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991.
Yu. Ya. Trifonov 《Journal of Engineering Thermophysics》2008,17(1):30-52
This paper is devoted to a theoretical analysis of nonlinear two-dimensional waves using the Navier-Stokes equations in their
full statement. Steady-state travelling wave regimes have been found and an analysis of their linear stability has been carried
out. It is shown that the flow regimes obtained using the Navier-Stokes equations are qualitatively different from the solutions
of Shkadov’s integral approach starting from some values of the Kapitza number. It is also found that the wave regimes of
the Navier-Stokes equations have an internal vortex at moderate Reynolds numbers. The results obtained using “the regularized
integral model” are in excellent agreement with the Navier-Stokes calculations for Re/Ka ≤2. Unlike the solutions found using an integral approach, it is shown that only a few types of nonlinear waves exist when
the full Navier-Stokes equations are considered.
The text was submitted by the author in English. 相似文献
992.
We systematically investigate the motion of slowly moving
matter--wave gap solitons in a nonlinear potential, produced by the
weak random spatial variation of the atomic scattering length. With
the weak randomness, we construct an effective-particle theory to
study the motion of gap solitons. Based on the effective-particle
theory, the effect of the randomness on gap solitons is obtained, and
the motion of gap solitons is finally solved. Moreover, the analytic
results for the general behaviours of gap soliton motion, such as the
ensemble-average speed and the reflection probability depending on
the weak randomness are obtained. We find that with the increase of
the random strength the ensemble-average speed of gap solitons
decreases slowly where the reduction is proportional to the variance
of the weak randomness, and the reflection probability becomes
larger. The theoretical results are in good agreement with the
numerical simulations based on the Gross--Pitaevskii equation. 相似文献
993.
The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances. 相似文献
994.
S.V.Ivanova 《中国光学快报(英文版)》2008,6(2)
By the 90°elastic light scattering investigation and far field observation in the range of 20-800℃,the relation between behavior of light scattering anomalies and evolution of nanodomain structures in lattice of barium sodium niobate(Ba2NaNb5O15,BSN)crystal was clarified.The correlation between anomalies on the temperature curves of the elastic light scattering intensity and temperature transformations of nanodomains was studied by X-ray and electron microscope methods.Phase transition near 500℃ and movement in field of scattering light could be explained by appearance of a new incommensurate phase. 相似文献
995.
Jacek Tabor 《Journal of Differential Equations》2002,180(1):171-197
996.
邓小刚 《中国科学A辑(英文版)》2002,45(3):356-370
Based on the method deriving dissipative compact linear schemes (DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis,the dissipative and dispersive features of DWCNS are discussed. In view of the modified wave number, the DWCNS are equivalent to the fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the accuracy of DWCNS. Boundary and near boundary schemes are developed and the asymptotic stabilities of DWCNS on both uniform and stretching grids are analyzed. The multi-dimensional implementations for Euler and Navier-Stokes equations are discussed. Several numerical inviscid and viscous results are given which show the good performances of the DWCNS for discontinuities capturing, high accuracy for boundary layer resolutions, good convergent rates (the root-mean-square of residuals approaching machine zero for solutions with strong shocks) and especially the damping effect on the spudous oscillations which were found in the solutions obtained by TVD and ENO schemes. 相似文献
997.
In this paper we prove the smoothness of solutions of a class of elliptic-parabolic nonlinear Levi type equations, represented as a sum of squares plus a vector field. By means of a freezing method the study of the operator is reduced to the analysis of a family of left invariant operators on a free nilpotent Lie group. The fundamental solution of the operator is used as a parametrix of the fundamental solution of the Levi operator, and provides an explicit representation formula for the solution of the given equation. Differentiating this formula and applying a bootstrap method, we prove that the solution is .
998.
Analogy is used to treat the system of non-interacting integrate-and-fire neurons as an ideal Fermi gas. It allows to obtain the nonlinear gain curve in the form of sigmoid in agreement with biological findings. As the by-product the gain-threshold mechanism in neurons is presented. Surprisingly enough, this is in agreement with new biological findings, too. Besides, the application of this mechanism to the dynamics of neurons leads to the non-monotone transfer function. 相似文献
999.
Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation (-1)n(talphay(n))(n)+q(t)y = 0 (*) are established. In these criteria, equation (*) is viewed as a perturbation of the conditionally oscillatory equation (-1)n(talphay(n))(n) - µ,t2n-y = 0, where
n, is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed. 相似文献
1000.
This is the first of two papers devoted to the study of a nonlocal evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider subcritical temperatures, for which there are two local equilibria, and begin the proof of a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibria; i.e., the fronts. We shall show in the second paper that an initial perturbation v
0 of a front that is sufficiently small in L
2 norm, and sufficiently localized that x
2
v
0(x)2
dx<, yields a solution that relaxes to another front, selected by a conservation law, in the L
1 norm at an algebraic rate that we explicitly estimate. There we also obtain rates for the relaxation in the L
2 norm and the rate of decrease of the excess free energy. Here we prove a number of estimates essential for this result. Moreover, the estimates proved here suffice to establish the main result in an important special case.on leave from 相似文献