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121.
Peter?EichelsbacherEmail author Matthias?L?we 《Probability Theory and Related Fields》2004,130(4):441-472
We derive moderate deviation principles for the overlap parameter in the Hopfield model of spin glasses and neural networks. If the inverse temperature is different from the critical inverse temperature c=1 and the number of patterns M(N) satisfies M(N)/N 0, the overlap parameter multiplied by N, 1/2 < < 1, obeys a moderate deviation principle with speed N1–2 and a quadratic rate function (i.e. the Gaussian limit for = 1/2 remains visible on the moderate deviation scale). At the critical temperature we need to multiply the overlap parameter by N, 1/4 < < 1. If then M(N) satisfies (M(N)6 log N M(N)2N4 log N)/N 0, the rescaled overlap parameter obeys a moderate deviation principle with speed N1–4 and a rate function that is basically a fourth power. The random term occurring in the Central Limit theorem for the overlap at c = 1 is no longer present on a moderate deviation scale. If the scaling is even closer to N1/4, e.g. if we multiply the overlap parameter by N1/4 log log N the moderate deviation principle breaks down. The case of variable temperature converging to one is also considered. If N converges to c fast enough, i.e. faster than the non-Gaussian rate function persists, whereas for N converging to one slower than the moderate deviations principle is given by the Gaussian rate. At the borderline the moderate deviation rate function is the one at criticality plus an additional Gaussian term.Research supported by the Volkswagen-Stiftung (RiP-program at Oberwolfach, Germany).Mathematics Subject Classification (2000): 60F10 (primary), 60K35, 82B44, 82D30 (secondary) 相似文献
122.
We point out a connection between reflection principles and generic large cardinals. One principle of pure reflection is introduced that is as strong as generic supercompactness of 2 by -closed forcing. This new concept implies CH and extends the reflection principles for stationary sets in a canonical way.Mathematics Subject Classification (2000): 03E50, 03E55 相似文献
123.
Aurel Spataru 《Proceedings of the American Mathematical Society》2004,132(11):3387-3395
Let be i.i.d. random variables with , and set . We prove that, for
under the assumption that and Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974).
under the assumption that and Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974).
124.
Auguste Besson 《Pramana》2004,62(3):537-540
The RunII of the Dø experiment was started in March 2001. The first preliminary results on searches for new physics are presented, with a luminosity of ~ 10 pb?1 from the data collected in 2001-2002. We report results in mSUGRA (jets + missingEt channel), GMSB (diphotons), RPV (trileptons and like sign dileptons) and large extra dimensions (dielectrons and diphotons). 相似文献
125.
The present review surveys the results of X-ray diffraction studies of large stoichiometric transition metal clusters containing from 20 to 145 atoms in metal cores surrounded by ligand shells (72 compounds). Structures of such clusters have fragments of close packings (face-centered cubic (f.c.c.), hexagonal close (h.c.p.), and body-centered cubic (b.c.c.) packings) characteristic of crystalline bulk metals as well as mixed packings (f.c.c./h.c.p.), local close packings with pentagonal symmetry, and strongly distorted amorphous packings. The observed packing types, their distortions, and the relationship between the atomic structures of metal cores and the atomic radial distribution functions (RDF) are discussed. The structural principles established for the large clusters are applied to analysis of the experimental RDF for metal nanoparticles determined by X-ray diffraction and EXAFS spectroscopy. 相似文献
126.
Włodzimierz Bryc 《Journal of Theoretical Probability》2003,16(4):935-955
We prove the large deviation principle for the joint empirical measure of pairs of random variables which are coupled by a totally symmetric interaction. The rate function is given by an explicit bilinear expression, which is finite only on product measures and hence is non-convex. 相似文献
127.
Fuqing Gao 《Journal of Theoretical Probability》2003,16(2):401-418
Let f
n
be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in
d
. It is proved that if the kernel function is an integrable function with bounded variation, and the common density function f of the random variables is continuous and f(x) 0 as |x| , then the moderate deviation principle and large deviation principle for
hold. 相似文献
128.
129.
Large Deviation Principle for Additive Functionals of Brownian Motion Corresponding to Kato Measures
Let (B
t
,P
W
x
) be the Brownian motion. Let be a Radon measure in the Kato class and A
t
the additive functional associated with . We prove that A
t
/t obeys the large deviation principle. 相似文献
130.
We address the problem of finding the worst possible traffic a
user of a telecommunications network can send.
We take worst to mean having the highest effective
bandwidth, a concept that arises in the Large Deviation theory of
queueing networks.
The traffic is assumed to be stationary and to satisfy leaky bucket
constraints, which represent the a priori knowledge the network
operator has concerning the traffic.
Firstly, we show that this optimization problem may be reduced to an
optimization over periodic traffic sources.
Then, using convexity methods, we show that the realizations of a
worst case source must have the following properties:
at each instant the transmission rate must be either zero,
the peak rate, or the leaky bucket rate; it may only be the latter when
the leaky bucket is empty or full;
each burst of activity must either start with the leaky
bucket empty or end with it full. 相似文献