广义随机KP方程的椭圆周期解

利用Hermite变换和Jacobi椭圆函数展开法研究(2+1)-维广义随机Kadomtsev-Petviashvili方程,并给出了它的随机椭圆周期解及随机孤立波解.     

太阳相对差分亮度的160.m010周期变化

本文报道了1986年太阳中心相对于边缘的差分亮度测量结果,所用波带是0.7—0.8μm。并分别使用两种光电二极管阵(16×16,32×32像元)作探测器,所得资料独立地进行功率谱计算,都清楚地显示出160^m变化周期,其平均振幅为8×10^-5太阳相对强度单位。本文还分析了Grimea天文台1976至1986年358天(1870^h)差分亮度观测的周期值,其振动周期的精确值为160.^m0099(±16),它的统计有效值在3σ以上。这一值与160.^m0100(±6)的红外观测值和Doppler差分速度观测值160.^m010(±1)符合得很好。     

脉冲比较微分系统解的φ0-稳定性

本文主要利用分段连续的Lyapunov函数得到脉冲比较微分系统(2)的φ₀-稳定性,并且通过比较方程,得到脉冲微分系统(1)的稳定性.     

亚太地区空间地球动力学研究计划(APSG)首期VLBI联测结果

1997年 1 0月中国科学院上海天文台与美国宇航局Goddard空间飞行中心(GSFC)成功组织实施了亚太地区空间地球动力学研究计划 (APSG)首期联测中的VLBI观测 .共 6个VLBI站参加 ,包括中国上海和乌鲁木齐站、美国阿拉斯加Gilcreek站和夏威夷Kokee站、日本鹿岛 (Kashima)站及澳大利亚塔斯玛尼亚的Hobart站 .各站之间的基线长度为 1 90 0～ 1 1 0 0 0km ,基线测量重复率约为 1 0× 1 0 ^-9.利用上述台站以往的VLBI观测 ,并结合全球VLBI观测数据进行了综合解算 ,获得了上述 6个VLBI站的基线变化率及台站的运动速率 .特别是检测到上海台和乌鲁木齐站相对于欧亚板块稳定区域分别存在向东 8mm/a和向北偏东 1 4mm/a的运动 ,这些结果直接验证了印度大陆的向北运动影响到了我国西北和东部地区的地壳运动.     

VY CMa水脉泽辐射的短时标变化

利用紫金山天文台青海观测站的13.7m毫米波射电望远镜,在1993年8月26日～9月24日的近1个月的时间里,每天监视大犬座VY(VYCMa)红超巨星拱星气体壳层中水脉泽辐射.发现一个强度相对变化为20%～25%,周期为10.3d的类正弦的快速振荡.这是迄今在红巨星中发现的变化周期最短的水脉泽辐射、给出了这个源的水分子脉泽谱线以及它的变化形态;利用细管状的完全饱和水脉泽辐射理论,估计了脉泽活动区的物理性质;初步分析了这种快速变化的成因.     

广义单纯形—中心设计I_(λ-)最优观测频数的一般解析表达式

本文引进发生函数矩阵与同构向量两个概念,利用它们讨论了与Scheffè单纯形—中心设计有关的0-1矩阵的一些性质。在I_(λ-)最优观测配置的分块算法的基础上,本文给出了q分量n阶广义单纯形—中心设计I_(λ-)最优观测频数的一般解析表达式。     

(3+1)-维耦合高阶非线性Schrdinger方程的光学多畸形波

本文研究带有高阶项、时间色散项和非线性系数项的复杂(3+1)-维高阶耦合非线性Schrdinger(3DHCNLSE)方程的精确解.首先,利用相似变换将非自治的方程转化为自治的耦合Hirota方程;其次,采用Darboux变换方法得到耦合Hirota方程带有任意常数的有理解;最后,给出变系数3DHCNLSE方程带有任意常数的1阶和2阶多畸形波解.本文获得的(3+1)-维(3D)多畸形波解可以用来描述深海动力学波和非线性光学纤维中出现的一些物理现象.     

乘积G-空间中周期跟踪性和等度连续的研究

介绍了拓扑群作用下乘积空间中G-周期跟踪性和G-等度连续的概念,利用乘积映射的性质,研究了乘积映射f×g与分映射f和g在这些动力学性质方面的关系,得到如下结果:1)乘积映射f×g具有G-周期跟踪性当且仅当f具有G_1-周期跟踪性,g具有G_2-周期跟踪性;2)乘积映射f×g具有G-等度连续当且仅当f具有G_1-等度连续,g具有G_2-等度连续.这些结论弥补了拓扑群作用下乘积空间中G-周期跟踪性和G-等度连续理论的缺失.     

二次系统(Ⅲ)n=0的极限环问题

本文研究了二次系统(Ⅲ)二次系统; Hopf分支; 极限环.国家自然科学基金(19871041)2004年2月20日2006年2月28日本文研究了二次系统(Ⅲ)二次系统; Hopf分支; 极限环.国家自然科学基金(19871041)2004年2月20日2006年2月28日本文研究了二次系统(Ⅲ)二次系统; Hopf分支; 极限环.国家自然科学基金(19871041)2004年2月20日2006年2月28日本文研究了二次系统(Ⅲ)n=0的极限环问题,利用Hopf分支理论,先考察其产生极限环的参数区域,对此外的参数区域,则运用定性分析的方法,分别给出了无环性的证明,并结合文[2]中的一个重要猜测进行讨沦,完善了谢文[5]的结论。     

含频散项的K(2,3)方程的精确行波解

本文研究了包含频散项的K(2,3)方程u_t+(u²)_x-(u³)_xxx=0的分支问题.利用动力系统的定性分析,并且借助Maple软件进行数值模拟得到行波解系统相应的相图,然后通过积分计算得到周期尖波解、类扭波和类反扭波的精确解的函数表达式,以及孤立波精确解的隐函数表达式.     

