正多边形的最优分割问题

记平面边长为1的正m边形为S_m,将S_m剖分成n块:S_(m1),S_(m2),…,S_(mn),这样的剖分称S_m的n剖分,并以T(m,n)表示.以d_(mi)表示区域S_(mi)(i=1,2,…,n)的直径(即区域S_(mi)任意两点之间距离的最大者).记D(m,n)=max{d_(m1),d_(m2),…,d_(mn)}及Ψ(m,n)=■{D(m,n)}.本文将估计Ψ(m,n)的上下界.证明Ψ(6,3)=3/2,Ψ(6,4)=3-3~(1/2),Ψ(6.6)=1,Ψ(6,7)=3/2,估计Ψ(6,n)的渐进性.提出几个猜想.     

Homoclinic Orbits for Second Order Discrete Hamiltonian Systems with Potential Changing Sign

In this paper, a class of second order discrete Hamiltonian systems without any periodicity assumptions are considered. Base on the critical point theory, some sufficient conditions for the existence of homoclinic orbits are obtained. The results obtained extend the results in [2006] by relaxing the assumptions on the sign of the potential.      

Specific heat ratio effects of compressible Rayleigh–Taylor instability studied by discrete Boltzmann method

Rayleigh–Taylor (RT) instability widely exists in nature and engineering fields. How to better understand the physical mechanism of RT instability is of great theoretical significance and practical value. At present, abundant results of RT instability have been obtained by traditional macroscopic methods. However, research on the thermodynamic non-equilibrium (TNE) effects in the process of system evolution is relatively scarce. In this paper, the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT instability. The evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium region. Firstly, as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region, the average TNE intensity first increases and then reduces, and it increases with the specific heat ratio decreasing; the specific heat ratio has the same effect on the global strength of the viscous stress tensor. Secondly, the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex structure. Thirdly, under the competition between the temperature gradients and the contact area of the two fluids, the average intensity of the non-equilibrium quantity related to the heat flux shows diversity, and the influence of the specific heat ratio is also quite remarkable.     

Quantum Maps with Memory from Generalized Lindblad Equation

In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.     

The Boundedness of Composition Operators on Triebel–Lizorkin and Besov Spaces with Different Homogeneities

In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zygmund singular integral operators with different homogeneities on these Triebel–Lizorkin and Besov spaces.     

The aliasing‐phenomenon in visual terms

In a recent paper it was shown that the aliasing phenomenon, which leads to a severe identification problem in the estimation of stochastic differential equations, can be overcome by using a polygonal (or higher) approximation for the time paths of the exogenous variables. This work attempts to visualize the problem and presents several simulated trajectories of a continuous time AR(2)‐process (Ornstein‐Uhlenbeck‐process) together with the observationally equivalent structures. Furthermore it is shown that aliasing can even change the analytical properties of the time paths of the system: whereas the first component of the Ornstein‐Uhlenbeck‐process is differentiable, the trajectories of the aliasing structures are continuous, but not differentiable any more.     

Hassel and Rogers狼与驼鹿模型讨论

分析了连续时间和离散时间的捕食-被捕食模型：Hassel and Rogers的狼与鹿相互作用的模型,发现它们的轨线有一定程度的相似,但从生态意义上讲,离散模型更合适。     

Chip-Firing and the Critical Group of a Graph

A variant of the chip-firing game on a graph is defined. It is shown that the set of configurations that are stable and recurrent for this game can be given the structure of an abelian group, and that the order of the group is equal to the tree number of the graph. In certain cases the game can be used to illuminate the structure of the group.     

Global stability for n-species lotka-volterra systems with delay,ii: reducible cases,sufficiency

In this paper an n-species delayed Lotka-Volterra system without de1ayed intraspecific competitions is considered. It is proved that the system is globally stable for all off-diagonal delays T_ij≥0 provided the interaction matrix A of the system satisfies the weakly diagonally dominant Condition (WDD)     

A novel convenient finite difference method for shallow water waves derived by fifth-order Kortweg and De-Vries-type equation

In this research, two new finite difference schemes are derived and presented for estimating a solution to the fifth-order Kortweg and De-Vries equation. The global conservation law on any time–space regions which yields a three-level linear-implicit algorithm with a diagonal system is exactly preserved by the intended finite difference method. Theoretically verified and numerically proved, the created schemes are unconditionally stable and have the second-order accuracy both in time and space. The obtained results guarantee that the novel idea offers a new aspect to analyze the wave behavior.