A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems

We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico-electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.     

Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems

This paper studies the Hojman conserved quantity, a non-Noether conserved quantity, deduced by special weak Noether symmetry for Lagrange systems. Under special infinitesimal transformations in which the time is not variable, its criterion is given and a method of how to seek the Hojman conserved quantity is presented. A Hojman conserved quantity can be found by using the special weak Noether symmetry.     

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.     

Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation

In this paper,we consider the response analysis of a Duffing-Rayleigh system with fractional derivative under Gaussian white noise excitation.A stochastic averaging procedure for this system is developed by using the generalized harmonic functions.First,the system state is approximated by a diffusive Markov process.Then,the stationary probability densities are derived from the averaged Ito stochastic differential equation of the system.The accuracy of the analytical results is validated by the results from the Monte Carlo simulation of the original system.Moreover,the effects of different system parameters and noise intensity on the response of the system are also discussed.     

Noether’s theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by El-Nabulsi. First, the El-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and El-Nabulsi–Hamilton’s canonical equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second,the definitions and criteria of El-Nabulsi–Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of El-Nabulsi–Hamilton action under the infinitesimal transformations of the group. Finally, Noether’s theorems for the non-conservative Hamilton system under the El-Nabulsi dynamical system are established,which reveal the relationship between the Noether symmetry and the conserved quantity of the system.     

Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.     

Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic system of Chetaev’s type with variable mass

Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic, non-conservative system of Chetaev's type with variable mass are studied. The differential equations of motion of the Nielsen equation for the system, the definition and criterion of Mei symmetry, and the condition and the form of Mei conserved quantity deduced directly by Mei symmetry for the system are obtained. An example is given to illustrate the application of the results.     

On fractional systems with Riemann-Liouville derivatives and distributed delays – Choice of initial conditions,existence and uniqueness of the solutions

A comparative analysis among the possible types of initial conditions including (or not) derivatives in the Riemann-Liouville sense for incommensurate fractional differential systems with distributed delays is proposed. The provided analysis is essentially based on the possibility to attribute physical meaning to the initial conditions expressed in terms of Riemann-Liouville fractional derivatives. This allows the values of the initial functions for the mentioned initial conditions to be obtained by appropriate measurements or observations. In addition, an initial problem with non-continuous initial conditions partially expressed in terms of Riemann-Liouville fractional derivatives is considered and existence and uniqueness of a (1 ? α)-continuous solution of this initial problem is proved.     

Neutrino masses,leptonic flavor mixing,and muon(g−2)in the seesaw model with the U(1)Lμ-Lrgauge symmetry

The latest measurements of the anomalous muon magnetic moment a_μ≡(g_μ-2)/2show a 4:2σdiscrepancy between the theoretical prediction of the Standard Model and the experimental observations.To account for such a discrepancy,we consider a possible extension of the type-(I+II)seesaw model for neutrino mass generation with a gauged L_μ-L_rsymmetry.By explicitly constructing an economical model with only one extra scalar singlet,we demonstrate that the gauge symmetry U(1)L_μ-L_rand its spontaneous breaking are crucial not only for explaining the muon result but also for generating the neutrino masses and leptonic flavor mixing.Various phenomenological implications and experimental constraints on the model parameters are also discussed.     

Conductivity reconstruction algorithms and numerical simulations for magneto–acousto–electrical tomography with piston transducer in scan mode

Conductivities tomography with the interactions of magnetic field, electrical field, and ultrasound field is presented in this paper. We utilize a beam of ultrasound in scanning mode instead of the traditional ultrasound field generated by point source. Many formulae for the reconstruction of conductivities are derived from the voltage signals detected by two electrodes arranged somewhere on tissue＇s surface. In a forward problem, the numerical solutions of ultrasound fields generated by the piston transducer are calculated using the angular spectrum method and its Green＇s function is designed approximately in far fields. In an inverse problems, the magneto-acousto-electrical voltage signals are proved to satisfy the wave equations if the voltage signals are extended to the whole region from the boundary locations of transducers. Thus the time-reversal method is applied to reconstructing the curl of the reciprocal current density. In addition, a least square iteration method of recovering conductivities from reciprocal current densities is discussed.     

Noether symmetries of discrete mechanico-electrical systems

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.     

机电系统的统一对称性

研究机电系统的统一对称性. 由系统的Lagrange-Maxwell方程, 给出系统的统一对称性的定义和判据, 得到了系统的统一对称性导出Noether守恒量，Hojman守恒量和Mei守恒量. 举例说明结果的应用. 关键词： 机电系统 统一对称性 守恒量     

Hamilton系统的Mei对称性、Noether对称性和Lie对称性

研究Hamilton系统的形式不变性即Mei对称性，给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明本文结果的应用. 关键词： Hamilton系统 Mei对称性 Noether对称性 Lie对称性 守恒量     

动力学系统Noether对称性的几何表示

利用现代微分几何方法研究了Lagrange系统、Hamilton系统和Birkhoff系统的Noether对称性,并导出系统相应的Noether守恒量,最后给出了应用算例.     

Noether-Mei symmetry of a discrete mechanico-electrical system

Noether-Mei symmetry of a discrete mechanico-electrical system on a regular lattice is investigated.Firstly,the Noether symmetry of a discrete mechanico-electrical system is reviewed,and the motion equations and energy equations are derived.Secondly,the definition of Noether-Mei symmetry for the system is presented,and the criterion is derived.Thirdly,conserved quantities induced by Noether-Mei symmetry with their existence conditions are obtained.Finally,an example is discussed to illustrate the results.     

Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates

The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and a conserved quantity of the system. The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry, and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented. An example is discussed to show the applications of the results.     

机电动力系统的动量依赖对称性和非Noether守恒量

研究了Lagrange-Maxwell机电动力系统的Hamilton正则方程及动量依赖对称性的定义、判据、结构方程和守恒量的形式.研究表明，结构方程中的函数ψ只需是对称群的不变量.得到求解机电动力系统守恒量的新方法，并给出了应用实例. 关键词： 机电动力系统 Lie群分析 对称性 守恒量     

离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量

本文研究离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量. 构建了离散差分序列变质量Hamilton系统的差分动力学方程, 给出了离散差分序列变质量Hamilton系统差分动力学方程在无限小变 换群下的Lie对称性的确定方程和定义, 得到了离散力学系统Lie对称性导致Noether守恒量的条件及形式, 举例说明结果的应用. 关键词： 离散力学 Hamilton系统 Lie对称性 Noether守恒量     

Noether symmetry for fractional Hamiltonian system

Fractional Hamiltonian systems within combined Riemann-Liouville fractional order derivative and combined Caputo fractional order derivative are established. Then Noether quasi-symmetry and conserved quantity for the fractional Hamiltonian systems are presented. Thirdly, perturbation to Noether quasi-symmetry and adiabatic invariant are studied. Several special cases are discussed in each section. And finally, two applications, i.e., the fractional Lotka biochemical oscillator model and the fractional isotropic harmonic oscillator model, are discussed to illustrate the results and methods.