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991.
We study the parameterized complexity of the problems of determining whether a graph contains a k-edge subgraph (k-vertex induced subgraph) that is a Π-graph for Π-graphs being one of the following four classes of graphs: Eulerian graphs, even graphs, odd graphs, and connected odd graphs. We also consider the parameterized complexity of their parametric dual problems.For these sixteen problems, we show that eight of them are fixed parameter tractable and four are W[1]-hard. Our main techniques are the color-coding method of Alon, Yuster and Zwick, and the random separation method of Cai, Chan and Chan. 相似文献
992.
Shravan K. Veerapaneni Abtin Rahimian George Biros Denis Zorin 《Journal of computational physics》2011,230(14):5610-5634
Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend the study of Veerapaneni et al. [S.K. Veerapaneni, D. Gueyffier, G. Biros, D. Zorin, A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows, Journal of Computational Physics 228 (19) (2009) 7233–7249] to general non-axisymmetric vesicle flows in three dimensions. 相似文献
993.
994.
Maurits Graaf Richard J. Boucherie Johann L. Hurink Jan‐Kees van Ommeren 《Random Structures and Algorithms》2019,55(1):89-103
We present an average case analysis of the minimum spanning tree heuristic for the power assignment problem. The worst‐case approximation ratio of this heuristic is 2. We show that in Euclidean d‐dimensional space, when the vertex set consists of a set of i.i.d. uniform random independent, identically distributed random variables in [0,1]d, and the distance power gradient equals the dimension d, the minimum spanning tree‐based power assignment converges completely to a constant depending only on d. 相似文献
995.
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, i.e., frequency estimation. For the basic formulation of the fixed-point algorithm we show that it converges to the solution of a related minimization problem, namely the one obtained by replacing the original objective function with its convex envelope and keeping the structured matrix constraint unchanged.It often happens that this solution agrees with the solution to the original minimization problem, and we provide a simple criterion for when this is true. We also provide more general fixed-point algorithms that can be used to treat the problems of making weighted approximations by sums of exponentials given equally or unequally spaced sampling. We apply the method to the case of missing data, although the above mentioned convergence results do not hold in this case. However, it turns out that the method often gives perfect reconstruction (up to machine precision) in such cases. We also discuss multidimensional extensions, and illustrate how the proposed algorithms can be used to recover sums of exponentials in several variables, but when samples are available only along a curve. 相似文献
996.
Ulf G. Indahl 《Journal of Chemometrics》2014,28(3):168-180
The insight from, and conclusions of this paper motivate efficient and numerically robust ‘new’ variants of algorithms for solving the single response partial least squares regression (PLS1) problem. Prototype MATLAB code for these variants are included in the Appendix. The analysis of and conclusions regarding PLS1 modelling are based on a rich and nontrivial application of numerous key concepts from elementary linear algebra. The investigation starts with a simple analysis of the nonlinear iterative partial least squares (NIPALS) PLS1 algorithm variant computing orthonormal scores and weights. A rigorous interpretation of the squared P ‐loadings as the variable‐wise explained sum of squares is presented. We show that the orthonormal row‐subspace basis of W ‐weights can be found from a recurrence equation. Consequently, the NIPALS deflation steps of the centered predictor matrix can be replaced by a corresponding sequence of Gram–Schmidt steps that compute the orthonormal column‐subspace basis of T ‐scores from the associated non‐orthogonal scores. The transitions between the non‐orthogonal and orthonormal scores and weights (illustrated by an easy‐to‐grasp commutative diagram), respectively, are both given by QR factorizations of the non‐orthogonal matrices. The properties of singular value decomposition combined with the mappings between the alternative representations of the PLS1 ‘truncated’ X data (including P t W ) are taken to justify an invariance principle to distinguish between the PLS1 truncation alternatives. The fundamental orthogonal truncation of PLS1 is illustrated by a Lanczos bidiagonalization type of algorithm where the predictor matrix deflation is required to be different from the standard NIPALS deflation. A mathematical argument concluding the PLS1 inconsistency debate (published in 2009 in this journal) is also presented. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
997.
998.
The Ball basis was introduced for cubic polynomials by Ball, and two different generalizations for higher degree m polynomials have been called the Said–Ball and the Wang–Ball basis, respectively. In this paper, we analyze some shape preserving and stability properties of these bases. We prove that the Wang–Ball basis is strictly monotonicity preserving for all m. However, it is not geometrically convexity preserving and is not totally positive for m>3, in contrast with the Said–Ball basis. We prove that the Said–Ball basis is better conditioned than the Wang–Ball basis and we include a stable conversion between both generalized Ball bases. The Wang–Ball basis has an evaluation algorithm with linear complexity. We perform an error analysis of the evaluation algorithms of both bases and compare them with other algorithms for polynomial evaluation. 相似文献
999.
We discuss how a new pricing scheme can be integrated within a communication network. The pricing scheme is based on the availability
of end-to-end communications, and is an alternative to congestion pricing, which is not applicable when communication capacity
is higher than demand (as happens in most communication backbone networks). We also investigate how, based on this scheme,
an optimization algorithm for updating the network topology can be applied. The network update problem is modeled as a combinatorial
optimization problem, which is approximately solved using a Genetic Algorithm. The good results obtained in a case study show
that the method is robust and can be applied even when end-to-end availability measures can only be computed approximately
(in this case, using a Monte Carlo method).
This research is part of the PAIR associated research project, supported by the INRIA, France, and has also received the support
of ECOS-Sud, under Action U03E02. The participation of Pablo Rodríguez was supported by the French Embassy in Uruguay as part
of the French Ministère des Affaires étrangères scientific cooperation program; and by the “Programa de Jóvenes Investigadores”
of CSIC, UDELAR, Uruguay. 相似文献
1000.
In the partially ordered knapsack problem (POK) we are given a set N of items and a partial order ?P on N. Each item has a size and an associated weight. The objective is to pack a set N′⊆N of maximum weight in a knapsack of bounded size. N′ should be precedence-closed, i.e., be a valid prefix of ?P. POK is a natural generalization, for which very little is known, of the classical Knapsack problem. In this paper we present both positive and negative results. We give an FPTAS for the important case of a two-dimensional partial order, a class of partial orders which is a substantial generalization of the series-parallel class, and we identify the first non-trivial special case for which a polynomial-time algorithm exists. Our results have implications for approximation algorithms for scheduling precedence-constrained jobs on a single machine to minimize the sum of weighted completion times, a problem closely related to POK. 相似文献