查询词典 modified bessel function

Moreover, the quasi-analytical expressions of the relative concentrations at the mobile region and the immobile region are deduced respectively by using Bessel equation, Bessel function and the method of Laplace transform under the initial concentration zero and the first or second boundary condition of a semi-infinite one-dimensional space.

并分别在初始浓度为零，半无限一维空间内第一类边界条件和第二类边界条件下，利用Bessel方程、Bessel函数和Laplace变换法推导出了可动区和不动区溶质相对浓度的准解析表达式。

Painting with a Bessel function matlab graphics, deepen their understanding of Bessel functions.

详细说明：用matlab绘画出贝塞尔函数图形，加深对贝塞尔函数的认识。

It may be a modified terminal bud, as in the grapevine; a modified lateral branch, as in the passion flower; a modified leaf, as in Clematis Montana; a modified leaflet, as seen in many of the pea family; or a modified inflorescence, as in Virginia creeper.

它可能源于一个变态的芽，比如葡萄藤；或源于一个变态的枝，如西番莲；也可为一个变态的叶片，如 Clematic Montana ，亦或是一个小叶，如豆科；还可能是变态的花或花序，如五叶地锦。

In the dissertation, a new stabilization method, equal-density method was adopted to prepare modified asphalts with storage stability at high temperature. In this method, a compound was prepared by premixing polymer and filler, and the compound was mixed with asphalt to prepare Polymer-Modified Asphalt by changing the ratio of polymer and filler. The asphalts with good storage stability were formed with the addition of filler, by regulating the density difference between polymer and asphalt. With identifying the effect of composition factor and the technique conditions on mechanical properties of polymer/filler compound and the molecular distribution of the polymer, identifying the effect of composition factor and the technique conditions on the properties and structure of polymer/filler modified asphalt, Styrene-Butadiene-Styrene copolymer, Low Density PolyEthylene, Styrene-Ethylene-Butadiene-Styrene block copolymer modified asphalts with good storage stability and performance were prepared. Rheological method, gel content analysis and swelling measurement were adopted to elucidate the interaction between the polymer and filler. Filler reduced the difference between the polymer and asphalt with the premixing technique, which led to the improvement of the storage stability of the modified asphalts. The thermo-oxidative aging process of base asphalt and PMA were studied and the effect of antioxidant additives on the base asphalt and PMA were analyzed.

本论文采用等密度方法，即预先混合聚合物与填料制备复合物，复合物在沥青中会吸收油份而溶胀，改变填料的用量从而调节聚合物与沥青的密度差异的方法，制备出高温贮存稳定的改性沥青，并研究了工艺条件和配方因素对聚合物/填料复合物力学和聚合物分子量分布的影响，系统考察了工艺条件和配方因素对聚合物/填料改性沥青性能与形态结构的影响，研制出性能优良、高温贮存稳定的苯乙烯-丁二烯-苯乙烯三嵌段共聚物、氢化SBS、低密度聚乙烯改性沥青，并通过流变学分析方法及凝胶和溶胀测试探讨了聚合物与填料的相互作用，指出经过预混工艺填料改变了聚合物与沥青的密度差异，以此说明聚合物/填料改性沥青高温贮存稳定的原因；研究了基质沥青和聚合物改性沥青热氧老化过程，并分析了抗氧剂对基质沥青及聚合物改性沥青的影响，探讨了抗氧剂提高沥青耐老化性能的原因。

A new method based on the Fourier-Bessel series is proposed to calculate the higher-order harmonic components of a nonlinear ultrasound field in absorbing medium and an analytical solution of a series form is obtained. A closed analytical solution of the higher-order harmonics in the zeroth-order Bessel ultrasound field and the focused Gaussian ultrasound field is deduced to study the field property, especially the near-field property.

提出了一种基于Fourier-Bessel级数的新方法，用于计算吸收媒质中非线性超声场的高次谐波分量，得到其级数形式的解析解，由此推导出吸收媒质中零阶Bessel超声场、Gauss聚焦超声场高次谐波的封闭解析解，进而对其声场特性尤其是近场特性进行了研究。

Finally the connections between the Lebesgue measure for its image and Bessel-Ricsz capacity are discussed and an explicit Bessel-Riesz capacity estimate is obtained.

利用鞅的方法讨论了广义布朗单的碰撞概率与容度之间的关系，给出了其碰撞概率的容度估计。

In this paper, the propagation and focus properties for several modes describing hollow beam are analyzed, and the focus properties for hollow gaussian mode are particularly discussed. Furthermore, a new mode, high-order Bessel-Gauss mode, is put forward to describe hollow beams. The results for high order Bessel-Gauss beams propagating through lens focusing system and free space are derived by terms of Collins integral formula.

本文分析了几种描述空心光束数学模型的传输特性和聚焦特性，着重讨论了描述非中空光束的数学模型的聚焦特性；同时提出了一种描述完全中空的空心光束的新模型――高阶贝赛耳高斯模型，并且运用Collins积分公式，分析了这种新模型的空心光束的传输特性和聚焦特性。

The double integration can be simplified to standard Bessel integration through the relation of Bessel functions.

利用贝塞尔函数的性质可将该二重积分化为标准的贝塞尔积分，然后采用直接数值积分的方法计算该积分。

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

The problem of multi-objective usually meet many conflict each other and can not use the objective of the same standard unit, then to employ membership function of fuzzy theory,at first each objective function to change fuzzy set and express with membership function, membership function include the maximum constraint, minimum constraint, the decrease function of monotonic property, to become optimal of the multi-objective function, but still to scanty of weighting value with regard to adjustment of objective function, thus this thesis proposes the method of combine orthogonal arrays and particle swarm optimization to solve the problem of multi-objective optimal power flow, each objective function separately add weighting value, to setting each weighting value of objective function in order to the result of anticipating.

多目标最佳化的问题通常会面临到许多互相冲突且不能用同ㄧ标准单位的目标，於是利用模糊理论中的归属函数，首先将各目标函数转换成模糊集合并以归属函数表示，归属函数包含了最大限制值、最小限制值、单调的递减函数所组成，将各目标函数利用归属函数表示，形成单一目标函数的最佳化，但是仍缺乏权重值对於目标函数的调整，於是本篇论文提出ㄧ种权重值设定与粒子群优演算法的方法去解决多目标最佳电力潮流的问题，将各目标函上分别加上权重值设定各目标函数的权重值，得到预期的效果。

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