查询词典 finite constructibility

In this paper, we develop the theory of Killing form over any finite dimensional Hopf algebras, and discuss the deep relations between the non-degeneracy of Killing form and the adjoint representations of Hopf algebras.

中文摘要：本硕士论文的主要内容是在有限维Hopf代数上建立了Killing型的一般理论，揭示了Killing型的非退化性与Hopf代数的伴随表示之间的深刻联系。

The new method is a combination of characteristic approximation to handle the convection part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller time truncation is gained at the same time, and a mixed finite elementspatial approximation to deal with the diffusion part, the sealer unknown and the adjoint vector function are approximated optimally and simultaneously.

此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散，从而保证格式在流动锋线前沿逼近的高稳定性，消除了数值弥散现象，并得到了较小的时间截断误差；另一方面，对方程的扩散项采用混合元离散，可同时高精度逼近未知函数及其伴随向量函数，理论分析表明，此方法是稳定的，具有最优的L~2逼近精度。

The characteristic approximation is used to handle the convection part along the direc-tion of fluid namely characteristic direction to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion; The mixed finite element spatial approximation is employed to deal with diffusion part and approximate the scalar unknown and the adjoint vector function optimally and simultaneously; In order to preserve the integral conservation of the method, we introduce the modified characteristic method.

该方法对方程的对流部分沿流体流动的方向即特征方向离散以保证格式在流动的锋线前沿逼近的高稳定性，消除数值弥散现象；对方程的扩散部分采用最低次混合有限元方法离散、同时以高精度逼近未知函数及未知函数的梯度；为保证方法的整体守恒性，在格式中引入修正项。

How to establish the adjoint medel is discussed by using the Gateaux differential of function and the concepts of the adjoint operators in Hibert space. At the same time it is verified that selecting proper finite difference scheme can ensure discrete form remaining the same adjoint r...

文中利用泛函的Gateaux微分和Hilbert空间上伴随算子的概念讨论了连续的伴随模型的建立，并通过选择适当的差分格式离散伴随模型，使其保持连续时的伴随关系，同时给出了水温初始场最优化过程及相应的同化试验数值结果。

Firstly, we analyze the deficiencies ofexisting ones, extend domains of fuzzy logical operators from the cap product withtwo sets to them with arbitrary (finite, enumerable, or non-enumerable) number ofsets to form two general mappings so as to conform them to the fuzzy conjunctionand infimum, and to fuzzy disjunction and supremum, respectively, and fuzzify theset inclusion of fuzzy sets. Similar to the classical adjunction, the concept of fuzzyadjunction is introduced.

首先分析了原有"模糊形态学"框架的缺陷，进而将模糊合取和模糊析取算子的定义域从两个集合的笛卡儿乘积推广到任意多个集合的笛卡儿乘积，形成两个一般的映射，使得模糊合取与下确界、模糊析取与上确界保持一致，以此将模糊集的包含关系一般化。

Further, by means of investigation and admeasurement, theoretical analysis and finite element simulation, the security analysis of ancient brick-and-clay city gate structure are performed.

接着，通过现场检测、理论分析及有限元模拟，对砖土拱城门结构进行了安全性分析。

Combined with Zhongshan-gate in Nanjing,by means of investigation and admeasurement, theoretical analysis and finite element simulation, the security analysis and reinforcement research of ancient brick-and-clay city gate structure are performed. The results would be the scientific reference to the reinforcement of brick-and-clay city gate. At the same time, the reinforcement method of barking concrete structure, another available method to renovations of brick-and-clay city gate, is put forward in this paper.

本文结合南京中山门，综合运用调查检测、理论分析和有限元模拟的方法，对砖土拱城门结构进行了安全性分析和加固技术研究，为砖土拱城门结构的加固维修提供切实可靠的科学依据；同时提出内衬混凝土空间箱型结构的加固方法，为今后对其它砖土拱城门结构的研究保护提供一定的参考。

The uniform design method is used to select initial points. The admissible domain, based on initial points obtained, is partitioned into finite sub-domains. A modified Hooke-Jeeves algorithm is proposed to each sub-domain.

以均匀设计方法选初始点，并依此把允许区域分解为有限多个子域，在每个子域上构造了改进的Hooke-Jeeves优化算法。

At the same time, we prove that the best linear unbiased prediction of a linear predictable variable Qy and the best linear unbiased prediction βn=(X"sV-1Xs)-1 X"sVs-1ys of regression coefficients of the finite populations βn=(X"V-1X)-1X"V-1y are admissible under matrix loss function and in the class of the linear predictions and the class that contains all predictions, and under quadratic loss function in the class of the linear predictions.

在线性预测类和一切预测类中是可容许预测，而在二次损失函数下其在线性预测类中是可容许预测。

The main factors affecting the soil-structure interface behaviors were found experimentally and theoretically, including: 1 the thickness of the interface that is five to six times the average grain size of the soil; 2 the aeolotropy of interface, which is responsible for anisotropic response of the stress-strain response of the interface; 3 two physical states, including crashing and compression of the soil near the structure surface, which govern the stress-strain response of the interface strongly; 4 two shear deformation components due to sliding and constraint of the structure surface relative to the soil respectively, which forms the deformation of the interface; 5 the volumetric strain due to dilatancy, which is found to be composed of a reversible dilatancy component and an irreversible dilatancy component. 4. A unified constitutive model of the interface, based on new elasto-plasticity damage theory, was developed. It was confirmed to be effective for the conditions considering monotonic and cyclic shearing, coupling effect of shear and volumetric strains, evolution of physical state, micro-structure aeolotropy of the soil and the resulting aeolotropy of the interface as well as the three normal boundary conditions stated above. 5. 2D and 3D finite element formulations of the present model were derived and incorporated into the FEM codes. They were applied to the evaluation of practical engineering problems with different typical interfaces between soil and structure. The new model was shown to be reasonable and effective.

确定了粗粒土与结构接触面厚度约为5～6倍的平均粒径，首次揭示了接触面的细观结构异向性以及由此所引起的宏观剪切异向性，发现了在单调和往返剪切荷载作用下土颗粒破碎和剪切压密两种物态变化机制共同支配着接触面力学性质的变化，通过细观分析证实了接触面的变形可分解为一般同时发生的土与结构交界面上的滑移变形以及结构面位移约束范围之内土体本身的剪切变形两部分，观测到接触面受剪时表现出明显的相对法向位移，并可分解为可逆性和不可逆性两个分量；(4)建立了第一个能够统一地描述单调与往返剪切特性、剪应变与体应变耦合特性、细观结构和宏观剪切异向性以及土颗粒破碎等物态变化特性的土与结构接触面弹塑性损伤本构数学模型，并采用多种法向边界条件复杂加载路径的试验成果验证了新模型的合理性和有效性；(5)提出了新模型的二、三维有限元格式并结合实际边值问题进行了应用计算分析，比较了不同接触面本构模型对计算结果的影响，证实了新模型及其有限元格式不仅能够合理地描述土与结构接触面的主要力学特性，还能够较好地反映土体与结构物在接触面处的滑移、脱开等不连续现象。

We were cousins—his grandfather was King of Scots,and his great-grandfather was Henry VII of England.

我们是堂姐弟——他的祖父曾是苏格兰国王，他的曾祖父是英格兰的亨利二世。

I do want to help you, but I am in a quandary now!

我是想帮你，但是我现在左右为难啊！