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排序方式: 共有226条查询结果,搜索用时 122 毫秒
1.
非局部摩擦在几种塑性成形工艺中的应用   总被引:8,自引:0,他引:8  
为了考虑金属材料表面微凸结构对模具与工件接触区域上的非局部摩擦效应,在几种金属塑性成形加工问题中,首次采用Oden等提出的非局部摩擦定律代替经典的库仑摩擦定律,利用主应力法或工程法建立了相应问题的积微分形式的力平衡方程.在简化的情况下,采用摄动法求得接触面上接触压力在非局部摩擦下的近似解析解,并分析了影响接触压力非局部效应的相关因素.  相似文献
2.
Convergence Analysis of Perturbed Feasible Descent Methods   总被引:5,自引:0,他引:5  
We develop a general approach to convergence analysis of feasible descent methods in the presence of perturbations. The important novel feature of our analysis is that perturbations need not tend to zero in the limit. In that case, standard convergence analysis techniques are not applicable. Therefore, a new approach is needed. We show that, in the presence of perturbations, a certain -approximate solution can be obtained, where depends linearly on the level of perturbations. Applications to the gradient projection, proximal minimization, extragradient and incremental gradient algorithms are described.  相似文献
3.
Incremental Gradient Algorithms with Stepsizes Bounded Away from Zero   总被引:4,自引:0,他引:4  
We consider the class of incremental gradient methods for minimizing a sum of continuously differentiable functions. An important novel feature of our analysis is that the stepsizes are kept bounded away from zero. We derive the first convergence results of any kind for this computationally important case. In particular, we show that a certain -approximate solution can be obtained and establish the linear dependence of on the stepsize limit. Incremental gradient methods are particularly well-suited for large neural network training problems where obtaining an approximate solution is typically sufficient and is often preferable to computing an exact solution. Thus, in the context of neural networks, the approach presented here is related to the principle of tolerant training. Our results justify numerous stepsize rules that were derived on the basis of extensive numerical experimentation but for which no theoretical analysis was previously available. In addition, convergence to (exact) stationary points is established when the gradient satisfies a certain growth property.  相似文献
4.
Finding all solutions to polynomial systems and other systems of equations   总被引:4,自引:0,他引:4  
In a previous paper, the authors suggested a procedure for obtaining all solutions to certain systems ofn equations inn complex variables. The idea was to start with a trivial system of equations to which all solutions were easily known. The trivial system was then perturbed into the given system. During the perturbation process, one followed the solution paths from each of the trivial solutions into the solutions of the given system. All solutions to the given system were thereby obtained.This paper utilizes a different approach that eliminates the requirement of the previous paper for a leading dominating term in each equation. We add a dominating term artificially and then fade it. Also we rely on mathematically more fundamental concepts from differential topology. These advancements permit the calculation of all solutions to arbitrary polynomials and to various other systems ofn equations inn complex variables. In addition, information on the number of solutions can be obtained without calculation.Work supported in part by NSF Grant No. MCS77-15509 and ARO Grant No. DAAG-29-78-G-0160.Work supported in part by ARO Grant No. DAAG-29-78-G-0160  相似文献
5.
Incremental Gradient Algorithms with Stepsizes Bounded Away from Zero   总被引:4,自引:0,他引:4  
We consider the class of incremental gradient methods for minimizing a sum of continuously differentiable functions. An important novel feature of our analysis is that the stepsizes are kept bounded away from zero. We derive the first convergence results of any kind for this computationally important case. In particular, we show that a certain -approximate solution can be obtained and establish the linear dependence of on the stepsize limit. Incremental gradient methods are particularly well-suited for large neural network training problems where obtaining an approximate solution is typically sufficient and is often preferable to computing an exact solution. Thus, in the context of neural networks, the approach presented here is related to the principle of tolerant training. Our results justify numerous stepsize rules that were derived on the basis of extensive numerical experimentation but for which no theoretical analysis was previously available. In addition, convergence to (exact) stationary points is established when the gradient satisfies a certain growth property.  相似文献
6.
一类非线性微分差分方程的近似解   总被引:4,自引:0,他引:4       下载免费PDF全文
本文对一类非线性微分差分方程求得一致有效渐近展开式,给出了共振解的近似解析表达式,并推广了Nayfeh和Mook的结果.  相似文献
7.
In this paper, we consider the approximate solution of the type Ⅰ , Ⅲ initial boundary valued problems of the second order linear parabolic partial differential equations. We use a new difference scheme by suitably combining the difference and the basic recursion of elements in the bivariate spline space S21(Δmn(2)) to construct the approximate solutions. We have proved their convengence. And we will give a flow diagraph to display curved surface on a computer, and give an example.  相似文献
8.
一类奇异积分方程组的样条间接近似解法   总被引:3,自引:0,他引:3  
王小林 《数学杂志》1997,17(1):113-116
本文利用三次复插值样条函数给了定义于复平面上光滑封闭曲线上的一类奇异积分方程组(1)的一种间接近似解法,讨论了误差估计和一致收敛性。  相似文献
9.
AbstractThis paper is mainly concerned with solving the following two problems: Problem I. Given X Cnxm, A = diag( 1, 2, ..... , m) Cmxm . Find A ABSRnxn such thatAX = XAwhere ABSRnxn is the set of all real n x n anti-bisymmetric matrices. Problem II. Given A RnXn. Find A SE such thatwhere || || is Frobenius norm, and SE denotes the solution set of Problem I.The necessary and sufficient conditions for the solvability of Problem I have been studied. The general form of SB has been given. For Problem II the expression of the solution has been provided.  相似文献
10.
W2^2(D)空间第一类算子方程近似解   总被引:3,自引:0,他引:3  
0引言本文在具有再生核的Sobolev空间W_2~2(D)中研究第一类算子方程的近似求解问题,本文利用再生核空间技巧得到的方程(1)的近似解un(M)有如下特点:1近似解un(M)的构成只需用到f在有限个节点{Wi}1n D上的值;2当{Mi}1在D中稠密时,可以得到方程解析解u(M)的表达式,并且而且误差随节点个数n的增加接空间范数单调下降.数值算例表明,该方法是有效的.1W22(D)空间及其再生核记D=[a,b]×[c,d]为有限区域,设是D上一组互异节点系.在[1]中,设W22[a,b]={u…  相似文献
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