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41.
Dominique de Werra 《Graphs and Combinatorics》2003,19(2):263-278
The theorem of Birkhoff – von Neumann concerns bistochastic matrices (i.e., matrices with nonnegative real entries such that
all row sums and all column sums are equal to one). We consider here real matrices with entries unrestricted in sign and we
extend the notion of permutation matrices (integral bistochastic matrices); some generalizations of the theorem are derived
by using elementary properties of graph theory.
Received: October 10, 2000 Final version received: April 11, 2002 相似文献
42.
Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra
Katharine M. Mullen Mikas Vengris Ivo H. M. van Stokkum 《Journal of Global Optimization》2007,38(2):201-213
The multiexponential analysis problem of fitting kinetic models to time-resolved spectra is often solved using gradient-based
algorithms that treat the spectral parameters as conditionally linear. We make a comparison of the two most-applied such algorithms,
alternating least squares and variable projection. A numerical study examines computational efficiency and linear approximation
standard error estimates. A new derivation of the Fisher information matrix under the full Golub-Pereyra gradient allows a
numerical comparison of parameter precision under variable projection variants. Under the criteria of efficiency, quality
of standard error estimates and parameter precision, we conclude that the Kaufman variable projection technique performs well,
while techniques based on alternating least squares have significant disadvantages for application in the problem domain. 相似文献
43.
M. Sun 《Applied Mathematics and Optimization》1996,34(3):267-277
We focus on numerically solving a typical type of Hamilton-Jacobi-Bellman (HJB) equations arising from a class of optimal controls with a standard multidimensional diffusion model. Solving such an equation results in the value function and an optimal feedback control law. The Bellman's curse of dimensionality seems to be the main obstacle to applicability of most numerical algorithms for solving HJB. We decompose HJB into a number of lower-dimensional problems, and discuss how the usual alternating direction method can be extended for solving HJB. We present some convergence results, as well as preliminary experimental outcomes.This research was funded in part by an RGC grant from the University of Alabama. 相似文献
44.
We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex
functions subject to linear constraints. The method consists of solving consecutively in each iteration two optimization problems
which contain in the objective function both Lagrangian and proximal terms. The minimizers determine the new proximal terms
and a simple update of the Lagrangian terms follows. We prove a convergence theorem which extends existing results by relaxing
the assumption of uniqueness of minimizers. Another novelty is that we allow penalty matrices, and these may vary per iteration.
This can be beneficial in applications, since it allows additional tuning of the method to the problem and can lead to faster
convergence relative to fixed penalties. As an application, we derive a decomposition scheme for block angular optimization
and present computational results on a class of dual block angular problems.
This material is based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410 and by NSF
Grants CCR-8907671, CDA-9024618 and CCR-9306807. 相似文献
45.
D. Han 《Applied Mathematics and Optimization》2002,45(1):63-74
The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever
the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as
structurally difficult to solve as the original one. To overcome this disadvantage, in this paper we propose a new alternating
direction method for solving a class of nonlinear monotone variational inequality problems. In each iteration the method just
makes an orthogonal projection to a simple set and some function evaluations. We report some preliminary computational results
to illustrate the efficiency of the method.
Accepted 4 May 2001. Online publication 19 October, 2001. 相似文献
46.
The one-dimensional Hubbard model with different on-site interaction on the even (Ua) and odd (Ub) sites is considered within the framework of the weak coupling approach. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a commensurability gap in the charge excitation spectrum for Ua ≠ Ub and Ua>0 or Ub>0. Depending on the relation between the bare coupling constants the system shows four different regimes of behaviour in the infrared limit corresponding to normal metal, nonmagnetic insulator, antiferromagnetic insulator and superconducting states. The extended model including interaction between particles on nearest and next-nearest neighbour sites is also considered. 相似文献
47.
Marcel Herzog 《Journal of Combinatorial Theory, Series A》2008,115(7):1235-1245
Given integers k,l?2, where either l is odd or k is even, we denote by n=n(k,l) the largest integer such that each element of An is a product of k cycles of length l. For an odd l, k is the diameter of the undirected Cayley graph Cay(An,Cl), where Cl is the set of all l-cycles in An. We prove that if k?2 and l?9 is odd and divisible by 3, then . This extends earlier results by Bertram [E. Bertram, Even permutations as a product of two conjugate cycles, J. Combin. Theory 12 (1972) 368-380] and Bertram and Herzog [E. Bertram, M. Herzog, Powers of cycle-classes in symmetric groups, J. Combin. Theory Ser. A 94 (2001) 87-99]. 相似文献
48.
We construct infinitely many hyperbolic links with x-distance far from the set of (possibly, splittable) alternating links in the concordance class of every link. A sensitive result is given for the concordance class of every (possibly, split) alternating link. Our proof uses an estimate of the τ-distance by an Alexander invariant and the topological imitation theory, both established earlier by the author. 相似文献
49.
Min Yang 《Applied mathematics and computation》2010,215(9):3239-3248
In this paper, we develop a two-time level alternating direction implicit (ADI) method for a class of second-order hyperbolic problems on a rectangular domain. The method builds on the finite volume method with biquadratic basis functions for the discretization in space, and a Crank-Nicolson approach for the time stepping. We obtain a second-order error estimation in the H1 norm. Numerical experiments are performed to demonstrate the theoretical findings. 相似文献
50.
We propose a modified alternating direction method for solving convex quadratically constrained quadratic semidefinite optimization problems. The method is a first-order method, therefore requires much less computational effort per iteration than the second-order approaches such as the interior point methods or the smoothing Newton methods. In fact, only a single inexact metric projection onto the positive semidefinite cone is required at each iteration. We prove global convergence and provide numerical evidence to show the effectiveness of this method. 相似文献