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31.
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33.
In this paper, we establish a theoretical framework of path-following interior point algorithms for the linear complementarity
problems over symmetric cones (SCLCP) with the Cartesian P
*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-,
semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh
to the Cartesian P
*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008) 相似文献
34.
《Optimization》2012,61(9):1957-1982
We present new infeasible path-following methods for linear monotone complementarity problems based on Auslender, Teboulle and Ben-Tiba’s log-quadratic barrier functions. The central paths associated with these barriers are always well defined and, for those problems which have a solution, convergent to a pair of complementary solutions. Starting points in these paths are easy to compute. The theoretical iteration-complexity of these new path-following methods is derived and improved by a strategy which uses relaxed hybrid proximal-extragradient steps to control the quadratic term. Encouraging preliminary numerical experiments are presented. 相似文献
35.
Given a continuous P0-function F : Rn Rn, we describe a method of constructing trajectories associated with the P0-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P0-function lead to P0-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P0-equations when the underlying function is P0. To generate the trajectories, we perturb the given P0-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem. 相似文献
36.
We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html. 相似文献
37.
We study local convergence of quasi-Newton methods for solving systems of nonlinear equations defined by B-differentiable functions. We extend the classical linear and superlinear convergence results for general quasi-Newton methods as well as for Broyden's method. We also show how Broyden's method may be applied to nonlinear complementarity problems and illustrate its computational performance on two small examples. 相似文献
38.
M. J. Todd 《Journal of Optimization Theory and Applications》1976,20(4):397-416
Lemke's algorithm for the linear complementarity problem fails when a desired pivot is not blocked. A projective transformation overcomes this difficulty. The transformation is performed computationally by adjoining a new row to a schema of the problem and pivoting on the element in this row and the unit constant column. Two new algorithms result; some conditions for their success are discussed.This research was partially supported by National Science Foundation, Grant GK-42092. 相似文献
39.
An interior point method for monotone linear complementarity problems acting in a wide neighborhood of the central path is
presented. The method has
-iteration complexity and is superlinearly convergent even when the problem does not possess a strictly complementary solution.
Mathematics Subject Classification (2000): 49M15, 65K05, 90C33
Work supported by the National Science Foundation under Grant No. 0139701.
An erratum to this article is available at. 相似文献
40.
The main interpretations of the quantum-mechanical wave function are presented emphasizing how they can be divided into two ensembles: The ones that deny and the other ones that attribute a form of reality to quantum waves. It is also shown why these waves cannot be classical and must be submitted to the restriction of the complementarity principle. Applying the concept of smooth complementarity, it is shown that there can be no reason to attribute reality only to the events and not to the wave or to the initial state of a given system. Thereafter, an experiment proposed by the authors is presented, where it is shown that the wave-like behaviour allows predictions that are not allowed on the grounds of a particle-like behaviour. In conclusion, we upheld that quantum waves must be real even if they do not belong to the same ontological level of events, which connected with particle detections.Institute of Philosophy, University of Urbino, Urbino 610 29, Italy; tarizzi@uniurb.it 相似文献