Generalized geometry theory on constrained rotating relativistic Birkhoffian systems

This paper focuses on studying the generalized geometry theory of constrained rotating relativistic Birkhoffian systems. Based on the fact that relativistic rotating inertia is embedded in the Birkhoffian systems, the Pfaff action of rotating relativistic Birkhoffian systems was defined. The Pfaff-Birkhoff principles and Birkhoff＇s equations of the constrained rotating relativistic systems were obtained. The geometrical description, the exact properties and their forms on R T^＊M for the constrained rotating relativistic Birkhoffian systems are given. The global analyses of the autonomous, semi-autonomous and non-autonomous constrained relativistic Birkhoff＇s equations as well as the geometrical properties of energy change for the constrained rotating relativistic Birkhoffian systems were also conducted.

Constraining Equation of State of Dark Matter:Including Weak Gravitational Lensing

Usually the equation of state （EoS） of dark matter is zero when it is cold, however there exists the possibility of a （effective） nonzero EoS of dark matter due to its decay and interaction with dark energy. In this work, we try to constrain the EoS of dark matter/JAdm using the currently available cosmic observations which include the geometrical and dynamical measurements. For the geometrical measurements, the luminosity distance of type Ia supernovae, the angular diameter distance and comoving sound horizon from baryon acoustic oscillations and the cosmic microwave background radiation will be employed. The data points from the redshift-space distortion and weak gravitational lensing will be taken as dynamical measurements. Using the Markov chain Monte Carlomethod, we obtain a very tight constraint on the-EoS of dark matter：wdm=0.0000532 ＋0.000692＋0.00136＋0.00183 -0.000686-0.00136-0.00177.

An alternating direction method of multipliers for elliptic equation constrained optimization problem

We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet boundary control,Robin boundary control,and right-hand side control problems are considered here.These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization,then are solved by ADMM.The ADMM is an efficient first order algorithm with global convergence,which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers.We shall present exhaustive convergence analysis of ADMM for these different type optimization problems.The numerical experiments are performed to verify the efficiency of the method.

Conserved Quantity for Fractional Constrained Hamiltonian System

Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular system is studied.Firstly,the fractional constrained Hamilton equation and the fractional inherent constraint are presented.Secondly,Lie symmetry and conserved quantity are analyzed,including determined equation,limited equation,additional limited equation and structural equation.And finally,an example is given to illustrate the methods and results.

Noether Theorem for Fractional Singular Systems

Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional primary constraints and the fractional constrained Hamilton equations are given.Then,the fractional Noether theorems of the two fractional singular systems are established,including the fractional Noether identities,the fractional Noether quasi-identities and the fractional conserved quantities.Finally,the results obtained are illustrated by two examples.

Time-domain Finite Element Method for Transient Electric Field and Transient Charge Density on Dielectric Interface

This paper is devoted to solving the transient electric field and transient charge density on the dielectric interface under the electroquasistatic(EQS)field conditions with high accuracy.The proposed method is suitable for both 2-D and 3-D applications.Firstly,the governing equations represented by scalar electric potential are discretized by the nodal finite element method(FEM)in space and the finite difference method in time.Secondly,the transient constrained electric field equation on the boundary(TCEFEB)is derived to calculate the normal component of the transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface.Finally,a 2-D numerical example is employed to demonstrate the validity of the proposed method.Furthermore,the comparisons of the numerical accuracy of the proposed method in this paper with the existing FEMs for electric field intensity and charge density on the dielectric interface are conducted.The results show that the numerical accuracy of the proposed method for calculating the normal component of transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface is close to that of nodal electric potential and an order of magnitude higher than those of existing FEMs.

Qualitative Simulation of Non-linear SISO System

The main target of Qualitative reasoning (QS) is to seek a computational theory in order to analog the human’s ability to acquisition and reasoning for physical common sense knowledge.Afte the publication of the first special volume of qualitative reasoning in Journal of AI at 1984,it has been admitted generally that there are three main methods of qualitative reasoning.Although the original goal of three methods are closed, all aim to the "Naive physics", the qualitative simulation method initiated by B.J.Kuipers now has already had a distance with the "Naive physics". It is being combined with sophisticated mathematical tools and becomes a powerful tool for describing the possible behaviors of incomplete systems, meanwhile, the application areas of qualitative simulation have been expanded from physical area to physiology, chemical engineering, automatic control, and economics, etc.. In this paper, we apply the QSIM algorithm to simulate a SISO system characterized by incomplete knowledge and use FPA method to analyze the qualitative stability of such system.