E环的结构

含有可数个(有限个或无限个)非幂零的极小理想的可换结合环称为E环。引理1:设N是E环R的非幂零的极小理想,则N是一个域,且是R的直和项。证明由题意知N=N~2≠0,所以对任一非零元a∈N有aN≠0.否则C={a|a∈N,aN=0}≠0,于是C+CR是R的理想,又因C+CR(?)N,且由N的极小性,得C+CR=N,于是由交换性得N~2=0。这与N是非幂零的条件矛盾。注意到aN(?)N,且aN也是R的理想,于是aN=N,     

局部Haar条件下的Chebyshev同时逼近

本文在局部Haar条件下，讨论了紧空间上非线性Dunham型Chebyshev同时逼近，得到了同时逼近为局部最佳的充分必要条件，给出了与非线性同时逼近问题等价的相关线性同时逼近问题；证明了极小集的存在性，在这个极小集上的局冲淡最佳逼近为局部最佳的；获得了区间上非线性同时逼近的交错定理；证明了非线性同时逼近的a阶（a≥1)的强唯一常数等于其相关线性同时逼近的a阶强唯一常数。     

探析一类泛函的径向极小元的局部一致估计

本文在带权的Ginzburg-Landau型泛函的径向极小元的整体估计的基础上,通过适当引入辅助泛函,以此来降低该整体估计右端的增长速度,最后使之不再增长或负增长,从而最终建立所需的局部一致估计,为日后研究径向极小元的极限行为做铺垫.     

“一元一次方程”综合测试题

一、选择题1.若关于x的方程(2k-1)x2-(2k 1)x 3=0是一元一次方程,则k的值为().A.0B.1C.12D.22.若关于x的方程4m-3x=1的解是-1,则m的值为().A.-2B.-12C.-1D.13.某件商品连续两次降价10%,两次降价后该商品的售价为a元,则该商品的原价为().A.0.92a元B.1.12a元C.a1.12元D.0.a81元4.     

l-群的根系Γ_1(G)的极小条件

若G是l 群 ,Γ1(G)是G的所有正则子群所构成的根系 .Gα∈Γ1(G)称为原子元 ,如果对于 Gβ∈Γ1(G)且Gβ Gα,必有Gβ=Gα.Γ1(G)称为满足极小条件 ,如果Γ1(G)中的每个元都至少包含一个原子元 .主要结果是 :(1)Γ1(G)中的原子元Gα 具有形式Gα=a┸ 当且仅当 {PGcα}是归纳的 .(2 )G∈Bw[1] ,Γ1(G)满足极小条件当且仅当Γm(G) Γ1(G) .     

一四元数矩阵方程的最小二乘解

利用四元数体上自共轭矩阵的奇异值分解,得到了实四元数矩阵方程X+AXB=C的最小二乘解的表达式,同时给出了在相应解集中矩阵方程的极小范数解.     

环域上p-Ginzburg-Landau泛函的径向极小元的唯一性与正则化

研究了p-Ginzburg-Landau型泛函的径向极小元在环域上的极限行为,鉴于极小元于环域内无零点,证明了极小元的唯一性与正则化.     

0-1规划的填充函数算法

文章首先给出搜索0-1规划局部极小解的邻域搜索算法,在此基础上给出了填充函数算法.该算法的思想是在求得总体优化问题的一个局部极小点后,构造填充函数,通过极小化该填充函数找到比当前局部极小解更好的解 该方法是一种直接算法,我们通过具体的数值实验证实了该算法是有效的.     

退化抛物型方程零阶项系数和初值的反演问题

研究了最优控制问题极小元的局部适定性。该优化问题涉及同时重构退化抛物型方程初始值和零阶项系数的反问题。与一般的优化问题不同,这里构造的代价函数是一个二元函数,包含两个自变量和两个独立的正则化参数,并推导出极小元必须满足的必要条件。特别地,由于代价函数中两个未知系数的状态不同,单参数优化问题的共轭理论不能应用于该问题。通过假设终端时间T相对较小,得到了关于极小元的L2估计,由此可推导出极小元的唯一性和稳定性。     

2003年四川省初中数学竞赛

一、选择题 (每小题 6分 ,共 36分 )1.甲在集市上先买了 3只羊 ,平均每只a元 ,稍后又买了 2只羊 ,平均每只b元 .后来他以每只a +b2 元的价格把羊全部卖给了乙 ,结果发现赔了钱 .赔钱的原因是 (　　 ) .(A)a =b　　　　　 (B)a >b(C)a 相似文献   

