查询词典 Bessel functions

First, the physical models associated with dislocations and cracks are respectively converted to mixed boundary value problems in mathematics. Secondly, by using the Fourier transform, a dual integral equation for a crack and an algebraic equation for a dislocation can be derived from the boundary conditions relating with a crack and a dislocation, respectively. Solving these equations, exact analytical solutions can be obtained in terms of Bessel functions in close-form.

先把位错和裂纹的物理模型写成与它们相关的边值问题，然后，利用Fourier变换将这些边值问题化成一个对偶积分方程(对位错而言，得到一个代数方程)，求解此对偶积分方程，可以获得以Bessel函数给出的封闭形式的分析解。

By using eigenvalue method and Bessel functions, the closed solutions of 3D transient temperature field in each layer of the cylinder were deduced.

利用特征值法和Bessel函数，导出了各层柱体中三维瞬态温度场的封闭解析解。

The problem of overflow during the computation of Green's function can be successfully solved by subtracting the exponential term from the modified Bessel functions.

采用将变型Bessel函数的指数项单独列出的方式有效地解决了Green函数计算中的上溢问题。

Summation of the corresponding Bessel functions gives reinforcement for the inner

总结了相应的Bessel函数给出加固内

The problem of overflow during the computation of Green′s function has been successfully solved by subtracting the exponential term from the modified Bessel functions.

采用将变型Bessel函数的指数项单独列出的方式有效地解决了Green函数计算中的上溢问题。

Finally, making use of integral equalities associated with Bessel functions, the explicit expressions for elastic displacement and stress fields induced by these defects can be obtained in terms of elementary functions.

最后，通过一些Bessel函数的积分恒等式，便可给出在这些准晶中由这些缺陷所诱导出的以初等函数的明显表达式表示的弹性位移场和应力场。

Then,introducing stretching transform and using the Bessel functions of 1/4 and-1/4 order,the interior layer solution is constructed.

然后引入伸展变量变换，并利用1/4和-1/4阶Bessel函数，构造在转向点附近的内层解。

Then the scattering waves are represented bythe series of Bessel functions expansions.

它是用一个半径足够大的大圆弧拟合半空间表面，再将所有的散射波展开成Fourier-Bessel级数的形式。

The results about the magnetic vector potential of current-carrying ring and the electric potential of uniform charged ring which are expressed by Bessel functions are further calculated and analyzed.

用Bessel函数积分对圆环电流磁矢势及均匀带电圆环电势作进一步的计算分析，引申出磁感应强度及电场强度新的级数表达式，分析讨论了所得结果。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。