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71.
Vincenzo Recupero 《Journal of Mathematical Analysis and Applications》2004,300(2):387-407
In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds. 相似文献
72.
Chien Lun Hung Yi Sheng Yeh 《International Journal of Infrared and Millimeter Waves》2003,24(12):2025-2041
Coaxial cavities are used in high power gyrotrons as the beam-wave interaction structure. Much research has been devoted to their mode selective properties. A coaxial cavity lacks a sharp boundary at its open end, so it has some physical features that can only be observed using a spectral model, such as frequency-dependent field profiles and mode overlapping effects. These properties are important since cold tests are usually conducted in the frequency domain. This study applies the incident/reflected wave boundary condition to the wave equation of a weakly irregular coaxial waveguide. The resistivity of the wall is considered in the analysis. Calculations reveal that the fixed-position spectrum yields an uncertain resonant frequency and quality factor. Although the maximum-field spectrum can uniquely determine the properties of the coaxial cavity, the resonant frequency obtained using the maximum-field spectral model is inconsistent with that obtained using the temporal model. The field-energy spectrum explains the low Q nature of the coaxial cavity. Moreover, resonant frequencies evaluated using the field-energy spectrum agree precisely with those evaluated using the temporal model. 相似文献
73.
High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical
systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However,
when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels
that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads
to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating
and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation.
The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the
gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably
big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments
on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects
and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow,
transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different
air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required
rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates
that the quality factor, Q, follows a power law, Q ∝P
–r
, with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity
slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple
case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity
concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h
0/L<0.01). As this ratio increases, the range of validity decreases. 相似文献
74.
The effect of the temperature factor, that is, the ratio of the body temperature to the freestream stagnation temperature, on the structure of the separated flow formed in the presence of a concave corner in a supersonic stream is studied. The strong influence of the temperature factor on the separation zone length and the flow-generated aerodynamic characteristics is established. It is shown that for fairly large deflection angles this flow cannot be described by free interaction, or triple deck, theory. 相似文献
75.
Su-Yun Huang Chuhsing Kate Hsiao Ching-Wei Chang 《Annals of the Institute of Statistical Mathematics》2003,55(3):655-670
The article provides a refinement for the volume-corrected Laplace-Metropolis estimator of the marginal likelihood of DiCiccioet al. The correction volume of probability α in DiCiccioet al. is fixed and suggested to take the value α=0.05. In this article α is selected based on an asymptotic analysis to minimize
the mean square relative error (MSRE). This optimal choice of α is shown to be invariant under linear transformations. The
invariance property leads to easy implementation for multivariate problems. An implementation procedure is provided for practical
use. A simulation study and a real data example are presented. 相似文献
76.
77.
Let G be a graph and f : V(G)→{1,3,5,…}. Then a subgraph H of G is called a (1,f)-odd subgraph if degH(x){1,3,…,f(x)} for all xV(H). If f(x)=1 for all xV(G), then a (1,f)-odd subgraph is nothing but a matching. A (1,f)-odd subgraph H of G is said to be maximum if G has no (1,f)-odd subgraph K such that |K|>|H|. We show that (1,f)-odd subgraphs have some properties similar to those of matchings, in particular, we give a formula for the order of a maximum (1,f)-odd subgraph, which is similar to that for the order of a maximum matching. 相似文献
78.
对于Bellman最优性原理,本文举出实例表明:(1)策略不一定有(合理的)子策略;(2)子策略不一定存在最优子策略;(3)最优策略不一定有最优子策略;(4)用最短路与反证法来论述最优性原理的正确性,不能肯定成立;(5)Bellman最优性原理与其递推公式并不等价。 讨论四类最优策略之后,给出最优性原理与递推公式等价的一个充分性定理。 相似文献
79.
Luciano Galeone Roberto Garrappa 《Journal of Computational and Applied Mathematics》1997,80(2):377-195
We study convergence properties of time-point relaxation (TR) Runge-Kutta methods for linear systems of ordinary differential equations. TR methods are implemented by decoupling systems in Gauss-Jacobi, Gauss-Seidel and successive overrelaxation modes (continuous-time iterations) and then solving the resulting subsystems by means of continuous extensions of Runge-Kutta (CRK) methods (discretized iterations). By iterating to convergence, these methods tend to the same limit called diagonally split Runge-Kutta (DSRK) method. We prove that TR methods are equivalent to decouple in the same modes the linear algebraic system obtained by applying DSRK limit method. This issue allows us to study the convergence of TR methods by using standard principles of convergence of iterative methods for linear algebraic systems. For a particular problem regions of convergence are plotted. 相似文献
80.