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61.
Jacek Gondzio 《European Journal of Operational Research》2012,218(3):587-601
Interior point methods for optimization have been around for more than 25 years now. Their presence has shaken up the field of optimization. Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization. Among the most impressive of them are their low-degree polynomial worst-case complexity and an unrivalled ability to deliver optimal solutions in an almost constant number of iterations which depends very little, if at all, on the problem dimension. Interior point methods are competitive when dealing with small problems of dimensions below one million constraints and variables and are beyond competition when applied to large problems of dimensions going into millions of constraints and variables.In this survey we will discuss several issues related to interior point methods including the proof of the worst-case complexity result, the reasons for their amazingly fast practical convergence and the features responsible for their ability to solve very large problems. The ever-growing sizes of optimization problems impose new requirements on optimization methods and software. In the final part of this paper we will therefore address a redesign of interior point methods to allow them to work in a matrix-free regime and to make them well-suited to solving even larger problems. 相似文献
62.
The present work concerns with the investigation of the interior transmission problem, which is naturally associated to the
inverse elastic scattering problem of determining the support of an isotropic homogeneous penetrable body from a knowledge
of the time harmonic incident plane waves and the far-field patterns of the corresponding scattered wave-fields. Our approach
combines a boundary integral formulation of the problem and a compact perturbation argument to establish the discreteness
of the set of transmission eigenvalues and the well-posedness of the interior transmission problem under the most general
assumptions on the elastic parameters of the underlying media.
相似文献
63.
随着法治社会的构建,依法治教进程的加快以及教育法的普及,我国高校(国立)与大学生的法律关系已成为近年来争议颇多的问题。以高校与学生之间具有行政色彩的权力关系以及与不具有行政色彩的民事关系为基点,从维护学生权益角度出发,审视高校的法律地位及其与学生之间的法律关系,并探讨其应对之策。 相似文献
64.
A SCALED CENTRAL PATH FOR LINEAR PROGRAMMING 总被引:9,自引:0,他引:9
Ya-xiang Yuan 《计算数学(英文版)》2001,19(1):35-40
1. IntroductionIllterior poillt methods are one of the most illtensively studied topics in optinistion. Thousands of publications have been appeared on inferior point ndhods. A very good recent reviewis given by [4]. Interior point methods have very good theoretical properties including thenice polynomial complexity prOPerty. And more haportat is that numerous applications haveshown that interior point methods are very efficient for solving large sparse linear progr~ngproblemS. Interior poil… 相似文献
65.
廖代广 《湖南城市学院学报(自然科学版)》2005,14(3):34-36
建筑物经装饰后,由于光污染、空气污染以及放射性氡的污染而危害身体健康.人们在使用建筑物时,应采取相应措施,使这些危害降到最低限度. 相似文献
66.
Support-graph preconditioners have been shown to be a valuable tool for the iterative solution, via a Preconditioned Conjugate
Gradient method, of the KKT systems that must be solved at each iteration of an Interior Point algorithm for the solution
of Min Cost Flow problems. These preconditioners extract a proper triangulated subgraph, with “large” weight, of the original
graph: in practice, trees and Brother-Connected Trees (BCTs) of depth two have been shown to be the most computationally efficient
families of subgraphs. In the literature, approximate versions of the Kruskal algorithm for maximum-weight spanning trees
have most often been used for choosing the subgraphs; Prim-based approaches have been used for trees, but no comparison have
ever been reported. We propose Prim-based heuristics for BCTs, which require nontrivial modifications w.r.t. the previously
proposed Kruskal-based approaches, and present a computational comparison of the different approaches, which shows that Prim-based
heuristics are most often preferable to Kruskal-based ones.
This paper has been partially supported by the UE Marie Curie Research Training Network no. 504438 ADONET. 相似文献
67.
王行翔 《安徽师范大学学报(自然科学版)》1992,15(4):33-36
本文讨论了径向胁强为零的球对称的荷电理想流体的情况。我们求得了一个新的解,并对此解的性质作了讨论。这个解包含了一个电磁质量模型。 相似文献
68.
This paper presents passive and active vibro-acoustic noise control methods for attenuating the interior noise level in box structures which can be an analogy of cabins of vehicle and aircraft. The structural intensity (SI) approach is adopted to identify the predominant vibration panels and interior noise sources for box structures. In the study, the finite element method is used to determine the structural vibration and structural intensity in the box surfaces. According to structural intensity vectors plot and structural intensity stream lines presentation, the possible effective control positions where the dampers may be attached and the active control forces may act to reduce vibration and interior noise, are identified. From the study, it can be demonstrated that the structural intensity approach and stream line presentation are possible methods for identifying the vibro-acoustic interior noise source and predominant panels which may be modified to reduce the interior noise level. The structural intensity methodology, passive and active noise control results can be extended to the further study of the vibration and interior noise control of actual cabins of vehicles and aircraft. 相似文献
69.
Mehrotra-type predictor–corrector algorithms are the backbone of most Interior Point Methods based software packages. Salahi et al. [M. Salahi, J. Peng, T. Terlaky, On Mehrotra-type predictor–corrector algorithms, Technical Report 2005/4, Advanced Optimization Lab., McMaster University, Hamilton, ON, Canada. http://www.cas.mcmaster.ca/~oplab/publication] in their recent works have shown some ill behaviors of Mehrotra’s original algorithm which motivated them to modify it in order to achieve the polynomial iteration complexity while preserving its practical efficiency. In this paper we analyze the same algorithm from a different perspective and give a condition on the maximum feasible step size in the predictor step, violation of which might lead to a very small or even zero step size in the corrector step. If the maximum step size in the predictor step is above a certain threshold, then we cut it to satisfy the derived condition. This enables us to prove that the algorithm terminates finitely. 相似文献
70.