奇异

Secondly, by applying inverse Fourier integral transform to the displacement, and uniting the constitutive and geometrical equations, the analytical expression of stress in Laplace domain were derived. Thirdly, by defining dislocation density functions, the Cauchy singular integral equations were obtained according to the boundary condition and interface connection conditions, and the problem was reduced to algebraic equations by Chebyshev orthogonal polynomial. Based the these, the unknown coefficient of the algebraic equations can be solved by Schmidt method. Finally, the time response of dynamic stress intensity factor and energy release rate are obtained by inverse Laplace transform.

首先，利用积分变换方法，推导出粘弹性层的控制方程组；其次，引入位错密度函数，并结合边界条件和界面连接条件，导出反映裂纹尖端奇异性的Cauchy型奇异积分方程组，然后，应用Chebyshev正交多项式化奇异积分方程组为代数方程组，并采用Schmidt方法对其数值求解，最后，经过Laplace逆变换，求得动态应力强度因子和能量释放率的时间响应。

This paper defines j-dual automorphism and anti- automorphism of de Bruijn Good graph Gn over F2+vF2 ring.

文章定义了F2+vF2环上的de Bruijn Good图Gn的j对偶自同构及反自同构，并给出了在F2+vF2环上移位寄存器非奇异的充要条件，以及非奇异反馈函数与其自同构函数的表达式。

In contrast, the singular use of oils reveal a singular mastery of the medium, as Tian Liang's brushwork and the visual impact of his compositions are suggestive of either mixed media or atypically non-Western materials.

相比之下，使用的油奇异揭示了介质的奇异掌握，因为田亮的笔法和他作品的视觉冲击，是不是混合媒介或不典型非西方的材料启发。

By using thenatural boundary element method which is set up by professor Feng Kang,the Neu-mann boundary problem of the harmonic equation on the half-upper plane is reducedto the Hadamard type singular integral equation,the integral region of which is un-bound,and then we turn it into corresponding bilinear form.

通过由冯康教授开创的自然边界元方法，将上半平面调和方程的Neumann边值问题归化为Hadamard型强奇异自然边界积分方程，并且此积分方程是无界域上的强奇异自然边界积分方程，然后将它转化为相应的变分形式。

Then by matching the traction along the branches and the boundary of the strip, Cauchy singular equations were obtained, in which the point dislocation and the distributed dislocation density served as the unknown function.

根据板条边界和裂纹面上的应力边界条件，建立以集中位错强度和分布位错密度为未知函数的Cauchy型奇异积分方程，利用半开型积分法则将该奇异积分方程化为代数方程求解。

The techniques commonly used are some matrix-factorizations such as the generalized singular value decomposition, the canonical correlation decomposition, and the quotient singular value decomposition.

常用的方法是借助于一些矩阵分解，如广义奇异值分解，典型相关分解，和商奇异值分解等。

The main jobs of the paper are as follows, Multi-scale decomposition and reconstruction of wavelet transform is utilized to filter the noise of negative-pressure-wave, which is brought by leakage. With the capacity to detect the signal singularity quickly and accurately, wavelet transform was used to catch the break point of pressure signal. Accordingly, the work improved the location accuracy.

主要研究工作有：利用小波变换的多分辨率分解和重构技术，对采集到的管道泄漏产生的负压波信号进行消噪处理，并对几个影响消噪质量的关键因素及其选取方法进行了分析；再利用小波变换技术对信号奇异点的快速、准确的识别能力，对经消噪后的负压波信号进行奇异点捕捉，从而实现更精确的单条燃气管道泄漏定位。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

The problem of a curved rigid line or crack crossing the interface of the circular inclusion are studied by the principal part analysis method of Cauchy type integral equation. The singular stress index at the intersection and the singular stress at the angular regions near the intersection are obtained. The singular stress coefficients of rigid line at intersection and the stress intensity factors of crack at intersection are defined by using the singular stress.

利用Cauchy型奇异积分方程的主部分析方法对曲线型刚性线和曲线裂纹和圆夹杂界面的相交问题进行了研究，得出刚性线以及裂纹和界面交点处的奇性应力指数以及交点处角形域内的奇性应力，并利用奇性应力分别定义了刚性线在交点处的应力奇异因子和裂纹在交点处的应力强度因子。

This paper discusses the Noether theorem of complete singular integral equation which containsboth the convolution kernel and the Cauchy kernel, and comes up with the Noether theoremwhich is similar to the Fredholm integral equation, the convolution equation and the singularintegral equation.

本文讨论了既含卷积核又含Cauchy核的完全奇异积分方程的Noether定理，得到了与Fredholm积分方程、卷积型积分方程、奇异积分方程相类似的Noether定理。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。