公式集

It is found that under the same vibration mode, the equivalent inductance of the single layer piezoelectric transformer is the twice of the same quality piezoelectric oscillator; 2 Based on the density energy formula, the three-dimensional lump type equivalent circuit of the piezoelectric transformer has been set up.

发现在相同的振动模式下，单层压电变压器的等效电感是相同质量压电振子的两倍； 2）以能量密度公式为基础，建立了压电变压器的三维集总式等效电路图。

Due to equivalent transformation during the simplification procedure of equations, the solution set of equations can neither expand and nor contract, and also the transformed equations for four displacement functions are compact in the form and easy to find their solutions.

由于方程化简过程是等价变形，从而可以保证方程的解集既不会扩大也不会缩小，而位移势函数便给出了一维六方准晶中弹性解的一个通解公式。

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface, resulting in accelerating the Euler iteration process in solving the differential equation of curvature line. Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance.

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线。

By singular value decomposition method, we obtain inversion formula of the generalized Radon transform with weight function, and study the support and range condition of it.

用奇异值分解的方法对带权的广义Radon变换的反演作了讨论，得到了反演公式并对其支集定理和值域条件进行了研究。

Many valued logic ; quantifier ; Tableau method ; upset/downset in set ; regular formula

多值逻辑；量词； Tableau方法；集合的上集/下集；正则公式

For the partial products generation, the novel method of Booth encoding combined with partial products generating is put up, which can directly map the multiplicand and multiplicator to partition products without generating the BOOTH encoding results. For the optimization of Wallace tree adding, the series formulas of full-adder and 4-2 Compressor realization are introduced to guidance the selection. For the non-bias round, forwarding round disposal in Wallace tree method is brought forward to avoid the final multi-bit adder. Also, the idea of delay-oriented partition of the MAC frame is put up to achieve the perfect match with multi-pipeline DSP architecture.

提出了一种构建多模式算法最小并集的MAC通用结构思想与一种划分MAC通用结构以适应多流水级DSP处理器设计的通用MAC设计方法；对于BOOTH编码和部分积产生，提出了直接建立被乘数与部分积的多路选择映射关系的BOOTH编码和部分积联合产生方法；对于最优Wallace树型加法实现，提出了全加器和4-2 compressor电路实现Wallace树加法所需的关键加法路径级数公式以指导实现选择；对于无偏舍入处理，提出了在Wallace树处理舍入问题的舍入运算前置方法；提出了以时延为导向的MAC各部分单元组合与流水线匹配具体方法。

In chapter 4,we discuss the size and shape of the point set 〓 in 〓.Acalculation formula of Procrustes shape distance is given.

第四章介绍〓中点集〓的形状和容量，给出了形状之间的Procrustes距离的计算公式。

In view of disadvantages in present defect reconstruction methods,such as over-long time or excessive need for training samples,a new defect reconstruction method based on similar model and genetic algorithm was investigated as follows:similar model between non-axisymetric defect and axisymetric defect was represented,and proportionality factor was deduced by skin depth equation.

针对以往缺陷重构方法中普遍存在的计算时间长或需要大量训练样本的缺点，提出一种基于相似模型和遗传算法的缺陷快速重构方法，分析非轴对称缺陷与轴对称缺陷之间存在的相似模型，并利用集肤深度公式推导出两者之间的缩比因子，从而将耗时巨大的缺陷重构问题转换为二维轴对称情况下的计算问题；同时为进一步缩短重构时间，提出一种加快遗传算法收敛速度的方法。

Through formula Derivation and Helmholtz reciprocity theorem,devices for parallel beam of P polarized light could be designed.

借助公式推导法及Helmholtz互易定理，可设计出平行入射P偏振光的光束集束器件。

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。