查询词典 series solution

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。

Compressed acetylene access to a clean series of towers, tower 2 clean washed by the oxidation of sodium hypochlorite solution to remove sulfur, phosphorus and other impurities, and then into the tower and 10% to 15% alkali solution and, after purification acetylene by the cooling device of the initial removal of the water saturation after the sperm of more than 98.5 purity acetylene synthesis process used to send VCM.

压缩后的乙炔进入串联的1号清净塔、2号清净塔，经次氯酸钠溶液洗涤氧化除去硫、磷等杂质后，再进人中和塔用10%～15%碱液中和，净化后的乙炔经预冷器初步除去饱和的水分后，纯度98.5%以上的精乙炔送VCM合成工序使用。

A generalized mathematical model was developed to describe the distribution of over-potential.Dimensionless variables μ and ω that characterize the polarization and influence of side electrode reaction in the system,were derived from modeling.Adomian's decomposition methodADM）was used to solve the nonlinear differential equation of the model to obtain an approximate analytical solution,which was in the form of algebraic expressions of infinite power series.By the solution,the relationship between over-potential distribution and average selectivity could be easily calculated without solving the nonlinear model time and again.

建立了描述超电势分布的普遍化数学模型，归纳出表征电极极化和副反应影响的量纲1数μ和ω，并用ADM（Adomian's decomposition method）对该非线性微分方程模型求解；所获得的逼近解代数表达式，可方便地计算不同参数下超电势分布对平均选择性的影响，而毋需反复求解模型微分方程。

In 3D scalar Helmholtz equation computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by The GMT.

首次从理论上证明，在三维静电场分析中，存在一种无穷级数收敛，且有一定普遍性的解析解；推导出三维静电场分析的多极理论通解及其使用规则，证明或解释广义多极技术不能证明或解释的若干使用规则，用多极理论求解工程实际中的三维静电场边值问题。

In 2D eddy current field computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by the GMT, and solves several real engineering examples of 2D eddy current field boundary-value problems by the MT.

本文从电磁理论和有关数学定理出发，通过引入内极、外极、内交角的概念，建立一种新的电磁场计算体系——电磁场分析中的多极理论；从理论上证明，在电磁场分析中存在一种无穷级数收敛，且有一定普遍性的解析解。

Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method.

首先采用静态内压下的应力强度因子作为参考解，得到了带径向边裂纹厚壁圆筒的权函数；然后用振型函数方法推导无裂纹厚壁圆筒在冲击内压下的动应力响应，分析中将相应的弹性动力学方程解分为满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加，利用傅立叶-贝塞尔级数展开，推导出了厚壁圆筒内动应力的响应历程和分布规律；最后由动应力权函数方法导出带径向边裂纹厚壁筒在冲击内压下的动态应力强度因子计算公式。

With the idea of finite approximation, we study a new solution method for the satellite altimetry problem. Our result shows that if the continental part of the earth is sphere cap, then the solution of satellite altimetry problem can be transformed into a linear system of equations with variants of the coefficients of spherical harmonic series. We prove that the linear system of equations is separated about the orders of spherical harmonic series.

研究了球界面下卫星测高问题的解法，利用有限逼近方法得到了下列结论：若陆地部分是球冠，则卫星测高问题的解可以转换成关于球谐级数位系数的线性方程组，并且位系数的阶和次是以分离形式出现的，从而确保该解法具有实用意义。

The suitable detection wavelength was selected through qualitative determination of wave spectrum. With 95% ethanol as the reference solution, the standard curve was drawed with a series of different concn. of standard solution of chlorogenic acid, and the Absorbance of extracting solution was determined and the chlorogenic acid content in filtrate was calculated.

波谱定性检验选择适宜的测定波长，以95%乙醇为参比溶液，用配制好的一系列不同浓度的绿原酸标准溶液绘制标准曲线，测定提取液的吸光度，计算滤液中绿原酸的含量。

The company mainly engaged in a number of products have the following series: 1, highly efficient environment-friendly metal surface treatment series: stainless steel pickling passivation cream, stainless steel pickling passivation fluid, stainless steel pickling passivation head hot paste, ultra-low carbon steel acid Passivation wash cream, stainless steel high-performance cleaning fluid, stainless steel passivation fluid, carbon steel pickling paste, pickling paste titanium, stainless steel brightener washing, descaling Wang, copper surface detergent cleaning agent, electric stainless steel polishing fluid, anti - welding slag splashing paint, universal cleaning agent, senior metals rust oil, phosphating solution, degreasing agents, rust-proof paper, waterproof moisture-proof wrapping paper series.

高效环保型金属表面处理系列：不锈钢酸洗钝化膏，不锈钢酸洗钝化液，不锈钢热压封头酸洗钝化膏，超低碳钢酸洗钝化膏，不锈钢高效清洗液，不锈钢钝化液，碳钢酸洗膏，钛合金酸洗膏，不锈钢清洗光亮剂，除垢王，铜制品表面除垢清洗剂，不锈钢电抛光液，防焊渣飞溅涂料，万能清洗剂，高级金属防锈油，磷化液，脱脂剂，防锈纸，防水防潮包装纸系列。

The optimal boron concentration for growth of pea (Pisum sativum L.) andcucumber (Cucumis Sativus L.) plants was screened by designing a series of boronconcentration in nutrient solution and the influeuce of boron deficiency or toxicityon integrity of cell membrane in different organs of the two plants was studied bymeasuring pH of the nutrient solution,〓 concentration and conductance in rootexudate solution and extracting solution of different organs from the two plants.

用不同浓度硼的营养液培养豌豆、黄瓜植株，筛选和确定在温室条件下生长所需的最适硼浓度和硼毒害浓度；进而通过对缺硼、对照和硼毒害处理后营养液pH变化，根分泌物和不同组织浸提液中K+浓度和电导率的测定，研究了缺硼和硼毒害对两种植物不同组织细胞膜完整性的影响。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。