Bochner-Martinelli型积分的边界性质

对 Cn中具光滑边界Ω的有界域 D和属于指数α( 0 <α <1 )的 Lipschitz空间 Lip(α,Ω )中的每个函数φ,我们不仅证明了 Bochner- Martinelli型积分Φ ( z) =∫Ωφ(ζ) K(ζ,z)(其中 K(ζ,z)为 Bochner- Martinelli型积分核 )表示的内、外极限值Φ +( t) ,Φ - ( t)属于 Lip(β,Ω ) ( 0 <β <α <1 )而且可分别延拓成 D和 Dc上的指数为β的 Holder连续函数 ,并由此给出了 Bochner- Martinelli变换的 Plemelj跳跃公式 .

Bochner-Martinelli型积分在分片光滑边界域上的边界性质

研究了Cn 中具分片光滑边界的域的特性 .作为最近的结果 [1]的推广 ,得到了Coxoдkий Plemelj公式表示的内外极限值Φ+(t)和Φ-(t)都是H lder连续函数 .

Vortex-Source Method for the 3D Incompressible Irrotational Flow

The weighted residuals method was used for obtaining the boundary integral representation of the velocity of the three-dimensional inviscid irrotational flow. It is shown that velocity in an arbitrary point of domain can be expressed through its values on the boundary. Boundary integral equations of the second kind for solving boundary-valued problems of the first and second kinds are developed. The result has been also generalised to the case of solenoidal vector fields with potential vorticity. It is shown that the resulting integral equations are Fredholm integral equations of the second kind and allow effective numerical solving of corresponding boundary-valued problems. Examples of numerical solutions for a sphere and an ellipsoid are given for demonstration of efficiency of the offered method.

An advanced segmentation using area and boundary tracing technique in extraction of lungs region

A new method is presented for the segmentation of pulmonary parenchyma. The proposed method is based on the area calculation of different objects in the image. The main purpose of the proposed algorithm is the segment of the lungs images from the computer tomography(CT) images. The original image is binarized using the bit-plane slicing technique and among the different images the best binarized image is chosen. After binarization, the labeling is done and the area of each label is calculated from which the next level of binarized image is obtained. Then, the boundary tracing algorithm is applied to get another level of binarized image. The proposed method is able to extract lung region from the original images. The experimental results show the significance of the proposed method.

An Alternative Method to Study Wave Scattering by Semi-infinite Inertial Surfaces

A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.

On Solvability of an Inverse Boundary Value Problem for a Fourth Order Elliptic Equation

In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.

The Singular Integral of an Analytic Polyhedron

Combining R.Harvey and J.Porking′s methods and traditional methods, we define the current Cauchy principal values in this paper by using homotopy formula and integral transformations. We study the boundary value of Weil type polyhedron integrals and obtain Plemelj formulas, which are different from the methods usually in the studies of boundary value problems.

Variable-step integration method for milling chatter stability prediction with multiple delays

This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.

Dynamic conducting crack propagation in piezoelectric materials:Mode-II problem

This paper studies the dynamic conducting crack propagation in piezoelectric solids under suddenly in-plane shear loading. Based on the integral transform methods and the Wiener-Hopf technique, the resulting mixed boundary value problem is solved. The analytical solutions of the dynamic stress intensity factor and dynamic electric displacement intensity factor for the Mode II case are derived. Furthermore, the numerical results are presented to illustrate the characteristics of the dynamic crack propagation. It is shown that the universal functions for the dynamic stress and electric displacement intensity factors vanish if the crack propagation speed equals the generalized Rayleigh speed. The results indicate that the defined electro-mechanical coupling coefficient is of great importance to the universal functions and stress intensity factor history.