model is given and the simulation shows the validity of our result,

New solutions from nonlocal symmetry of the generalized fifth order KdV equation

The nonlocal symmetry of the generalized fifth order KdV equation(FOKdV) is first obtained by using the related Lax pair and then localizing it in a new enlarged system by introducing some new variables. On this basis, new Ba¨cklund transformation is obtained through Lie’s first theorem. Furthermore, the general form of Lie point symmetry for the enlarged FOKdV system is found and new interaction solutions for the generalized FOKdV equation are explored by using a symmetry reduction method.

Existence and Uniqueness of Solution for a Fractional Order Integro-Differential Equation with Non-Local and Global Boundary Conditions

In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1].

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.

On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation

In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.

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.

地方法规范的“飞出”适用

国家通过行政区划制度实现了对国土空间的有效治理,但形成了行政壁垒和区域发展不平衡。“飞地经济”推动了国土动态空间的重构,需要具有竞争力的管理制度溢出和良法的“飞出”适用。在民商事领域,可以通过冲突法及法律选择制度解决地方法规范的跨界适用。地方行政法规范“飞出”适用的基本规则是“协议—批准”。基于公私法的划分、国家结构形式和地方治理制度,“协议—批准”的实现形式存在差异。在实行普通法制度的联邦制国家,联邦成员可以按民商事冲突法及其意思自治原则,约定其行政法规范的“飞出”适用。实行单一制的国家(联邦成员)除了个别共同法外,对地方行政法规范的“飞出”适用都实行批准制度,包括批准“准据法”、批准行政区划拟制和批准委托管辖制度。无论公私法是否存在分野,地方主体都可以协商约定“飞地经济”的行政管辖权,但自治地方具有更强的自主能力。在实行地方自治的情况下,约定“飞地经济”的行政管辖权多由本级或中央民意机关批准,有的甚至需要行政机关和民意机关的双重批准。行政管辖权是一种实施法律的公权力,它的溢出意味着地方法规范的“飞出”适用。

祖坟之争:清水江下游地区的居住正统性与地方秩序建构

一起争夺祖坟的案件引发我们对清水江下游地区复杂人群关系的探究。明清时期的清水江下游地区,围绕着木材的种植与经营活动,世居乡民与外来移民在这一区域内不同村寨内展开了一场合作与争竞并存的长期互动过程,形成了此区域内不同人群交往活动的极具地方特色的历史表达。对于“起源优先”原则的强调正是对于“居住正统性”的诉求,也体现了这一区域社会内的地方秩序的具体样态。

改进人工势场法解决局部最小值路径规划研究

当移动机器人在行进过程中使用传统人工势场法(artificial potential field method, APF)进行路径规划时,通常会陷入局部最优困境,无法顺利到达目标点。为解决这一问题,首先,对APF算法规划路径失败原因进行分析,其次设置情况判断条件,判断当机器人陷入局部最小值时,通过在合适位置增加临时引导点的方法,引导其跳出局部极小值点;其次,引入分数阶微积分思想方法结合APF算法,提出混合阶次的分数阶梯度下降法进行位置信息迭代,优化算法的收敛速度和收敛精度;最后,用MATLAB软件对该方法进行仿真,实验结果表明提出的方法可以有效解决局部最小值问题,而且在速度、精度上都有明显的提高,且能适应较为复杂的多障碍物环境,验证了改进方法的有效性、正确性。

基于参数化降阶模型的非线性气动弹性高效分析

针对非线性气动弹性分析时需要在时域求解多个流场参数条件下结构运动方程而造成的计算消耗过大的问题,提出了一种适用于参数变化时非定常流场高效计算的参数化降阶模型,不仅可以应用于计算机翼等结构的总体气动力还可以得到每个时刻的结构表面的流场数据分布,并成功应用于典型机翼的跨声速颤振边界的计算,大大地提高了计算效率.结果显示,单流场条件时降阶模型的计算速度比直接使用时域分析方法提高了3倍;在计算多流场参数条件下,参数化降阶模型相比于使用单流场降阶模型计算速度提高了3.5倍,相较于时域分析方法提高了10倍.

