导出方程

It presents a novel hypothesis that the limit angle of the opposite phyllotaxis in plants is a πω2 by the theory of analogy at first time.

采用差分方程理论和互生植物叶序分数序列的极限ω2 导出植物对生叶序序列和叶序分数。

A refinement expression of Lip-FIF is derived by using the fixed point equation satisfied by FIF.

利用分形插值函数满足的不动点方程，我们导出了Lip-FIF的一个细分表达式。

Based on the variational principle of virtual voltage and virtual displacement derived in this thesis and the classical theory of linear laminated plates, and by using the constitutive equations of elastic piezoelectric materials, and the DKQ quadrilateral plate bending element, the finite element modeling for the fabric reinforced laminated plates with nonlinear voltage-electric strain relationship of piezoelectric actuators has been established for the first time in this thesis. And the expressions for the electric loadings with obvious mechanical meaning and convenient for computation are established, which can be used to the deformation analysis of laminated plates with piezoelectric actuators under specified voltages.

以本文直接导出的压电结构的虚电势—虚位移变分原理为基础，依据经典线性层合板理论和压电弹性体的本构方程，采用基于离散法线假设的DKQ四结点任意四边形薄板弯曲单元，首次建立了考虑非线性电压—电应变关系的含压电致动器的纤维增强型层合板的有限元分析模型，并推导建立了力学意义明确、便于计算的电荷载表达式，可用于指定电压条件下纤维增强型叠层合成板的变形分析。

The paper introduces a differential equation derived from Markov theory and probability generating function.

文章介绍用Markov理论与母函数方法建立相关微分方程，并导出近似解析解，着重对常数源在系统中的涨落作了数学描述，给出了数值例子。

The anodic oxidation reactions of borohydride ion involves a novel and complex reaction system of three hydrogen valence states: protide H(superscript --protium H(superscript 0*-proton H(superscript +. Based on cyclic voltammetry and polarization studies, a multi-step mechanism for the oxidation of BH4-on Cu anode in NaOH solution was presented, and a kinetic expression containing the coverages of BH(superscript - subscript 4) and OH-adsorbed on the surface of Cu anode was deduced by the steady state approximation theory.

鉴于BH(上标-下标 4)阳极氧化反应涉及一个复杂的氢负离子H(上标-下标 4)－氢单原子H(上标 0*)－质子H之间价态转化的新颖反应体系，在循环伏安和极化实验研究基础上，提出了NaOH溶液中BH(上标-下标 4)在Cu电极上氧化反应的多步骤机理，导出了包含表面吸附态BH(上标-下标 4， ad)和OH覆盖率θ和θ的电极反应动力学方程。

The generalized magnetostatic field reciprocity theorem is deduced by the language of differential forms.

应用微分几何语言导出了广义静磁场互易定理，并应用该定理推导了漏磁无损检测数值分析中的富内德和蒙积分方程和线圈电感增量公

Based on up_ and down_going wave decomposition and elastic wave power reciprocity theorem, this paper derives, in the lateral velocity varying case, linear prediction operators expression and the generalized spectral factorization equation for reflection dataset.

本文基于上下行波分解及弹性波互易定理，导出横向变速介质条件下线性预测算子的表达式和反射数据的广义谱分解方程。

In this paper a recursion equation of butterfly FFT is represented according to which a program is given.

实际应用中全部点的FFT算法是冗余的，为解决少数点的FFT算法，文章导出了蝶形FFT的递归方程，给出实现少数点应用程序，进而提出直接多项式方法，较全部点迭代FFT算法具有更高的效

Some basic equations of dual beam scan are derived,such as,the position vector for the incident point,the scalar expression for reflected ray,scan pattern on observation plane ect.

文摘：应用几何光学理论研究了多光束转镜扫描场的非对称性，导出多光束扫描入射点位置矢量、反射线标量表达式、观察面上的扫描轨迹方程，并研究了扫描远场的非对称性。

Using the characteristic of the regular curve boundary for a bending plate in engineering,the analytic integral formulae of assistant states in boundary element method with the linear element for a Kirchhoff circular plate are introduced and the systematic equation of BEM is established in this paper.

利用一般弯曲薄板边界为规则曲线的特点，对工程常用的圆形弯曲薄板，采用线性单元，导出K irchhoff圆板各辅助态的边界积分解析表达式，建立问题的边界元法系统方程，从而使薄板的边界元分析完全避免通常使用的高斯积分，明显提高计算精度。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。