Conformal invariance for nonholonomic system of Chetaev’s type with variable mass

Conformal invariance and conserved quantities for a nonholonomic system of Chetaev’s type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obtained to make the system’s conformal invariance Lie symmetrical. The conformal invariance of the weak and strong Lie symmetries for the system is given. The corresponding conserved quantities of the system are derived. Finally, an application of the result is shown with an example.     

Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism

In the context of the covariant teleparallel framework, we use the 2-form translational momentum to compute the total energy of two general spherically symmetric frames. The first one is characterized by an arbitrary function H(r), which preserves the spherical symmetry and reproduces all the previous solutions, while the other one is characterized by a parameter ξ which ensures the vanishing of the axial of trace of the torsion. We calculate the total energy by using two procedures, i.e., when the Weitzenböck connection Γ_α^β is trivial, and show how H(r) and ξ play the role of an inertia that leads the total energy to be unphysical. Therefore, we take into account Γ_α^β and show that although the space×we use contain an arbitrary function and one parameter, they have no effect on the form of the total energy and momentum as it should be.     

A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system

A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied.Under the infinitesimal transformation of the groups,from the definition and the criterion of Mei symmetry,a type of structural equation and conserved quantity for the system by proposition 2 are obtained,and the inferences in two special cases are given.Finally,an example is given to illustrate the application of the results.     

Symmetry of Lagrangians of holonomic nonconservative system in event space

This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result in the end.     

Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians,namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton principle based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler–Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established.The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both classical and discrete cases are given. Finally, an example in Friedmann–Robertson–Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.     

装配型企业订货量分配与订单排产联合决策研究

针对供应商交货数量不确定环境下,多品种小批量装配型制造企业因生产物料不配套造成生产计划不可行甚至客户订单拖期的问题,从企业运作整体出发,考虑订货量分配决策对订单生产和交货的影响,以最小化采购成本和最小化订单排产相关成本为优化目标,在允许零部件拖期交货且供应商提供拖期价格折扣条件下,建立订货量分配与订单排产联合优化模型。针对可行解空间巨大、传统数学规划方法难以求解的问题,从增强搜索性能角度出发,设计基于自定义邻域搜索算子的局部搜索机制和基于随机与种群重构变异机制的改进粒子群算法的模型求解策略。通过应用实例对本文模型和算法进行了有效性验证和灵敏度分析,结果表明,相比于传统的分散决策方案,本文模型能够有效降低整体成本水平,引入的改进机制能够显著提升算法搜索性能,为企业供应风险下的运营决策制定提供理论参考。     

用子波分析修正检测壁湍流猝发的VITA法

应用壁湍流脉动速度信号子波分析的一系列方法对检测壁湍流猝发事件的VITA法进行了修正。其中,用能量最大准则确定VITA法短时间平均周期;以子波变换能量最大尺度脉动速度的短时间平均方差的局部极大值点作为检测函数的中心点,取代了传统VITA法中对短时间周期平均方差选用门限值的方法,避免了VITA法检测结果对门限值的主观经验依赖性,提高了VITA法检测壁湍流猝发事件的客观性和准确性。     

关于两参数Birnbaum-Saunders疲劳寿命分布统计分析的2个注记

通过Monte-Carlo模拟说明目前用于求解两参数Birnbaum-Saunders疲劳寿命分布尺度参数的2种方法可能无法得到尺度参数的区间估计.进一步指出,在利用广义枢轴量法给出尺度参数以及参数函数的置信区间过程中存在错误,并用反例进行了说明,同时给出了正确的证明.     

Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives

In this paper, we present the fractional Hamilton's canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton's canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results.