查询词典 approximation function

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。

The powerful function of a new computer language MATLAB, produced by the America Mathworks company, is the mathematical software system for the calculation in science engineering. It can efficiently solve problems in science and engineering such as numerical linear hypercomplex system, digital approximation, optimization, numerical quadrature etc. It also has characters of beautiful interface and convenience for users.

MATLAB是Mathworks公司推出的适用於科学和工程计算的数学软件系统，可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题，且具有可视化图形处理、使用方便、开放式多功能於一体的新一代计算机语言。

In this method,without depending upon small parameter,a trial function with possible unknowns is used as initial approximation,then a correction functional is constructed by means of a general Lagrange multiplier ,which can be identified via variational theory.

本文提出了一种求解非线性方程的迭代算法，它不依赖于小参数，是先给方程一个带待定函数的试函数作为初始近似解，然后用拉氏乘子法构造一个迭代公式。

Relative derivatives of such nodal interpolation function are also calculated by numerical approximation.

相对的导出节点内插函数也是经由数值近似计算。

Using the approximation of steady collisional-radiative equilibrium model, the interstage line intensity ratios of the K-shell lines of aluminum were given as a function of electron temperature and density.

利用稳态碰撞辐射平衡近似条件下的等离子体光谱辐射动力学模型，给出了Al激光等离子体Ly β线与He β线强度比以及Ly γ线与He γ线强度比与电子温度的函数关系。

Modifications to the conventional layer by layer optimization method make it possible to avoid computing Hessian Matrix and its inverse form, thus it can decrease computational complexity dramatically. Simulation results for some practical problems such as function approximation and XOR problem, have demonstrated improvements over classical back-propagation algorithm and conventional layer by layer optimization algorithm.

本文在传统逐层优化算法上的改进避免了反复计算 Hessian 矩阵及其逆矩阵，因而可以减少计算量，对一些应用问题，如函数逼近、异或等问题的仿真实验证实了新的算法比经典的 BP 算法以及现存的逐层优化算法的训练速度更快、可靠性更好。

Estimation of the attenuation law is based on the inverse transfer function of the object approximation in the frequency domain.

估算的衰减规律，是基于逆传递函数的对象近似的频域。

Using RBF neural network substitutes BP network as the approximation of implicit performance function, and the response surface is formed in the sphere of hyper-pyramid at iteration step.

采用径向基函数神经网络，代替目前常用的BP网络，迭代过程中在超锥体的范围内构造响应面，逼近隐式的非线性功能函数。

In the fifth part, we obtained a solution of the boundary function for the Laplace equation by knowing some of its interior points values of five-point difference approximation.

给出从Laplace方程的解的内点值求边界函数的方法。

Lastly, we discuss the energy-band structure of ultracold atoms in optical lattice by means of Green function method and in addition, procure the superfluid-Mott phase transition condition in mean-field approximation which is in agreement with the result in the literature.

最后利用格林函数方法讨论了光格子中超冷原子的能带结构，根据Mott相存在能隙的判据我们在平均场近似下重新得到superfluid-Mott相变条件，该结论与相关文献一致。

Many will continue to choose to live in duality and in conflict.

许多人将继续选择活在二元对立性和冲突中。

I find that students of the University of Physical Education all wear sportswear at first sight.

我发现：体育大学的学生乍一看，都是穿运动衣，大家都一样