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141.
Venansius Baryamureeba 《Numerical Linear Algebra with Applications》2002,9(2):93-106
A sequence of least‐squares problems of the form miny∥G1/2(AT y?h)∥2, where G is an n×n positive‐definite diagonal weight matrix, and A an m×n (m?n) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We suggest low‐rank correction preconditioners for such problems, and a mixed solver (a combination of a direct solver and an iterative solver). The numerical results show that our technique for selecting the low‐rank correction matrix is very effective. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
142.
TESTING DIFFERENT CONJUGATE GRADIENT METHODS FOR LARGE—SCALE UNCONSTRAINED OPTIMIZATION 总被引:6,自引:0,他引:6
Yu-hongDai QinNi 《计算数学(英文版)》2003,21(3):311-320
In this PaPer we test different conjugate gradient (CG) methods for solving large-scale unconstrained optimization problems.The methods are divided in two groups:the first group includes five basic CG methods and the second five hybrid CG methods.A collection of medium-scale and large-scale test problems are drawn from a standard code of test problems.CUTE.The conjugate gradient methods are ranked according to the numerical results.Some remarks are given. 相似文献
143.
Multiplicative programs are a difficult class of nonconvex programs that have received increasing attention because of their many applications. However, given their nonconvex nature, few theoretical results are available. In this paper, we study a particular case of these programs which involves the maximization of a quasiconcave function over a linear constraint set. Using results from conjugate function theory and generalized geometric programming, we derive a complete duality theory. The results are further specialized to linear multiplicative programming. 相似文献
144.
自反Banach空间中的相补问题 总被引:1,自引:1,他引:0
在自反Banach空间中证明了相补问题解的存在性定理,改进了[1]中的一个主要结果. 相似文献
145.
Linear systems with complex coefficients arise from various physical problems. Examples are the Helmholtz equation and Maxwell equations approximated by finite difference or finite element methods, that lead to large sparse linear systems. When the continuous problem is reduced to integral equations, after discretization, one obtains a dense linear system. The resulting matrices are generally non-Hermitian but, most of the time, symmetric and consequently the classical conjugate gradient method cannot be directly applied. Usually, these linear systems have to be solved with a large number of unknowns because, for instance, in electromagnetic scattering problems the mesh size must be related to the wave length of the incoming wave. The higher the frequency of the incoming wave, the smaller the mesh size must be. When one wants to solve 3D-problems, it is no longer practical to use direct method solvers, because of the huge memory they need. So iterative methods are attractive for this kind of problems, even though their convergence cannot be always guaranteed with theoretical results. In this paper we derive several methods from a unified framework and we numerically compare these algorithms on some test problems. 相似文献
146.
Hongya Gao 《Journal of Mathematical Analysis and Applications》2003,281(1):253-263
We first prove a local weighted integral inequality for conjugate A-harmonic tensors. Then, as an application of our local result, we prove a global weighted integral inequality for conjugate A-harmonic tensors in Ls(μ)-averaging domains, which can be considered as a generalization of the classical result. Finally, we give applications of the above results to quasiregular mappings. 相似文献
147.
Wenyu Sun Liusheng Hou Chuangying Dang 《Computational Optimization and Applications》2008,40(1):59-72
It is well-known that the conjugate gradient method is widely used for solving large scale optimization problems. In this
paper a modified trust-region method with Beale’s Preconditioned Conjugate Gradient (BPCG) technique is developed for solving
unconstrained optimization problems. The modified version adopts an adaptive rule and retains some useful information when
an unsuccessful iteration occurs, and therefore improves the efficiency of the method. The behavior and the convergence properties
are discussed. Some numerical experiments are reported.
This work was partially supported by Grant of the National Natural Science Foundation of China, Grant: 20040319003 of the
Doctoral Site of the Education Ministry of China, and SRG: 7001428 of City University of Hong Kong. 相似文献
148.
L. C. W. Dixon P. G. Ducksbury P. Singh 《Journal of Optimization Theory and Applications》1985,47(3):285-300
In this paper, we describe an implementation and give performance results for a conjugate gradient algorithm for unconstrained optimization. The algorithm is based upon the Nazareth three-term formula and incorporates Allwright preconditioning matrices and restart tests. The performance results for this combination compare favorably with existing codes.The support of the Science and Engineering Research Council is gratefully acknowledged. 相似文献
149.
Andrzej Kozek 《Journal of multivariate analysis》1977,7(1):89-106
A general method for obtaining inequalities of Cramér-Rao type for convex loss functions is presented. It is shown under rather weak assumptions that there are at least as many such inequalities as best unbiased estimators. More precisely, it is shown that an estimator is efficient with respect to an inequality of Cramér-Rao type if and only if it is the best in the class of unbiased estimators. Moreover, theorems of Blyth and Roberts (“Proceedings Sixth Berkeley Symposium on Math. Statist. Prob.,”) and of Blyth (Ann. Statist.2, 464–473) are extended. We make an use of methods of convex analysis and properties of convex integral functionals on Orlicz spaces. 相似文献
150.
We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix
as the classical algorithm, using two matrix–vector products per iteration without accessing AT. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal
[15] (without look-ahead), which requires three matrix–vector products per iteration. We also present a related transpose-free
version of the bi-conjugate gradients algorithm.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献