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1.
Crouzeix-Raviart type finite elements on anisotropic meshes   总被引:47,自引:0,他引:47  
Summary. The paper deals with a non-conforming finite element method on a class of anisotropic meshes. The Crouzeix-Raviart element is used on triangles and tetrahedra. For rectangles and prismatic (pentahedral) elements a novel set of trial functions is proposed. Anisotropic local interpolation error estimates are derived for all these types of element and for functions from classical and weighted Sobolev spaces. The consistency error is estimated for a general differential equation under weak regularity assumptions. As a particular application, an example is investigated where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges. A numerical test is described. Received May 19, 1999 / Revised version received February 2, 2000 / Published online February 5, 2001  相似文献
2.
Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework   总被引:43,自引:0,他引:43  
This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be ``embedded' into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem. Accepted 24 November 1999  相似文献
3.
Inexact implicit methods for monotone general variational inequalities   总被引:32,自引:0,他引:32  
Solving a variational inequality problem is equivalent to finding a solution of a system of nonsmooth equations. Recently, we proposed an implicit method, which solves monotone variational inequality problem via solving a series of systems of nonlinear smooth (whenever the operator is smooth) equations. It can exploit the facilities of the classical Newton–like methods for smooth equations. In this paper, we extend the method to solve a class of general variational inequality problems Moreover, we improve the implicit method to allow inexact solutions of the systems of nonlinear equations at each iteration. The method is shown to preserve the same convergence properties as the original implicit method. Received July 31, 1995 / Revised version received January 15, 1999? Published online May 28, 1999  相似文献
4.
肖争艳等: 绕积马氏链的状态分类   总被引:31,自引:0,他引:31       下载免费PDF全文
该文给出了绕积马氏链的特征数和状态的定义, 利用一般马氏链的理论讨论了随机环 境中的马氏链的各种状态的特征以及各类状态之间的联系, 还给出了在联合空间不可分解且 正则本质的条件下, 状态正则本质的充要条件. 最后举例说明了经典马氏链和随机环境中马氏链的状态的区别.  相似文献
5.
Image recovery via total variation minimization and related problems   总被引:31,自引:0,他引:31  
Summary. We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original TV minimization problem that handles correctly some situations where TV fails. Received December 21, 1995 / Revised version February 26, 1996  相似文献
6.
Credit risk optimization with Conditional Value-at-Risk criterion   总被引:27,自引:0,他引:27  
This paper examines a new approach for credit risk optimization. The model is based on the Conditional Value-at-Risk (CVaR) risk measure, the expected loss exceeding Value-at-Risk. CVaR is also known as Mean Excess, Mean Shortfall, or Tail VaR. This model can simultaneously adjust all positions in a portfolio of financial instruments in order to minimize CVaR subject to trading and return constraints. The credit risk distribution is generated by Monte Carlo simulations and the optimization problem is solved effectively by linear programming. The algorithm is very efficient; it can handle hundreds of instruments and thousands of scenarios in reasonable computer time. The approach is demonstrated with a portfolio of emerging market bonds. Received: November 1, 1999 / Accepted: October 1, 2000?Published online December 15, 2000  相似文献
7.
Summary. We consider systems of delay differential equations (DDEs) of the form with the initial condition . Recently, Torelli [10] introduced a concept of stability for numerical methods applied to dissipative nonlinear systems of DDEs (in some inner product norm), namely RN-stability, which is the straighforward generalization of the wellknown concept of BN-stability of numerical methods with respect to dissipative systems of ODEs. Dissipativity means that the solutions and corresponding to different initial functions and , respectively, satisfy the inequality , and is guaranteed by suitable conditions on the Lipschitz constants of the right-hand side function . A numerical method is said to be RN-stable if it preserves this contractivity property. After showing that, under slightly more stringent hypotheses on the Lipschitz constants and on the delay function , the solutions and are such that , in this paper we prove that RN-stable continuous Runge-Kutta methods preserve also this asymptotic stability property. Received March 29, 1996 / Revised version received August 12, 1996  相似文献
8.
Approximation by translates of refinable functions   总被引:23,自引:0,他引:23  
Summary. The functions are refinable if they are combinations of the rescaled and translated functions . This is very common in scientific computing on a regular mesh. The space of approximating functions with meshwidth is a subspace of with meshwidth . These refinable spaces have refinable basis functions. The accuracy of the computations depends on , the order of approximation, which is determined by the degree of polynomials that lie in . Most refinable functions (such as scaling functions in the theory of wavelets) have no simple formulas. The functions are known only through the coefficients in the refinement equation – scalars in the traditional case, matrices for multiwavelets. The scalar "sum rules" that determine are well known. We find the conditions on the matrices that yield approximation of order from . These are equivalent to the Strang–Fix conditions on the Fourier transforms , but for refinable functions they can be explicitly verified from the . Received August 31, 1994 / Revised version received May 2, 1995  相似文献
9.
Summary. The interpolation theorem for convex quadrilateral isoparametric finite elements is proved in the case when the condition is not satisfied, where is the diameter of the element and is the radius of an inscribed circle in . The interpolation error is in the -norm and in the -norm provided that the interpolated function belongs to . In the case when the long sides of the quadrilateral are parallel the constants appearing in the estimates are evaluated. Received September 1993 / Revised version received March 6, 1995  相似文献
10.
The cascadic multigrid method for elliptic problems   总被引:22,自引:0,他引:22  
Summary. The paper deals with certain adaptive multilevel methods at the confluence of nested multigrid methods and iterative methods based on the cascade principle of [10]. From the multigrid point of view, no correction cycles are needed; from the cascade principle view, a basic iteration method without any preconditioner is used at successive refinement levels. For a prescribed error tolerance on the final level, more iterations must be spent on coarser grids in order to allow for less iterations on finer grids. A first candidate of such a cascadic multigrid method was the recently suggested cascadic conjugate gradient method of [9], in short CCG method, whichused the CG method as basic iteration method on each level. In [18] it has been proven, that the CCG method is accurate with optimal complexity for elliptic problems in 2D and quasi-uniform triangulations. The present paper simplifies that theory and extends it to more general basic iteration methods like the traditional multigrid smoothers. Moreover, an adaptive control strategy for the number of iterations on successive refinement levels for possibly highly non-uniform grids is worked out on the basis of a posteriori estimates. Numerical tests confirm the efficiency and robustness of the cascadic multigrid method. Received November 12, 1994 / Revised version received October 12, 1995  相似文献
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