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In this paper, a successive supersymmetric rank‐1 decomposition of a real higher‐order supersymmetric tensor is considered. To obtain such a decomposition, we design a greedy method based on iteratively computing the best supersymmetric rank‐1 approximation of the residual tensors. We further show that a supersymmetric canonical decomposition could be obtained when the method is applied to an orthogonally diagonalizable supersymmetric tensor, and in particular, when the order is 2, this method generates the eigenvalue decomposition for symmetric matrices. Details of the algorithm designed and the numerical results are reported in this paper. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
13.
Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with
respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization
of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case
of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods
and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank
approximants. Properties of Gander methods are investigated in details.
AMS subject classification (2000) 65F30, 15A18 相似文献
14.
Yongge Tian 《Journal of Mathematical Analysis and Applications》2002,266(2):333-341
We present an alternative expression for the parallel sum of k Hermitian nonnegative definite matrices by using the Moore-Penrose inverse of a block matrix. 相似文献
15.
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Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G=Z??Z2, where ? is 2, 3, 4, and 6, respectively. In this paper, we define a flat deformation H(t,q) of the group algebra C[G] of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra H(t,q) for D4 is the Cherednik algebra of type C∨C1, which was studied by Noumi, Sahi, and Stokman, and controls Askey-Wilson polynomials. We prove that H(t,q) is the universal deformation of the twisted group algebra of G, and that this deformation is compatible with certain filtrations on C[G]. We also show that if q is a root of unity, then for generic t the algebra H(t,q) is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra eH(t,q)e provides a quantization of such surfaces. We also discuss connections of H(t,q) with preprojective algebras and Painlevé VI. 相似文献
17.
结构相角二阶代数式的应用:Ⅱ.正交空间群二阶式及其应用 总被引:1,自引:0,他引:1
以作者在前文中提出的单相角二阶代数式的推导方法为依据,在完成三斜、单斜空间群推导结果的基础上,进而又完成了正交晶系59个空间群二阶式的推导,从而提供了低级晶系(三斜、单斜和正交)全部74个空间群的简明、完备的二阶代数式运算用表。对三个晶体结构进行了相角估算,结果较好。文中提出了代数法应用的新特点,即“一种类型相角可用多种二阶式求得,多种类型相角也可用一种二阶式求算”。 相似文献
18.
Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function. 相似文献
19.
A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA
of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA
. Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA
. It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA
; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA
is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975. 相似文献
20.