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951.
Roger J Wallace 《Aequationes Mathematicae》1987,33(1):183-193
For a fixed non-negative integerp, letU 2p = {U 2p (n)},n ≥ 0, denote the sequence that is defined by the initial conditionsU 2p (0) =U 2p (1) =U 2p (2) = =U 2p (2p) = 1 and the restricted subadditive recursion $$U_{2p} (n + 2p + 1) = \mathop {\min }\limits_{0 \leqslant l \leqslant p} (U_{2p} (n + l) + U_{2p} (n + 2p - l)),n \geqslant 0$$ U 2p is of importance in the theory of sequential search for simple real zeros of real valued continuous 2p-th derivatives In this paper, several closed form expressions forU 2p (n), n > 2p, are determined, thereby providing insight into the structure ofU 2p Two of the properties thus illuminated are (a) the existence of exactlyp + 1 limit points (1 + 1/(p + 1 +i), 0 ≤i ≤p) of the associated sequence {U 2p (n + 1)/U 2p (n)},n ≥ 0, and (b) the relevance toU 2p of the classic number theoretic function ord 相似文献
952.
Summary We consider a walk from a stateA
1 to a stateA
n+1 in which the probability of remaining atA
i
isp
i
, and the probability of progressing fromA
i
toA
i+1 is 1 –p
i
. The probabilityW
nk
of reachingA
n+1 fromA
1 in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp
1,,p
n
. We determine the maximum value ofW
nk
and the (unique) choice (p
1,,p
n
) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday 相似文献
953.
R. L. S. Devine C. T. Foxon B. A. Joyce J. B. Clegg J. P. Gowers 《Applied Physics A: Materials Science & Processing》1987,44(2):195-200
Beryllium diffusion during MBE growth of (Al, Ga)As layers, (Al, Ga)As/GaAs heterojunctions and GaAs/AlAs superlattices has been studied by electrochemical C-V and secondary ion mass spectrometry (SIMS) concentration profiling, in conjunction with transmission electron microscopy. Diffusion times were comparatively short since they were limited to part of the growth sequence, so non-equilibrium effects had a significant influence. The results are consistent with an interstitial-substitutional mechanism in which lattice site incorporation becomes more difficult with increasing band gap enthalpy. Incorporation involves a kick-out reaction which leads to the observed disordering of the superlattices. 相似文献
954.
Peter J. Cameron 《Probability Theory and Related Fields》1987,76(4):523-531
Summary There is a natural probability measure on the set of all sum-free sets of natural numbers. If we represent such a set by its characteristic functions, then the zero-one random variabless(i) are far from independent, and we cannot expect a law of large numbers to hold for them. In this paper I conjecture a decomposition of into countably many more tractible pieces (up to a null set). I prove that each piece has positive measure, and show that, within each piece, a random set almost surely has a density which is a fixed rational number depending only on the piece. For example, the first such piece is made up of sets consisting entirely of odd numbers; it has probability 0.218 ..., and its members almost surely have density 1/4. 相似文献
955.
Summary The existence of a joint asymptotic distribution for the windings of a three-dimensional Brownian motion around a finite number of straight lines is obtained. This complements the recent studies, by Pitman- Yor, and the authors, of the joint asymptotic distribution for the windings of planar Brownian motion around a finite number of points.The following principle governs the passage from results in the plane to results in space:Let B be a three-dimensional Brownian motion, and P
1, ..., P
k, k planes which intersect two by two. Then, the convergences in distribution concerning the planar Brownian motions B
i (1ik), defined respectively as the orthogonal projections of B on P
i (1ik), take place jointly, and the corresponding limit variables are independent. 相似文献
956.
J. E. Yukich 《Probability Theory and Related Fields》1987,74(1):71-90
Summary Let,n1, be a sequence of classes of real-valued measurable functions defined on a probability space (S,,P). Under weak metric entropy conditions on,n1, and under growth conditions on we show that there are non-zero numerical constantsC
1 andC
2 such that where (n) is a non-decreasing function ofn related to the metric entropy of. A few applications of this general result are considered: we obtain a.s. rates of uniform convergence for the empirical process indexed by intervals as well as a.s. rates of uniform convergence for the empirical characteristic function over expanding intervals.Portions of this article were presented during the conference on Mathematical Stochastics (February 19–25, 1984) at Oberwolfach, West Germany 相似文献
957.
J. R. Norris L. C. G. Rogers David Williams 《Probability Theory and Related Fields》1987,74(2):271-287
Summary A natural model for a self-avoiding Brownian motion inR
d, when specialised and simplified tod=1, becomes the stochastic differential equation
, where {L(t, x):t0,xR} is the local time process ofX. ThoughX is not Markovian, an analogue of the Ray-Knight theorem holds for {L(,x):xR}, which allows one to prove in many cases of interest that
exists almost surely, and to identify the limit. 相似文献
958.
J. D. Deuschel 《Probability Theory and Related Fields》1987,76(3):325-340
Summary An infinite lattice system of interacting diffusion processes is characterized as a Gibbs distribution on
with continuous local conditional probabilities. Using estimates for the Vasserstein metric onC[0, 1], Dobrushin's contraction technique is applied in order to obtain information about macroscopic properties of the entire diffusion process. 相似文献
959.
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
960.
J. Sztrik 《The Journal of the Operational Research Society》1987,38(1):57-63
This paper discusses the equilibrium behaviour of the generalized M/G/n blocking system with heterogeneous servers. The system is evolving in a random environment controlled by an irreducible, aperiodic, m-state Markov chain Z(t). This paper deals with the main characteristics, such as utilization, the average length of busy period of the system, the mean number of occupied servers and the probability of blocking. Finally, numerical examples illustrate the problem in question. 相似文献