凸规划

It is generalization of linear and convex quadratic programming.

这可以被看作是一个特殊情况非线性规划或泛化的线性或凸二次规划。

There are a large number of non-convex functions in practical problems, and they have similar nature in the non-linear programming as convex functions.

实际问题中的大量函数都是非凸的，它们与凸函数在非线性规划中有一些相似的性质。

Therefore, the research on convexity and generalized convexity is one of the most important aspects in mathematical programming.

因此，对凸函数和广义凸函数的研究是数学规划中最重要的内容之一。

A deterministic global optimization algorithm based on Lagrangian dual is proposed for solving the nonconvex quadratic programming with nonconvex quadratic constraints, which is often encountered in technical design and operational research.

针对带有非凸二次函数约束的非凸二次规划问题，提出了一个基于拉格朗日对偶的确定型全局优化算法，这类优化算法可广泛应用于工程设计和非线性系统的鲁棒稳定性分析等实际问题中。

The equivalent relation between quasi-semi-E-convexity of functions and corresponding level sets is proved.

函数的凸性与广义凸性在数学规划以及最优化理论中起着非常重要的作用。

This paper study the connectedness of the set of cone efficient solution s for cone quasiconvex multiobjective programming in locally convex Hausdorff topological vector space.

本文研究局部凸的Hausdorff拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性问题。

Fuzzy inner product spaces are investigated by T-norm and T-conorm, and the inner product of fuzzy vectors is concerned.

在研究模糊向量空间、模糊凸集和模糊凸映射的基础上，我们研究了模糊规划的Lagrange对。。。

Objective To investigate the effect of posterior pedicle screw instrumentation and determine the impact of alternative surgical strategies to provide guidance for the operation planning. Methods A detailed three-dimensional finite element model of a 40° scoliotic lumbar with pedicle screw instrument were constructed by using the commercial finite element software ANSYS.

目的 通过有限元计算与刚体动力学相结合的方法，模拟后路椎弓根螺钉系统治疗脊柱侧凸的矫形过程，研究矫形过程中的生物力学特性，探讨不同矫形策略对临床结果的影响，为脊柱侧凸的手术规划提供依据。

Traditionally, a surface is usually scatted in an array of 3D data points which are topologically connected by rows and columns to form a rectangular mesh. This method can't meet the requirement of description and measurement for some complex surfaces. On the basis of tracing border points, a new method is proposed to deliver 3D data points of surfaces, which are topologically constructed with optimum rectangular and triangular mesh. In order to measure surface efficiently and safely with NC machine, an optimization of measurement paths is proposed to avoid interference between the measuring tool and the surface with holes. The curve design is the basis of surface modeling.

数控测量技术的发展为测量自动化、集成化、智能化提供了可能，而对于复杂曲面的自动测量规划则是测量技术中的难点问题，平行截面等数目测点分布和四边拓扑测点分布规划方法，不论在测点分布的合理性上还是在网格结构的优化方面，均难以满足形状或边界较复杂曲面的离散化描述和曲面造型的要求，为了实现任意拓扑曲面的自动测量，本文对复杂曲面的合理离散化描述和自动测量问题进行了研究，提出了基于边界跟踪、优化网格的测点自动分布规划和四边、三角混合网格的生成方法：同时对具有孔洞或测量干涉凸台等非完整曲面的测量路径优化问题进行了研究，提出了路径优化方法。

In this study, a commercial CAD/CAM Software is used to plan and generate the multi-axis tool path, and a table rotating/tilting type five-axis machining center is used to perform the experimental machining operation. The material of the die studied is NAK 80 die tool steel, and the geometries are modeled as concave and convex spherical surfaces. Milling parameters considered are spindle speed, feed rate, and different types of cutting tool path. The experimental results show that the surface roughness for concave spherical surface is about 0.247 μm and roundness is about 0.0283 mm and the surface roughness for convex spherical surface is about 0.250 μm and spherical roundness is about 0.0551 mm under the cutting conditions mentioned in this study.

本研究的实验方法与步骤包括利用商用CAD/CAM系统针对实验对象规划三轴/五轴同动加工路径，并经后处理程式转换，在本实验室之平台倾斜/旋转型之五轴加工机上进行实验，实验对象为NAK80模具钢材料之凹与凸球形曲面之加工，此外考虑的切削条件有主轴转速、进给速度、加工路径等，在本研究所设定之最佳切削条件下，凹球形曲面之真圆度约为0.0283 mm，粗糙度为0.247 μm，而在相同切削条件下，凸球形曲面之真圆度为0.0551 mm，粗糙度为0.250 μm。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。