广义算子半群与广义分布参数系统的适定性

首先,针对广义分布参数系统的求解问题,提出了由Hilbert空间中有界线性算子所引导的广义算子半群和广义积分半群;其次,讨论了广义预解算子的性质、广义算子半群与广义积分半群的性质;最后,研究了广义分布参数系统的适定性问题.     

The number of nonseparable maps on the projective plane

In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating functions are obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived. Moreover, if the number of edges is sufficiently large, then almost all nonseparable maps on the projective plane are not triangulation.     

On the relations of graph parameters and its total parameters

In this paper we get some relations between α（G）, α＇（G）, β（G）, β＇（G） and αT（G）, βT（G）. And all bounds in these relations are best possible, where α（G）, α＇（G）,/3（G）, β（G）, αT（G） and βT（G） are the covering number, edge-covering number, independent number, edge-independent number （or matching number）, total covering number and total independent number, respectively.     

Exact traveling wave solutions and bifurcations in a nonlinear elastic rod equation

The exact parametric representations of the traveling wave solutions for a nonlinear elastic rod equation are considered. By using the method of planar dynamical systems, in different parameter regions, the phase portraits of the corresponding traveling wave system are given. Exact explicit kink wave solutions, periodic wave solutions and some unbounded wave solutions are obtained.     

Stochastic Fractional Anderson Models with Fractional Noises

The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its HSlder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.     

THE REDUCED BASIS TECHNIQUE AS A COARSE SOLVER FOR PARAREAL IN TIME SIMULATIONS

In this paper, we extend the reduced basis methods for parameter dependent problems to the parareal in time algorithm introduced by Lions et al. [12] and solve a nonlinear evolutionary parabolic partial differential equation. The fine solver is based on the finite element method or spectral element method in space and a semi-implicit Runge-Kutta scheme in time. The coarse solver is based on a semi-implicit scheme in time and the reduced basis approximation in space. Of[line-online procedures are developed, and it is proved that the computational complexity of the on-line stage depends only on the dimension of the reduced basis space （typically small）. Parareal in time algorithms based on a multi-grids finite element method and a multi-degrees finite element method are also presented. Some numerical results are reported.     

一种研究敞口容器非稳态导热问题的新方法

在变导热系数条件下,把分段迭代法应用于解决非稳态导热物理问题的集总参数法,为敞口容器恒温热源加热过程中容器内的平均温度变化提供了一个简便的计算方法.利用该方法只需三次分段迭代,即可使得理论计算与实验数据结果吻合.     

不同波长蓝光LED对人体光生物节律效应的影响

以30名视力正常的学生为研究对象,采用剂量作业法、生理参数法和疲劳评价法研究了人体在峰值波长分别为468,457,453 nm的蓝光LED照明下的光生物节律效应。结果表明:在剂量作业法中,蓝光LED对错误率、工作速度和脑力工作指数的影响均为453 nm<457 nm<468 nm;在生理参数法中,468 nm蓝光LED对脉搏的变化影响最大,对收缩/舒张压的影响不明显;在疲劳评价法中,蓝光LED对人体舒适度的影响为453 nm<457 nm<468 nm。综上所述,在3种峰值波长蓝光中,468 nm的蓝光对人体光生物节律影响最大。     

有限深两层流体中内孤立波造波实验及其理论模型

将置于大尺度密度分层水槽上下层流体中的两块垂直板反方向平推, 以基于 Miyata-Choi-Camassa (MCC)理论解的内孤立波诱导上下层流体中的层平均水平速度作为其运动速度, 发展了一种振幅可控的双推板内孤立波实验室造波方法. 在此基础上, 针对有限深两层流体中定态内孤立波 Korteweg-de Vries (KdV), 扩展KdV (eKdV), MCC和修改的Kdv (mKdV)理论的适用性条件等问题, 开展了系列实验研究.结果表明, 对以水深为基准定义的非线性参数ε 和色散参数μ, 存在一个临界色散参数μ₀, 当μ < μ₀ 时, KdV理论适用于ε ≤μ 的情况, eKdV理论适用于μ < ε ≤√μ 的情况, 而MCC理论适用于ε > √μ 的情况, 而且当μ ≥μ₀ 时MCC理论也是适用的.结果进一步表明, 当上下层流体深度比并不接近其临界值时, mKdV理论主要适用于内孤立波振幅接近其理论极限振幅的情况, 但这时MCC理论同样适用.本项研究定量地表征了四类内孤立波理论的适用性条件, 为采用何种理论来表征实际海洋中的内孤立波特征提供了理论依据. 关键词： 两层流体 内孤立波 双板造波 临界色散参数     

一种直接测量W-J参数的实验方法

本文探索了一种直接测量W-J参数的方法. 实验选用NaCl作为试样, 在快速压缩过程中原位测量样品的温度和压力的变化值. 通过温度修正使测量值在原理上更符合等熵压缩过程的结果, 并采用大幅度增压结合中值定理得出中点压力处温度随压力的变化率, 进而根据R=(P/T) (∂T/∂P)_S关系式求出W-J参数, 整个过程没有引入其他参数. 此外, 作为对比, 我们还从相关的物态方程、经验公式和已知参数出发计算了NaCl的W-J参数及其随压力变化的关系. 结果表明: 实验测得的NaCl的W-J参数随压力增加而增加; 实验结果与计算值符合得很好. 这说明快速增压直接测量物质的W-J参数是一种可行且可靠的方法. 关键词： NaCl W-J参数 快速增压 高压