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991.
The equality of two critical points — the percolation thresholdp
H
and the pointp
T
where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP
— at the bond densityp=1–e
–
in the single parameter case. These are: (1)MhM/h+M
2+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a 3 structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents
and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that
. An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation
and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department 相似文献
992.
Michael A. Langston 《The Journal of the Operational Research Society》1987,38(6):539-544
When faced with a difficult combinatorial problem whose optimization may be prohibitively expensive, researchers frequently turn to the study of fast heuristic algorithms in an effort to guarantee near-optimal results. An important aspect in the evaluation of such an algorithm is the determination of its worst-case behaviour, relative to an optimization rule. We here focus attention on schemes for combining two or more heuristics so as demonstrably to improve the worst case that can occur. We survey successful, illustrative examples of such composite algorithms, concentrating on problems of central significance from domains such as scheduling, packing and routeing. We also attempt to illuminate the conditions under which these strategies can be successful and why. 相似文献
993.
Michael Mesterton-Gibbons 《Natural Resource Modeling》1987,2(1):109-134
By a combination of analytical reasoning and numerical experiment it is demonstrated that, for the combined harvesting of two ecologically independent species which grow logistically and are harvested at a rate proportional to both stock level and effort, there is a unique attainable equilibrium which yields positive revenue and to which the approach path satisfies all of Pontryagin's necessary conditions for maximizing the harvest's present value. A simple feedback law governs this approach and is conjectured to be the optimal policy. On that basis, criteria are found for the survival of the less productive species, as a function of the system parameters and initial stocks. An economic interpretation of the equilibrium is also given. 相似文献
994.
The two-dimensional non-linear model on a Riemannian symmetric spaceM=G/H is coupled to fermions with quartic self-interactions. The resulting hybrid model is presented in a gauge-dependent formulation, with a bosonic field taking values inG and a fermionic field transforming under a given representation of the gauge groupH. General criteria for classical integrability are presented: they essentially fix the Lagrangian of the model but leave the fermion representation completely arbitrary. It is shown that by a special choice for the fermion representation (derived from the adjoint representation ofG by an appropriate reduction) one arrives naturally at the supersymmetric non-linear model onM=G/H. The issue of quantum integrability is also discussed, though with less stringent results.Work partially supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brazil, and KFA Jülich, Federal Republic of GermanyOn leave of absence from Fakultät für Physik der Universität Freiburg, Federal Republic of Germany 相似文献
995.
Finite-size behavior near the first-order phase boundary of ferromagnetic spherical models is investigated for block- and cylinder-shaped systems ind dimensions. The bulk thermodynamic singularities are rounded and, asymptotically for large size, obey appropriate scaling laws. Both short-range interactions and long-range couplings, decaying like 1/rd+ with >0, are analyzed: the short-range results agree precisely with a recently developed scaling theory forO(n) symmetric systems in the limitn. More generally, the scaling functions are universal, depending only on . Explicit aspects of the shape and interactions enter only in the spin wave or Goldstone mode contributions which appear, technically, as corrections to scaling. An appendix analyzes the truncation error in the approximation, by many-fold sums, of multivariate integrals with integrands diverging like [jaj
j
2
]- as 0. 相似文献
996.
Michael P. Hartshorn Richard G. Jensen A. Grant Waller Graeme J. Wright 《Tetrahedron letters》1987,28(52):6701-6704
Reaction of the 15N-4-nitrodienone (1) with excess nitrogen dioxide in benzene for 16 h gives the 4,5,6-trinitro ketone (2), labelled (15NO2) at C6 but not at C4, and recovered 4-nitrodienone (1) in which extensive loss of 15NO2 has occurred. The mechanistic implications of these and related results are discussed. 相似文献
997.
Michael Scheutzow 《Probability Theory and Related Fields》1986,72(3):425-462
Summary We prove a propagation of chaos result for the mean-field limit of a model for a trimolecular chemical reaction called Brusselator. Then we show that the pair of nonlinear (i.e. law-dependent) stochastic differential equations describing the evolution of the concentration of the molecules at a given site in the mean field limit has a solution with a periodic law (in t). Finally we identify the limit and establish a central limit theorem for the periodic law in the case where the noise tends to zero.Part of this work was performed while on leave at the Department of Mathematics and Statistics, Carleton University, Ottawa, Canada and supported by NSERC operating grants of M. Csörgö and D. Dawson 相似文献
998.
Michael Klemm 《Geometriae Dedicata》1986,20(3):349-356
By a study of the integral code generated by the rows of the incidence matrix and its extention the following results are obtained: Let d
1,...,d
V(d
1|d
2,d
2|d
3...) be the elementary divisors of the incidence matrix of a symmetric (v,n+, ) design. Then d
v=(n+)n/g.c.d. (n, ). Moreover, if p is a prime such that p|n, p and if x
p denotes the p-part of x, then (d
idv+2–i)
p
=n
p for 2iv. For projective planes it can be shown that d
1=···=d
3n–2=1, hence
and
. The paper also contains some results about elementary divisors of incidence matrices G satisfying the condition G
tG=nI+ J.
Elementarteiler von Inzidenzmatrizen symmetrischer Blockpläne相似文献
999.
Zero field Mössbauer spectra and powder susceptibility measurements show that the condensed, hydrogen bonded network compound FeSO3 3H2O orders antiferromagnetically (TNéel 9.5 K). The related anhydrous material FeSO3 also shows antiferromagnetic exchange but no evidence of long range three-dimenstional magnetic order to as low as 1.4 K.Supported by the U.S. National Science Foundation Division of Materials Research—Solid State Chemistry Program Grant No. DMR 8313710. 相似文献
1000.