Existence of capillary-gravity water waves with piecewise constant vorticity

In this paper we construct small-amplitude periodic capillary-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is achieved by associating to the height function formulation of the water wave problem a diffraction problem where we impose suitable transmission conditions on each line where the vorticity function has a jump. The solutions of the diffraction problem, found by using local bifurcation theory, are the desired solutions of the hydrodynamical problem.     

A ray‐integral solution for the wave‐field in the Sommerfeld model

A ray‐integral solution is presented for the wave‐field in the Sommerfeld model (liquid half‐space over solid half‐space), where a point source is placed in the fluid and the two media (fluid and solid) of contrasting densities and wave speeds are homogeneous. This exact closed form solution is then used to evaluate complete time records of the acoustic pressure (at a point receiver located in the fluid in the vicinity of the penetrable fluid‐solid interface) for two Sommerfeld models: one where the shear wave speed in the solid bottom is lower than the sound speed in the fluid and the other where the shear wave speed is higher. These pressure response curves indicate the relative importance of the various wave‐forms (the critically refracted longitudinal and shear waves, the pseudo‐Rayleigh and Stoneley interface waves, the direct wave, and the totally reflected wave) contributing to the solution and the possibility of utilizing the arrival times of the refracted and interface waves to determine the bottom rigidity. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear Elastic Wave Propagation in Unsaturated,Unconsolidated Soils

By means of a macroscopic linear model for a poroelastic medium with three deformable components the acoustic behavior of four unconsolidated soil types, filled by water and air, is studied. Necessary material parameters are mainly gathered from the German standard DIN 4220. It provides some useful parameters, as for example, van Genuchten parameters, for thirty-one different soil types including sands, silts and clays. There appear four body waves: three longitudinal waves and one shear wave. The slowest compressional wave does only exist if at least two pore fluids appear and is driven by the capillary pressure between the pore fluids. The wave analysis yields the dependence of velocities and attenuations of these waves on the saturation and on the frequency. This is compared to the so far most frequently studied case of partially saturated sandstones. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于小波分析的价格周期识别——以天然橡胶和合成橡胶价格为例

使用1997年1月到2009年12月国内天然橡胶、国内合成橡胶、国际天然橡胶的月平均价格数据,运用小波去噪方法、H-P滤波法、B-K滤波法识别了各类价格的周期性并进行了比较.研究结果表明:不同方法得到的周期变化基本一致,小波去噪和BK滤波下周期相对多,HP滤波下波动幅度大;小波去噪法下各类价格对PPI具有最强的预测力,在此方法下国内天然橡胶、合成橡胶价格的平均周期长度约为22个月,国际天然橡胶约为21个月.     

蛙交感神经细胞内的孤立脉冲钙波

在一定的胞外环境刺激下,蛙交感神经细胞内存在一类沿着细胞膜径向向内传播的孤立脉冲钙波．该文建立了一个描述蛙交感神经细胞内的钙波动力学模型．在分段线性近似下,模型方程在形式上等同于Sneyd的方程．因此,应用Sneyd的求解方法,我们得到了一维孤立脉冲波速和波形的解析表达式．所求得的孤立钙波的波速为21.5 μm/s,符合实验结果．     

关于《保辛水波动力学》的一个注记

研究完全非线性水波的数值模拟方法，将《保辛水波动力学》中提出的保辛摄动方法，扩展到非线性水波压强的分析.数值算例表明，该文方法可用于水波的非线性演化分析，也可用于模拟孤立波、尖锐波峰的涌波等非线性水波，并给出水波的压强分布.     

Propagation of axisymmetric waves in an initially twisted circular compound bimaterial cylinder with a soft inner and a stiff outer constituents

Within the scope of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of propagation of elastic waves in an initially stressed body, the problem on the propagation of axisymmetric waves in an initially twisted circular compound bimaterial cylinder is studied. A mathematical formulation of the problem is presented, and the corresponding solution method is proposed and employed. Numerical results are presented and discussed for the case where the material of the outer cylinder is stiffer than the inner solid one. In particular, it is established that, as a result of initial twisting of the compound cylinder, new axisymmetric wave modes appear in it.     

Scattering of an incident acoustic wave by an infinite elastic cylinder in a shallow sea

The scattering of sound waves by an isotropic elastic circular cylinder of infinite extent in a water of finite depth is investigated taking into account the shear waves that can exist in addition to compressional waves in scatterers of solid material. The axis of the cylinder is parallel to the water level. The reflected and transmitted energies are plotted for the various values of the radius of the cylinder, and the farfield scattered pressure is obtained for various depth and presented in a graphical form. Copyright © 2008 John Wiley & Sons, Ltd.     

Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium

Within the framework of the piecewise homogeneous body model with utilization of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the mathematical modeling of the torsional wave propagation in the initially stressed infinite body containing an initially stressed circular solid cylinder (case 1) and circular hollow cylinder (case 2) are proposed. In these cases, it has been assumed that in the constituents of the considered systems there exist only the normal homogeneous tensional or compressional initial stress acting along the cylinder, i.e. in the direction of wave propagation. In the case where the mentioned initial stresses are not present, the proposed mathematical modeling coincides with that proposed and investigated by other authors within the classical linear theory of elastic waves. The mechanical properties of the cylinder and surrounding infinite medium have been described by the Murnaghan potential. The numerical results related to the torsional wave dispersion and the influence of the mentioned initial stresses on this dispersion are presented and discussed.