Application of the finite Hankel transform to a diffusion problem without azimuthal symmetry

The problem treated in this paper concerns calculating the evolution of the pressure in a single-phase, slightly compressible fluid in a porous medium consisting of communicating layers. The fluid is produced through a point sink located on the side of an otherwise sealed cylindrical wellbore. This location of the sink causes the flow around the wellbore to be azimuthally asymmetric.The problem is solved through successive application of Laplace, finite Fourier and finite Hankel transforms. Although apparently straightforward, this approach leads to serious numerical difficulties. The published form of the inversion formula for the finite Hankel transform leads to inaccurate computation for the higher azimuthal modes even with 128 bit arithmetic. An alternative form is developed which enables accurate evaluation of the solution with the more practical 64 bit arithmetic. The technique for two-layer solution presented here can be directly extended to a problem with a larger number of communicating layers. This is the first instance of successful application of the finite Hankel transform to an azimuthally asymmetric diffusion problem.     

用小波变换抑制SAR图像中的斑点噪声

抑制合成孔径雷达图像中的斑点噪声一直是处理图像并得到准确图像信息的难点，提出了一种基于小波变换抑制合成孔径雷达（SAR）图像中的斑点噪声的方法，对原有的小波变换方法作了改进，能更好地保留图像的边缘信息，并能简化计算量。在仿真实验中使用了合成的模拟图像和真实的合成孔径雷图像，并与以往的小波去噪滤波方法以及一些经典的斑点噪声滤波方法（包括中值滤波，Lee滤波，Frost滤波）进行比较，在综合考虑了滤波算法在均匀区域对斑点噪声的抑制能力以及保留边缘信息能力的情况下，提出的算法有更好的效果。     

降低雷达接收机中噪声的几种方法

噪声是影响雷达接收机灵敏度的重要因素。本文通过讨论雷达接收机噪声的来源，分析并提出了集中降低雷达接收机内部和外部噪声的几种方法，具有一定的实际意义。     

DC-DC电荷泵的研究与设计

以Dickson电荷泵的基本原理为出发点，研究了一种将正电压输入转为负电压输出的开关电容电路。由于开关电容的充放电特点，为确定电容时间常数，采用非交叠时钟控制信号避免了由于时钟交叠而造成的当电容充电还未完成即对下一级电容进行放电的现象。同时，参考功率MOS-FET的电容模型通过增大驱动电路的电流减小了开关管的上升延时，提高了开关动作的速度，使转换效率得到明显提高。此电路结构简单，性能优良，易于集成，可广泛应用于输出负电压的电源产品中。     

估计小波系数方差邻域大小的研究

利用小波变换去噪时小波系数方差的估计对去噪结果影响很大。自然图像小波分解后得到的系数在不同的分辨率中差异很大,所以利用邻域估计中心点方差时,不同分辨率应有不同大小的邻域。首先对在邻域中利用极大似然准则估计中心点方差进行分析,再结合自然图像小波分解后的系数在不同分辨率子带中,根据平稳性和重要性选择邻域的大小。最后进行去噪实验,并取得正交小波分解下理想的去噪性能。     

基于数字化二次曝光干涉的光学元件波前畸变测量

将傅立叶变换条纹分析方法与二次曝光全息干涉计量相结合，提出了数字化二次曝光干涉术，用于测量光学元件引入的波前畸变。文中给出了理论分析，模拟与光学实验结果证实提出的方法具有高精度、快速的波前测量特点，可应用于激光系统中光学元件的波前畸变在线检测。     

拉普拉斯变换的图形分析

以单边指数函数为例，分析了拉普拉斯变换象函数F(s)在其收敛域内随σ和ω的变化规律，通过|F(s)|曲面图来观察这些规律，并解释了图中某些特定点及剖面的含义，以形象化的方式加深对拉普拉斯变换的认识。借助MATLAB的绘图功能绘制出F(s)的曲面图、剖面图及信号的频谱图，从中可以观察到频域与复频域的关系以及系统函数的零极点分布等。     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

Comparison of volumes by means of the areas of central sections

The Busemann–Petty problem asks whether origin-symmetric convex bodies in Rⁿ with smaller areas of all central hyperplane sections necessarily have smaller n-dimensional volume. The solution was completed in the end of the 1990s, and the answer is affirmative if n4 and negative if n5. Since the answer is negative in most dimensions, it is natural to ask what information about the volumes of central sections of two bodies does allow to compare the n-dimensional volumes of these bodies in all dimensions. In this article we give an answer to this question in terms of certain powers of the Laplace operator applied to the section function of the body.     

Reciprocally convex functions

We say that f is reciprocally convex if x?f(x) is concave and x?f(1/x) is convex on (0,+∞). Reciprocally convex functions generate a sequence of quasi-arithmetic means, with the first one between harmonic and arithmetic mean and others above the arithmetic mean. We present several examples related to the gamma function and we show that if f is a Stieltjes transform, then −f is reciprocally convex. An application in probability is also presented.