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171.
Clare D'Cruz 《代数通讯》2013,41(2):693-698
In an upcoming article we study harmonic analysis on the quantum E(2) group within an algebraic framework: we explicitly construct Fourier transforms between quantum E(2) and its Pontryagin dual, involving q-Bessel functions as kernel, prove Plancherel &; inversion formulas etc. In the present paper we propose an algebraic setting in which to perform harmonic analysis on non-compact, non-discrete quantum groups and in particular on quantum E(2). We are mainly concerned with the construction of positive and faithful invariant functionals on an algebraic level, KMS properties, etc. 相似文献
172.
173.
We introduce a new flexible mesh adaptation approach to efficiently compute a quantity of interest by the finite element method. Efficiently, we mean that the method provides an evaluation of that quantity up to a predetermined accuracy at a lower computational cost than other classical methods. The central pillar of the method is our scalar error estimator based on sensitivities of the quantity of interest to the residuals. These sensitivities result from the computation of a continuous adjoint problem. The mesh adaptation strategy can drive anisotropic mesh adaptation from a general scalar error contribution of each element. The full potential of our error estimator is then reached. The proposed method is validated by evaluating the lift, the drag, and the hydraulic losses on a 2D benchmark case: the flow around a cylinder at a Reynolds number of 20. 相似文献
174.
We study locally conformal symplectic (LCS) structures of the second kind on a Lie algebra. We show a method to construct new examples of Lie algebras admitting LCS structures of the second kind starting with a lower dimensional Lie algebra endowed with a LCS structure and a suitable extension. Moreover, we characterize all LCS Lie algebras obtained with our construction. Finally, we study the existence of lattices in the associated simply connected Lie groups in order to obtain compact examples of manifolds admitting this kind of structure. 相似文献
175.
176.
Consider the third order differential operator L given by
and the related linear differential equation L(x)(t) + x(t) = 0. We study the relations between L, its adjoint operator, the canonical representation of L, the operator obtained by a cyclic permutation of coefficients a
i
, i = 1,2,3, in L and the relations between the corresponding equations.We give the commutative diagrams for such equations and show some applications (oscillation, property A). 相似文献
177.
Rod Gow 《Geometriae Dedicata》1997,64(3):283-295
Let K be a field of characteristic 2 and letV be a vector space of dimension 2m over K. Let f be a non-degenerate alternating bilinear form defined on V × V. The symplectic group Sp(2m, K) acts on the exterior powers
k
V for 0 k. 2m There is a contraction map defined on the exterior algebra , which commutes with the Sp(2m, K) action and satisfies 2 = 0 and (
k
V)
k–1
V We prove that (
k
V)= ker
k–1
V except when k=m+2. In the exceptional case, (
m+2
V) has codimension 2m in ker
m
V and we show that the quotient module ker
m
V/
m+2
V is a spin module for Sp(2m,K). When K is algebraically closed, we show that this spin module occurs with multiplicity 1 in
m
V and multiplicity 0 in all other components of V. 相似文献
178.
Alexandre V. Borovik Israel Gelfand Neil White 《Journal of Algebraic Combinatorics》1998,8(3):235-252
A symplectic matroid is a collection B of k-element subsets of J = {1, 2, ..., n, 1*, 2*, ...; n*}, each of which contains not both of i and i* for every i n, and which has the additional property that for any linear ordering of J such that i j implies j* i* and i j* implies j i* for all i, j n, B has a member which dominates element-wise every other member of B. Symplectic matroids are a special case of Coxeter matroids, namely the case where the Coxeter group is the hyperoctahedral group, the group of symmetries of the n-cube. In this paper we develop the basic properties of symplectic matroids in a largely self-contained and elementary fashion. Many of these results are analogous to results for ordinary matroids (which are Coxeter matroids for the symmetric group), yet most are not generalizable to arbitrary Coxeter matroids. For example, representable symplectic matroids arise from totally isotropic subspaces of a symplectic space very similarly to the way in which representable ordinary matroids arise from a subspace of a vector space. We also examine Lagrangian matroids, which are the special case of symplectic matroids where k = n, and which are equivalent to Bouchet's symmetric matroids or 2-matroids. 相似文献
179.
P. Bieliavsky 《Geometriae Dedicata》1998,73(3):245-273
A symplectic symmetric space is a connected affine symmetric manifold M endowed with a symplectic structure which is invariant under the geodesic symmetries. When the transvection group G0 of such a symmetric space M is semisimple, its action on (M,) is strongly Hamiltonian; a classical theorem due to Kostant implies that the moment map associated to this action realises a G0-equivariant symplectic covering of a coadjoint orbit O in the dual of the Lie algebra
of G0. We show that this orbit itself admits a structure of symplectic symmetric space whose transvection algebra is
. The main result of this paper is the classification of symmetric orbits for any semisimple Lie group. The classification is given in terms of root systems of transvection algebras and therefore provides, in a symplectic framework, a theorem analogous to the Borel–de Siebenthal theorem for Riemannian symmetric spaces. When its dimension is greater than 2, such a symmetric orbit is not regular and, in general, neither Hermitian nor pseudo-Hermitian. 相似文献
180.
In De Bruyn Discrete math(to appear), one of the authors proved that there are six isomorphism classes of hyperplanes in the
dual polar space DW(5, q), q even, which arise from its Grassmann-embedding. In the present paper, we determine the combinatorial properties of these
hyperplanes. Specifically, for each such hyperplane H we calculate the number of quads Q for which is a certain configuration of points in Q and the number of points for which is a certain configuration of points in . By purely combinatorial techniques, we are also able to show that the set of hyperplanes of DW(5, q), q odd, which arise from its Grassmann-embedding can be divided into six subclasses if one takes only into account the above-mentioned
combinatorial properties. A complete classification of all hyperplanes of DW(5, q), q odd, which arise from its Grassmann-embedding, i.e. the division of the above-mentioned six classes into isomorphism classes,
will unlike in De Bruyn (to appear) most likely need a group-theoretical approach.
Postdoctoral Fellow of the Research Foundation—Flanders (Belgium). 相似文献