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71.
We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged. 相似文献
72.
Technical cellulose-2.5-acetates (CA 2.5) were characterized regarding their carbohydrate composition in comparison to the raw material. The association of the CA 2.5 samples in acetone was studied by size exclusion chromatography (SEC) using various acetone grades and styrene divinylbenzene copolymer columns. In HPLC grade acetone with and without addition of 1% water up to three different pre-humps eluted in front of the main fraction of the polymer. The evaluation of the main peak by light scattering measurements resulted in high molar masses indicating that for these technical CA 2.5 samples even the main fraction is not dissolved without association. No pre-humps or association phenomena were observed after addition of 1 ppm LiBr to HPLC grade acetone or with p.a. grade acetone. In addition pre-hump enriched and pre-hump free fractions were isolated by fractionated precipitation. The carbohydrate composition of these fractions was determined and correlated with their association pattern in SEC investigations. 相似文献
73.
Jürg Fröhlich Tai-Peng Tsai Horng-Tzer Yau 《Communications in Mathematical Physics》2002,225(2):223-274
We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show
that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a
soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ−1. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx).
Received: 30 June 2000 / Accepted: 25 June 2001 相似文献
74.
75.
A posteriori error estimators for the Stokes equations 总被引:5,自引:0,他引:5
Summary We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.This work was accomplished at the Universität Heidelberg with the support of the Deutsche Forschungsgemeinschaft 相似文献
76.
İ. B. Özdemir 《Experiments in fluids》1997,22(4):271-280
This paper is concerned with an experimental investigation of the mixing inside the vortex ring formed by the gravity slumping
motion of a dense cloud in a less dense atmosphere. The dynamics of the spreading and instantaneous structures of the turbulent
flow were examined by visualization, single and multi-point measurements of velocity and concentration for two heavy gases,
carbondioxide (CO2) and dichlorodifluoromethane (CCl2F2), in a configuration in that heavy gas, initially trapped in a reservoir, was released with the rise of a shutter into calm
air of a sector-shaped dispersion channel.
Visualization of the cloud as a whole showed a spreading motion in which an advancing frontal structure was followed by a
stratified flow with a layer of dense fluid of higher velocities near the wall and, on top of it, a layer of dilute fluid
whose concentration is controlled by the mixing mechanisms within the head. During the course of spreading, there was always
a phase in which the head attained to a constant speed of advance, which occurred as 0.13 m/s for CO2 and 0.48 m/s for CCl2F2. It was interesting to observe for CO2 that the phase of constant speed took place in between two acceleration phases; the former was due to the initial slumping
of the cloud at the exit of the reservoir, and the latter was attributed to the collapse of the head on the transition to
the passive dispersion phase.
Instantaneous two-dimensional velocity field, measured with particle image velocimeter (PIV), showed that the cloud overran
the ambient air which caused the approaching dense fluid deflected away from the wall with significant vertical velocities
and downstream-moving separation, and the air trapped under the head resulted in the density inversion which introduced further
intricacy to the turbulent structure of the head. Instabilities at the upper free shear layer due to density and velocity
discontinuity rolled into periodic array of vortices which engulfed a considerable amount of air as they were convected backwards
over the head, but the incorporation of heavy and light fluids was completed with the appearance of microscales after the
collapse on the stratified layer. Analyses of the cloud head at different downstream locations also revealed that its size
remained unchanged when the speed of advance was constant, allowing the rate of change of the cloud volume being modeled with
the rate of spreading.
Contours of concentration obtained from digitized PIV pictures confirmed the kinematic features of the mixing revealed by
the velocity field and that the concentration values within the large structures were higher than those at the upper part
of the stratified layer. Motivated by the experimental observations, a semi-empirical analysis was presented to describe the
results and based on local values of the Richardson and Reynolds numbers.
Received: 4 October 1995 / Accepted: 4 July 1996 相似文献
77.
As acknowledged in almost all monographs on the fracture of composite materials, one of the major fracture mechanism in unidirectional fibrous composites under uniaxial compression along the reinforcing elements is the stability loss of the material structure (the structural instability). According to this mechanism, theoretical investigations of the fracture along the fibres are reduced to those of the stability loss in the material structure, and the value of external critical forces is accepted as the value of failure forces. At present, numerous theoretical investigations have been carried out in this field with the use of the three-dimensional linearized theory of stability in the framework of the piecewise-homogeneous body model. However, in all the investigations it is assumed that the matrix and the fibre material are isotropic. It is evident that in many cases it is necessary to take into account the anisotropy of the matrix material when investigating the stability loss of fibres. In view of the above, in the framework of the piecewise-homogeneous body model using the three-dimensional linearized theory of stability, the present paper considers the stability loss of the fibre in the anisotropic (transversally isotropic) matrix. The effect of the properties of the matrix material on the critical values of the external loading is examined.Submitted to the 10th International Conference of Mechanics of Composite Materials (Riga, April 20–23, 1998).Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 603–611. September–October, 1997. 相似文献
78.
79.
Gunter M. Schütz 《Zeitschrift für Physik B Condensed Matter》1997,104(3):583-590
We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations. 相似文献
80.
We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic
reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized
by two numbers, T
1 and T
2 (‘reservoir temperatures’). If T
1 ≠ T
2, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat
fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with
an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T
1 and T
2, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T
1,T
2) > g
2 + α, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions.
Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007.
Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments
of Mathematics of McGill University and the University of Toronto, Canada.
Matthias Mück: Supported by DAAD under grant HSP III.
Israel Michael Sigal: Supported by NSERC under grant NA7901. 相似文献