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921.
Ellen Hisdal 《Fuzzy Sets and Systems》1980,4(3):275-291
It is suggested that there exists many fuzzy set systems, each with its specific pointwise operations for union and intersection. A general law of compound possibilities is valid for all these systems, as well as a general law for representing marginal possibility distributions as unions of fuzzy sets. Max-min fuzzy sets are a special case of a fuzzy set system which uses the pointwise operations of max and min for union and intersection respectively. Probabilistic fuzzy sets are another special case which uses the operations of addition and multiplication. Probably there exists an infinite number of fuzzy set operations and systems. It is shown why the law of idempotency for intersection is not required for such systems. An essential difference between the meaning of the operations of union and intersection in traditional measure theory as compared with their meaning in the theory of possibility is pointed out. The operation of particularization is used to illustrate that the two distinct classical theories of nonfuzzy relations and of probability are merely two aspects of a more generalized theory of fuzzy sets. It is shown that we must distinguish between particularization of conditional fuzzy sets and of joint fuzzy sets. The concept of restriction of nonfuzzy relations is a special case of particularization of both conditional and joint fuzzy sets. The computation of joint probabilities from conditional and marginal ones is a special case of particularization of conditional probabilistic fuzzy sets. The difference between linguistic modifiers of type 1 and particulating modifiers is pointed out, as well as a general difference between nouns and adjectives. 相似文献
922.
Shelby J. Haberman 《Journal of multivariate analysis》1980,10(3):398-404
Let Y be an N(μ, Σ) random variable on Rm, 1 ≤ m ≤ ∞, where Σ is positive definite. Let C be a nonempty convex set in Rm with closure . Let (·,-·) be the Eculidean inner product on Rm, and let μc be the conditional expected value of Y given Y ∈ C. For v ∈ Rm and s ≥ 0, let βs(v) be the expected value of |(v, Y) ? (v, μ)|s and let γs(v) be the conditional expected value of |(v, Y) ? (v, μc)|s given Y ∈ C. For s ≥ 1, γs(v) < βs(v) if and only if , and γs(v) < βs(v) for all v ≠ 0 if and only if for any v ∈ Rm such that v ≠ 0. 相似文献
923.
924.
925.
926.
Polyadic Concept Analysis 总被引:1,自引:0,他引:1
George Voutsadakis 《Order》2002,19(3):295-304
The framework and the basic results of Wille on triadic concept analysis, including his Basic Theorem of Triadic Concept Analysis, are here generalized to n-dimensional formal contexts. 相似文献
927.
Ibrahim K. Djire 《复变函数与椭圆型方程》2016,61(8):1133-1144
We present some basic properties of the so-called boundary relative extremal function and discuss boundary pluripolar sets and boundary pluripolar hulls. We show that for B-regular domains the boundary pluripolar hull is always trivial on the boundary of the domain and present a “boundary version” of Zeriahi’s theorem on the completeness of pluripolar sets. 相似文献
928.
The Coupled Perturbed Hartree-Fock (CPHF) scheme has been implemented in the CRYSTAL06 program, that uses a gaussian type basis set, for systems periodic in 1D (polymers), 2D (slabs), 3D (crystals) and, as a limiting case, 0D (molecules), which enables comparison with molecular codes. CPHF is applied to the calculation of the polarizability alpha of LiF in different aggregation states: finite and infinite chains, slabs, and cubic crystal. Correctness of the computational scheme for the various dimensionalities and its numerical efficiency are confirmed by the correct trend of alpha: alpha for a finite linear chain containing N LiF units with large N tends to the value for the infinite chain, N parallel chains give the slab value when N is sufficiently large, and N superimposed slabs tend to the bulk value. CPHF results compare well with those obtained with a saw-tooth potential approach, previously implemented in CRYSTAL. High numerical accuracy can easily be achieved at relatively low cost, with the same kind of dependence on the computational parameters as for the SCF cycle. Overall, the cost of one component of the dielectric tensor is roughly the same as for the SCF cycle, and it is dominated by the calculation of two-electron four-center integrals. 相似文献
929.
Davar Khoshnevisan Narn-Rueih Shieh Yimin Xiao 《Probability Theory and Related Fields》2008,140(1-2):129-167
Let X
1, ..., X
N
denote N independent, symmetric Lévy processes on R
d
. The corresponding additive Lévy process is defined as the following N-parameter random field on R
d
:
Khoshnevisan and Xiao (Ann Probab 30(1):62–100, 2002) have found a necessary and sufficient condition for the zero-set of to be non-trivial with positive probability. They also provide bounds for the Hausdorff dimension of which hold with positive probability in the case that can be non-void.
Here we prove that the Hausdorff dimension of is a constant almost surely on the event . Moreover, we derive a formula for the said constant. This portion of our work extends the well known formulas of Horowitz
(Israel J Math 6:176–182, 1968) and Hawkes (J Lond Math Soc 8:517–525, 1974) both of which hold for one-parameter Lévy processes.
More generally, we prove that for every nonrandom Borel set F in (0,∞)
N
, the Hausdorff dimension of is a constant almost surely on the event . This constant is computed explicitly in many cases.
The research of N.-R. S. was supported by a grant from the Taiwan NSC. 相似文献
930.
Christer Borell 《Probability Theory and Related Fields》2008,140(1-2):195-205
Let be an integer, let γ be the standard Gaussian measure on , and let . Given this paper gives a necessary and sufficient condition such that the inequality is true for all Borel sets A
1,...,A
m
in of strictly positive γ-measure or all convex Borel sets A
1,...,A
m
in of strictly positive γ-measure, respectively. In particular, the paper exhibits inequalities of the Brunn–Minkowski type
for γ which are true for all convex sets but not for all measurable sets.
相似文献