带权的Ginzburg-Landau型泛函的径向极小元唯一性研究

主要对带权的Ginzburg-Landau型泛函的径向极小元的唯一性进行研究。先证明出径向极小元的整体估计、极值原理和梯度估计,通过这些结论最终证明出带权Ginzburg-Landau型泛函的径向极小元是唯一的。     

带权的Ginzburg-Landau型泛函的径向极小元唯一性研究

主要对带权的Ginzburg-Landau型泛函的径向极小元的唯一性进行研究。先证明出径向极小元的整体估计、极值原理和梯度估计,通过这些结论最终证明出带权Ginzburg-Landau型泛函的径向极小元是唯一的。     

Vertical vibration of a large diameter pile embedded in inhomogeneous soil based on the Rayleigh-Love rod theory

The vertical vibration of a large diameter pile embedded in inhomogeneous soil with hysteretic type damping is investigated based on the 3D axisymmetric model. Firstly, the pile is assumed to be a Rayleigh-Love rod with the consideration of its transverse inertia effect. Following this assumption, the pile-soil system is divided into several segments according to the stratification of the surrounding soil, and the dynamic interactions of the adjacent soil layers are simulated using the distributed Voigt model. Meanwhile, the surrounding soil is discretized into finite annular vertical zones to consider its radial inhomogeneity, and the force equilibrium and displacement coordination are satisfied at the interfaces of the adjacent soil zones and the interface of the pile-soil. Then, the analytical solution in the frequency domain and the semi-analytical solution in the time domain are obtained by solving the vibration governing equations of pile-soil system. Based on the solutions, a parametric analysis is conducted to investigate the influence of the transverse inertia effect on the dynamic response of the large diameter pile and its relationship with the pile parameters and the radial inhomogeneity of the surrounding soil. Finally, a comparison with the measured result and two other calculated results is presented to verify the effectiveness of the present solution.     

3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials

The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.     

一个参数动态调节的全局凸填充函数算法

构造了有界闭箱上连续全局优化问题的一个新的全局凸填充函数,分析了该函数的几个性质,设计了一个基于该填充函数的全局优化算法。该算法通过动态调节参数来跳出当前收敛的局部极小解的邻域,数值试验表明该算法是有效的。     

无界域上带限制的非线性椭圆特征问题的多解和变号解

在径向对称的Sobolev空间中,利用约束变分方法,通过构造切伪梯度向量场,证明了无界区域上带限制的非线性椭圆特征问题正解、负解及变号解的存在性。     

求非线性整数规划的逐次下降方法

In this paper, a new method named as the gradually descent method was proposed to solve the discrete global optimization problem. With the aid of an auxiliary function, this method enables to convert the problem of finding one discrete minimizer of the objective function f to that of finding another at each cycle. The auxiliary function can ensure that a point, except a prescribed point, is not its integer stationary point if the value of objective function at the point is greater than the scalar which is chosen properly. This property leads to a better minimizer of f found more easily by some classical local search methods. The computational results show that this algorithm is quite efficient and reliable for solving nonlinear integer programming problems.     

Effect of radial depth on vibration and surface roughness during face milling of austenitic stainless steel

This paper studies the influence of radial depth on vibration, chip formation and surface roughness during face milling of AISI304 austenitic stainless steel with indexable cemented carbide milling cutters. The amplitude of vibration acceleration increased with the increasing radial depth up to 80 mm. And the domain vibration frequency varied with the radial depth. In this paper, three types of chips were found: C shape, long shape and spiral shape. The minimum surface roughness value occurred when the radial depth equalled 40 mm in the experiment. Irregular changes of chip curl radius and chip thickness could be attributed to different numbers of alternately engaged teeth when the feed and speed were fixed. Surface roughness is related to forced vibration and chip formation. Radial depth with different numbers of alternately engaged teeth could significantly influence the forced vibration, chip formation, and surface roughness.     

集值优化问题的弱有效解

集值映射的导数是解决集值优化问题的一个重要工具。论文借助于集值映射的相依导数,相邻导数,约切导数等几种导数,以Lagrange乘子的形式给出集值优化问题有弱最小解的必要条件、充分条件以及充分必要条件。