查询词典 Fresnel integral

In chapter 1,we simply introduce the development in the study of the boundedness of multilinear commutators of singular integral operators and fractional integral operators.

第2章讨论奇异积分算子和分数次积分算子与Besov函数生成的交换子在L~d上的映射性质。

Fractional integral is an essential branch of fractal theory. In this paper, the authors adopted fractional integral in the evaluation of time series dimension, which has a higher accuracy than other methods such as box dimension, gauge method and so on.

分数阶积分是分形理论的一个重要分支，应用分数阶积分进行时间序列维数估计，其精度比box维数、量规法等方法高。

By applying Abel transform the dual integral equations are reduced to Fredholm integral equation of the second kind.

文末给出了多孔饱和半空间表面动力柔度系数的计算曲线。

In this paper the direct boundary integral equation of two-dimensional Laplace equation for Dirichlet problem is considered, which is deduced by Green's formula and the fundamental solution, and is a Fredholm integral equation of the first kind.

本文考虑用Green 公式和基本解推导得出直接边界积分方程来求解二维Laplace 方程的Dirichlet 问题，该直接边界积分方程是第一类Fredholm 积分方程。

Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations, which are then reduced to a Fredholm integral equation of second kind by the Copson-Sih method, and anti-plane displacement, electric potential and stress are obtained.

通过Fourier积分变换，将混合边值问题转化为对偶积分方程，并利用Copson-Sih方法将对偶积分方程转化为第二类Fredholm积分方程进行求解，给出了反平面位移、电势及应力分量的解析表达式。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

Then, under the consideration of mixed boundary value condition, a pair of dual integral equations for the rocking vibrations of a disk on saturated grounds are obtained, which can be reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Consequently, the dynamic compliance coefficient is evaluated and numerical results are presented to portray the influence of poroelastic effects on the dynamic interaction problem.

对于刚性圆板，作者首先采用Hankel变换对波动方程进行求解，得到了该控制方程在Hankel变换域内的通解，然后由混合边值条件建立了饱和地基上刚性基础摇摆振动的对偶积分方程，并将其化为第二类Fredholm积分方程，用数值方法计算了不同频率下基础的动力柔度系数，从而考察孔隙水的存在对基础摇摆振动特性的影响。

By use of the method of integral equation, the second kind Fredholm's integral equation was deduced to solve the interaction factors of pile-pile, pile-soil and soil-soil. Using the principle of superposition, the piled raft foundation was calculated. The validity of the proposed method was verified through comparison with solutions obtained using other methods by existing theories of elasticity.

采用积分方程法推导出求解桩－桩、桩－土和土－土间相互作用系数所需要的第二类Fredholm积分方程，利用叠加原理对桩筏基础进行计算分析，通过与常规弹性理论方法计算结果的比较验证了本文方法的正确性。

Based on the Biot s two-phase theory for fluid-saturated porous media, considering the inertia force of the solid and the liquid, and the coupling function between the solid and the liquid, and the compressibility of the liquid in allusion to the character of the nearly saturated soils. The dynamic governing differential equations are solved by Hankel transform. Then, considering the boundary condition, the dual integral equations of vertical vibration are established which are reduced to Fredholm integral equation of the second kind.

本文基于Biot两相介质动力固结理论，针对准饱和土地基的特点，考虑了流体的可压缩性，土体和流体的惯性及水土之间的耦合作用，运用Hankel变换技术求解动力控制方程，然后按混合边值条件建立起对偶积分方程，并将其化为易于数值计算的第二类Fredholm积分方程，分别研究了准饱和土半空间地基、上覆单相弹性层的准饱和土地基和准饱和粘弹性地基上刚性基础的竖向振动特性。

Using Biot's 2D elastodynamic theory solves the saturated soil equation. The Fredholm integral equation of the second kind can be built by using the fundamental solution of circular load, the compatibility condition and superposition method. The Fredholm integral equation of the second kind of pile groups can be solved by using numerical method. The numerical solutions of pile groups axial forces, pore pressures under vertical harmonic loading and shear forces, moments and pore pressures under horizontal harmonic loading can be obtained.

采用Biot提出的三维波动原理，利用圆形简谐载荷作用下的Biot固结方程的基本解和桩土之间的变形协调条件，并采用叠加原理得到饱和土中群桩的第二类Fredholm积分方程，应用数值法求解群桩的第二类Fredholm积分方程，得到在垂直简谐载荷作用下群桩的轴力、孔压随桩身变化的数值结果以及在水平简谐载荷作用下群桩的剪力、弯矩和孔压随桩身变化的数值结果。

Methods Clinical data of 3 cases of bile duct injury during laparoscopic cholecystectomy were analyzed retrospectively.

回顾总结3例LC术中胆管损伤的临床资料，分析3例胆管损伤的原因及对策。

These techniques are applied to the gobang.

本文将这些技术用于五子棋中。