近似计算

During the simulation, themost important problem is to compute the geodesic distance as fast and exactly as possible. We modify the approximating method and make it work for the concave andmultiple sources.

在这个模拟方法中，使用了改进的近似快速计算三角网格上测地距离的方法，使之能处理凹面及多源点的情况。

Geometric optics is often simplified even further by making the

即使仍然使用近轴近似，这一技术可以部分描述衍射，能够精确计算激光束随距离传播的速率以及其最小的汇聚尺寸。

The magnet size （here the angle of the magnetic pole was used） modification to eliminate the phase shift was estimated by using a hard-edge approximation to the magnetic field distribution along a circle.

给出了由滑相角度估算磁极张角修正量的方法，根据滑相角度计算磁场沿圆周的平均值与等时性场的偏差；为消除此偏差，将磁场沿圆周的分布做硬边界近似，估算出磁极几何尺寸的修正量。

In sphere approximate, GPS/Gravity-BVP is Neumann problem over exterior spherical domains. Then the natural boundary reduction, suggested by Feng and Yu, is applied to deal with the three dimensional problems. By expansion in spherical harmonics, the natural integral equations of harmonic problems over exterior spherical domains are obtained. Meanwhile, a numerical method for solving geodetic BVP is developed.

在球近似下将GPS-边值问题转化为Neumann外问题，用自然边界元法进行自然边界归化，得到自然边界积分方程，再求自然边界积分方程的数值解，与其他边界元方法相比，自然边界元法的计算量大大减小，并且具有很好的逼近性质，能有效地处理奇异积分，是求解GPS-边值问题有效方法。

Most of them involves solving the gradient and Hessian of the object function, usually by means of symbolic differentiation.

它们大都涉及求解函数的梯度和海森矩阵，通常使用的计算方法是符号微分和差分近似。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

Because the weights are determined by the correlation of code sequence and estimation error of channels, which can be nearly determined by system load factor, we determine the sub-optimum weights by system load factor through simulations, and substitute the hard-decision symbol function by soft-decision hyperbolic tangent function to decrease the risk of error decision.

由于加权因子取决于前级符号估计的可靠性。也就是取决于扩频码互相关系数与信道估计精度，在随机扩频系统中，估计精度可近似由系统负荷决定，因此可根据系统负荷决定加权因子，以很小的性能降低代价换取计算量的极大降低。同时，为进一步降低误判风险，使用带有斜率控制因子的双曲正切函数代替常规的符号函数。

The characteristic of this method lies in transforming improper integral into the usual one. Thus various kinds of usual approximate integrals can be used, and the observed data may be calculated directly and conveniently to obtain necessary numerical accuracy.

该方法的特点是把Abel变换的广义积分变化成通常的积分，这样就能够使用各种通常的近似积分公式直接从实验数据计算到所要求的数据精度。

The reasons of the indeterminacy and the approximation property on the solution of ICA are presented.

从这3种方法的计算公式出发，分析了自然梯度算法的收敛条件，指出了ICA问题解的不确定性和近似性的根源。

The variations of the residual velocity with the initial velocity are obtained.

计算结果表明，在火炮初速范围内，长管体的剩余速度随撞击速度的增加近似为线性递增。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。