Numerical method of studying nonlinear interactions between long waves and multiple short waves

Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.     

金属离子负载修饰阳离子树脂在酯化反应中的研究

将催化精馏中常用作催化填料的强酸性阳离子交换树脂用金属离子负载修饰后，考察了树脂催化性能的改变及树脂结构对催化性能的影响。实验表明，经修饰后树脂的催化能力都高于原树脂，在不分水的情况下，合成乙酸乙酯时乙酸的转化率最高可达73％，具有很好的选择性，金属离子能与树脂的磺酸基团产生络合，提高了树指的催化性能，所形成的新酸中心不会被阳离子交换而失活。     

Electromagnetic backscattering from freak in （1＋1）-dimensional deep-water

To study the electromagnetic （EM） backscatter characteristics of freak waves at moderate incidence angles, we establish an EM backscattering model for freak waves in （1＋1）-dimensional deep water. The nonlinear interaction between freak waves and Bragg short waves is considered to be the basic hydrodynamic spectra modulation mechanism in the model. Numerical results suggest that the EM backscattering intensities of freak waves are less than those from the background sea surface at moderate incidence angles. The normalised radar cross sections （NRCSs） from freak waves are highly polarisation dependent, even at low incidence angles, which is different from the situation for normal sea waves; moreover, the NRCS of freak waves is more polarisation dependent than the background sea surface. NRCS discrepancies between freak waves and the background sea surface with using horizontal transmitting horizomtal （HH） polarisation are larger than those using vertical transmitting vertical （VV） polarisation, at moderate incident angles. NRCS discrepancies between freak waves and background sea surface decreases with the increase of incidence angle, in both HH and VV polarisation radars. As an application, in the synthetic-aperture radar （SAR） imaging of freak waves, we suggest that freak waves should have extremely low backscatter NRCSs for the freak wave facet with the strongest slope. Compared with the background sea surface, the freak waves should be darker in HH polarisation echo images than in VV echo images, in SAR images. Freak waves can be more easily detected from the background sea surface in HH polarisation images than in VV polarisation images. The possibility of detection of freak waves at low incidence angles is much higher than at high incidence angles.     

关于四个三幂等阵线性组合的可逆性和群逆

本文研究了四个三幂等阵线性组合的可逆性及群逆.利用矩阵分解的方法,获得了它们可逆及群逆的一些条件,并得到其逆和群逆的计算公式,这些结论完善了k幂等阵可逆性理论.     

～A0型箭图的一个表示的自同态代数的Cartan矩阵

为了探讨代数的Cartan矩阵的某些性质与代数分类的关系,通过研究完全域k上的A0型仿射箭图的一个有限维表示的自同态代数的结构与Jordan标准型的关系,并利用Jorelan标准型的组合信息得到了该自同态代数的Cartan矩阵,验证了Cartan矩阵猜想在此情形下不成立.最后提出了一个有关仿射箭图性质的猜想.     

纪特邮票发行需求量预测模型研究与实现

本文在调查了国家邮政局在纪特邮票发行过程中的具体操作和分析了纪特邮票数据本身的特点后 ,采用了三种预测方法分析了我国近 2 0年来纪特邮票预定量数据 ,建立了纪特邮票预定量的数学模型 ,预测了今后几年纪特邮票预定量数据。通过对数学模型的求解 ,本文获得一些纪特邮票发行的内在规律 ,而这些规律对决策结构在决策过程中有一定的参考作用。     

两个幂等矩阵组合的Drazin逆

证明了两个不同的非零幂等矩阵P,Q的组合A=aP+bQ+cPQ+dQP+ePQP+fQPQ+g(PQ)~2+h(QP)~2+i(QP)~2Q,(其中a,b,c,d,e,f,g,h,i∈C,a,b≠0)在条件(PQ)~2P=(PQ)~2下存在Drazin逆,并且给出其Drazin逆计算公式.     

埋入式光纤Bragg光栅应变传感器在隧道二次衬砌中的监测研究

隧道二次衬砌性能劣化是影响隧道健康运营的主要病害,对隧道二次衬砌进行监测是保证隧道健康运营的重要手段。应用埋入式光纤Bragg光栅应变传感器深入研究了隧道二次衬砌的变化。通过FBG(Fiber Bragg Grating)传感器在隧道内的布设及温度补偿技术,对隧道断面的应变变化情况进行了分析。结果表明,数据的曲线走势在一定程度上反映了隧道二次衬砌的变化,为进一步的病害预报提供了有效的支持。     

FBG在边坡稳定性监测中的有限元法优化布设

为实现FBG对边坡的稳定性监测,需要对传感器的布设进行优化。楚雄腰站变电站二级边坡,平台宽1.5m,坡角30°,材质为回填土,其背靠变电站,易受大型设备压力作用而影响稳定性。建立实际边坡模型,利用有限元强度折减法分析计算,结果显示,最大塑性应变出现在二级边坡平台表面及其附近。所以在二级边坡平台上布设3根应变桩来实现深层监测,实际监测结果显示,各应变桩最大应变分别:420με、400με、-360με,对应位置分别出现在深度1m、2m、2m处,现场观测平台表面及其附近出现裂缝,结果均能够与仿真优化布设结论较好吻合。     

光纤Bragg光栅应变桩在公路边坡中的监测研究

为实现对公路边坡的稳定性安全监测,需要检测边坡的应变变化。元绿公路K77+120~K77+215段为一坡度30°、高度差达65m的边坡,由于土质松散而形成一滑坡地带,在其自然坡面前端挖掘5个30m深钻孔,把光纤Bragg光栅应变传感器分别埋入5个钻孔之中,浇灌水泥使之固定,形成5个应变桩,实现对桩体的应变监测,从而反应边坡的应变变化情况。经过两个月的监测,1孔洞到5孔洞最大应变变化依次为400με、80με、130με、-60με、46με,且依次出现在6m、16m、14m、16m、30m深度的位置。表明此边坡在6m深度及15m深度地层结构比较松散。