Variations of water's local-structure induced by solvation of NaCl

The researches on the structure of water and its changes induced by solutes are of enduring interests. The changes of the local structure of liquid water induced by NaCl solute under ambient conditions are studied and presented quantitatively with some order parameters and visualized with 2-body and 3-body correlation functions. The results show that, after the NaCl are solvated, the translational order t of water is decreased for the suppression of the second hydration shells around H20 molecules; the tetrahedral order （q） of water is also decreased and its favorite distribution peak moves from 0.76 to 0.5. In addition, the orientational freedom k and the diffusion coefficient D of water molecules are reduced because of new formed hydrogen-bonding structures between water and solvated ions.

复调与回声:从《芙蓉镇》看新时期乡土小说的饮食书写策略

《芙蓉镇》作为20世纪80年代乡土伤痕小说的代表作,借助在场性观照与具身化解读的方式,直观且深刻地描绘出原乡社会在不同历史时期的秩序结构与发展态势。饮食书写是文学作品中最为常见的书写方式,以饮食书写隐喻社会生活也是常被使用的创作手法。从饮食书写的角度窥探这一时期以《芙蓉镇》为代表的乡土小说,能够梳理出关于乡土秩序更迭的“复调”与“回声”式书写策略;通过饮食书写展露乡村社会在传统伦理秩序与革命秩序不断更迭中的呈现状态,也寄寓着世俗伦理价值向度中对于原乡秩序肯定与颂扬的态度。

差序格局视域下民办社工机构参与乡村社区治理的过程与路径研究

乡村社区治理是我国基层治理的重要组成部分。民办社会工作服务机构通过发挥政治、专业以及地缘优势成为乡村社区治理的有效载体。在差序格局视角下,民办社会工作服务经历主动建立信任关系—重构社会支持网络—构建乡村社区共同体的治理过程,并提出中国特有乡土关系的特征下民办社会工作服务机构参与乡村社区治理的有效路径。

基于EOE_LMD和阶次跟踪分析的变转速轴承故障诊断

振动信号分析是轴承故障诊断中的重要技术手段之一。变转速工况下的滚动轴承振动信号是典型的非平稳信号,并且在转频变化较小的工况中还存在噪声干扰的问题,使传统的时频分析技术难以应用。为解决该问题,提出了一种基于经验最优包络(empirical optimal envelope,EOE)的局部均值分解(local mean decomposition,LMD)和采用分段线性插值的计算阶次跟踪(computing order tracking,COT)算法相结合的故障诊断方法。首先,确定低通滤波器的截止频率和滤波阶数,对滚动轴承振动信号进行滤波,并对滤波后的包络信号进行COT,以获得角域平稳信号。然后,利用EOE_LMD对重采样后的平稳信号进行处理,得到若干乘积函数(product function,PF)分量。最后,通过计算各分量的信息熵和相关系数,选取合适的分量进行阶次分析,以判断变转速滚动轴承的故障类型。结果表明,该方法可以消除转速波动对故障特征提取的影响,在不同转速变化条件下对滚动轴承具有良好的故障诊断能力。

局部超二次二阶哈密尔顿系统周期解的多重性

运用对称山路引理研究一类二阶哈密尔顿系统在局部超二次条件下周期解的多重性问题.得到了系统的能量泛函的无穷多个临界点.在此局部超二次条件下,二阶哈密尔顿系统有无穷多个周期解.

2维薛定谔方程的一种高精度紧致差分格式

该文对2维薛定谔方程利用局部一维化方法,将2维方程分裂为x、y方向的2个1维薛定谔方程,然后采用6阶紧致格式的离散方法来处理空间变量的2阶导数项,将薛定谔方程转化为一个常微分方程组.通过L-稳定Simpson方法对上述空间离散化得到的常微分方程进行离散化,得到了一种具有空间6阶精度和时间3阶精度的格式,并证明了该格式无条件稳定性.并通过数值模拟和对比方法验证了格式的有效性.