查询词典 modified bessel function

The total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions.

指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、n阶三角函数和n阶双曲函数等。都是S－函数的特殊形式。文中证明了关于S－函数及其各阶导数的性质的三个定理。

Analysis compared with different expression of temperature distribution on deposition and non-deposition in the tested inside-wall of pipeline,a nondimensional temperature function was founded to get a conclusion according to energy equation.Referring to Bessel function,a calculation equation of temperature distribution in the surface and heat-flow density of wax deposit layer in the laminar flow is deduced,as well as temperature distribution inside.This method provides a theoretic basis on the theory law o...

通过对试验环道上测试段相关数据的测试，对比分析测试段管壁有沉积物和无沉积物时测试段管壁内温度分布的不同表达式，根据能量方程建立了无量纲温度分布方程，利用贝赛尔函数推导出原油在层流状态下沉积层表面温度分布、沉积层热流密度、油流温度分布等相关温度场的计算公式，为研究蜡沉积规律，定性分析管路结蜡层厚度和制定合理的清管方案奠定了理论基础。

In this paper, based on the Bessel function, an Ordinary Differential Equation was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed.

在探索求解精度和计算效率的矛盾中，提出了结合求解常微分方程的节点制表、节点间插值的快速计算Gre en函数的方法并据此开发了一套三维深水时域Green函数的数值计算程序。

By use of the series representation of the Bessel function of the first kind and zero order, the approximate expression of the wave structure function under all conditions of atmospheric turbulence is derived.

由第一类零阶贝塞尔函数的级数展开推导出波结构函数在任意湍流条件下的近似表达式。

For scattering state, its wave function should tend to the spherical Bessel function with a certain phase shift outside the interaction region.

对于散射态，其波函数在相互作用区域以外，应趋近于带有相移的球贝塞尔函数。

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。

As an application example,numerical calculation was performed for partially coherent modified Bessel-Gaussian beams propagating in free space with hard-edge aperture,and the computation errors and application ranges of those analytical equations were discussed.

以部分相干修正贝塞尔－高斯光束在有光阑情况下自由空间的传输为例作了数值计算，对所得解析公式的计算误差和适用范围进行了讨论。

The mathematical method for calculating the infinite oscillating integration with complex argument modified Bessel functions is discussed. The borehole correction charts of the coils with metal mandrel are given.

给出了含复宗量变型Bessel函数无穷限振荡积分的数值计算方法和含金属心棒线圈系的井眼校正图版。

To match the boundary conditions, the modified Bessel functions are expanded to the planar wave in the interface. Then the eigenvalue equations of different polarizations are obtained by scalar approximation. At last, the relations between propagation losses and the states of polarizations, the geometric structures of the fiber, the refractive index and thickness of the polymer are calculated.

论文首先给出其等效折射率数学模型，在纤芯和包层中，光场用贝塞尔函数及虚宗量贝塞尔函数的求和表示，在聚合物和金属中用指数函数的求和表示，交界面上采用将虚宗量贝塞尔函数用平面波展开的方法匹配边界条件，然后利用标量近似求出极化D型光纤不同偏振态光场模式的本征值方程，最后通过数值计算得到光纤的传输损耗与抛磨平面和纤芯之间的距离，聚合物粘接材料的折射率和厚度，以及偏振态之间的关系。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of Gather zero measure, discussing the relation between almost continuous everywhere and existent of limit, it gets the theory which is from the function integrability to the consecution and from consecution to the limit existence .i.e. the almost limit existence is equal to the almost continuous everywhere in the integrable function of Riemann. It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，从而得到了从函数可积性到连续性，从连续性到极限存在性的函数特性理论，即可积函数中极限的几乎处处存在与几乎处处连续是等价的，得出比正规函数更加宽泛的统一条件，得出了有界变差函数是可积函数的结论。

Molecular Distillation is a kind of high vacuum distillation method, which is suitable for the separation of high boiling, heat sensitivity and viscidity products.

分子蒸馏技术是一种在高真空条件下进行的连续蒸馏过程，适合于分离高沸点、热敏性及具有生物活性的混合物。

They are to the Noughties what yuppies were to the Eighties .

那在六十年代是时髦的，但在八十年代肯定是过时了