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181.
We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary
dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy
at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions
the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually
obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling
limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also
equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager
limitT ΔS
MSA
/ΔE
MSA
→ 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while ford=2 this limit is 1.
On leave from Department of Physics, University of Puerto Rico, Mayagüez Campus, Mayagüez, Puerto Rico, 00681. 相似文献
182.
183.
A simple High performance liquid chromatographic (HPLC) method for the specific determination of the molecular weight and concentration of hyaluronic acid (HA) in complex mixtures has been developed. Hyaluronate-binding proteins isolated from bovine cartilage labelled by 125I or fluoresceinisothiocyanate were used as specific markers. The specific binding affinities of the markers were compared and were found to have association constants of 1.6 x 10(7) M-1 and 1.2 x 10(7) M-1 respectively. The HA levels and molecular weight distributions can be easily determined in the range 10-500 ng/mL in complex mixtures by the use of markers, molecular sieving HPLC columns and appropriate detectors. It has been demonstrated clearly that the method is useful for the highly specific determination of the parameters in complex biological samples such as serum and synovial fluids and is recommended for clinical applications. 相似文献
184.
185.
In the procduction of high-voltage insulating systems, disintegration and non-homogeneity occur in some cases and these factors can lead to the deterioration and even the breakdown such systems. In research into the causes of these phenomena DTA and TG were applied to study the course of hardening of the systems and to quantify the leaking substances. The results demonstrate the great value of thermal analysis in this field. 相似文献
186.
Dislocation motion in the real lattice of alloys is highly complex. In a certain temperature range the dynamic strain ageing phenomena have been reported. In this paper the influence of mobile solute atoms (as obstacles) on the motion of dislocation is analysed. Both processes are assumed to be thermally activated. A new model based on this assumption is proposed. The dislocation velocity and the friction stress (due to solute-dislocation interactions) are calculated. A change in the friction stress caused by solute mobility is discussed. 相似文献
187.
Given an integer n ≥ 2, let λ(n) := (log n)/(log γ(n)), where γ(n) = Π
p|n p, stand for the index of composition of n, with λ(1) = 1. We study the distribution function of (λ(n) – 1) log n as n runs through particular sets of integers, such as the shifted primes, the values of a given irreducible cubic polynomial
and the shifted powerful numbers.
Research supported in part by a grant from NSERC.
Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA.
Professor M.V. Subbarao passed away on February 15, 2006.
Received: 3 March 2006 Revised: 28 October 2006 相似文献
188.
Rostislav Vodák 《Mathematical Methods in the Applied Sciences》2007,30(1):43-75
We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross‐sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non‐smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
189.
In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
190.
We study percolation in the following random environment: let Z be a Poisson process of constant intensity on ℝ2, and form the Voronoi tessellation of ℝ2 with respect to Z. Colour each Voronoi cell black with probability p, independently of the other cells. We show that the critical probability is 1/2. More precisely, if p>1/2 then the union of the black cells contains an infinite component with probability 1, while if p<1/2 then the distribution of the size of the component of black cells containing a given point decays exponentially. These
results are analogous to Kesten's results for bond percolation in ℤ2.
The result corresponding to Harris' Theorem for bond percolation in ℤ2 is known: Zvavitch noted that one of the many proofs of this result can easily be adapted to the random Voronoi setting.
For Kesten's results, none of the existing proofs seems to adapt. The methods used here also give a new and very simple proof
of Kesten's Theorem for ℤ2; we hope they will be applicable in other contexts as well.
Research supported in part by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900
Research partially undertaken during a visit to the Forschungsinstitut für Mathematik, ETH Zürich, Switzerland 相似文献