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91.
92.
The Leapfrog method is a time-symmetric multistep method, widely used to solve the Euler equations and other Hamiltonian systems, due to its low cost and geometric properties. A drawback with Leapfrog is that it suffers from parasitism. This paper describes an iterative starting method, which may be used to reduce to machine precision the size of the parasitic components in the numerical solution at the start of the computation. The severity of parasitic growth is also a function of the differential equation, the main method and the time-step. When the tendency to parasitic growth is relatively mild, computational results indicate that using this iterative starting method may significantly increase the time-scale over which parasitic effects remain acceptably small. Using an iterative starting method, Leapfrog is applied to the cubic Schrödinger equation. The computational results show that the Hamiltonian and soliton behaviour are well-preserved over long time-scales. 相似文献
93.
A non‐iterative implicit algorithm for the solution of advection–diffusion equation on a sphere 下载免费PDF全文
Yuri N. Skiba 《国际流体数值方法杂志》2015,78(5):257-282
A numerical algorithm for the solution of advection–diffusion equation on the surface of a sphere is suggested. The velocity field on a sphere is assumed to be known and non‐divergent. The discretization of advection–diffusion equation in space is carried out with the help of the finite volume method, and the Gauss theorem is applied to each grid cell. For the discretization in time, the symmetrized double‐cycle componentwise splitting method and the Crank–Nicolson scheme are used. The numerical scheme is of second order approximation in space and time, correctly describes the balance of mass of substance in the forced and dissipative discrete system and is unconditionally stable. In the absence of external forcing and dissipation, the total mass and L2‐norm of solution of discrete system is conserved in time. The one‐dimensional periodic problems arising at splitting in the longitudinal direction are solved with Sherman–Morrison's formula and Thomas's algorithm. The one‐dimensional problems arising at splitting in the latitudinal direction are solved by the bordering method that requires a prior determination of the solution at the poles. The resulting linear systems have tridiagonal matrices and are solved by Thomas's algorithm. The suggested method is direct (without iterations) and rapid in realization. It can also be applied to linear and nonlinear diffusion problems, some elliptic problems and adjoint advection–diffusion problems on a sphere. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
94.
Quantitation of memantine hydrochloride bulk drug and its tablet formulation using proton nuclear magnetic resonance spectrometry 下载免费PDF全文
Archana Sahu Mallikarjun Narayanam Moolchand Kurmi Mayurbhai Kathadbhai Ladumor Saranjit Singh 《Magnetic resonance in chemistry : MRC》2016,54(8):632-636
The use of quantitative nuclear magnetic resonance spectrometry for the determination of non‐UV active memantine hydrochloride with relative simplicity and precision has been demonstrated in this study. The method was developed on a 500 MHz NMR instrument and was applied to determination of the drug in a tablet formulation. The analysis was performed by taking caffeine as an internal standard and D2O as the NMR solvent. The signal of methyl protons of memantine hydrochloride appeared at 0.75 ppm (singlet) relative to the signal of caffeine (internal standard) at 3.13 ppm (singlet). The method was found to be linear (r2 = 0.9989) in the drug concentration range of 0.025 to 0.80 mg/ml. The maximum relative standard deviation for accuracy and precision was <2. The limits of detection and quantification were 0.04 and 0.11 mg/ml, respectively. The robustness of the method was revealed by changing nine different parameters. The deviation for each parameter was also within the acceptable limits. The study highlighted possibility of direct determination of memantine hydrochloride in pure form and in its marketed tablet formulation by the use of quantitative NMR, without the need of derivatization, as is the requirement in HPLC studies. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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颗粒毛细效应是指将一根细管插入填充有颗粒物质的容器中并对管施加竖直振动时颗粒在管内上升并最终达到一个稳定的高度的现象, 该现象为颗粒物料的逆重力输运提供了一种潜在的技术途径. 为探究颗粒毛细效应的影响因素, 采用离散元方法, 模拟再现了颗粒毛细效应过程,展示了不同管径下颗粒竖直方向速度演变特性, 考察了不同容器宽度和振动条件下颗粒最终毛细上升高度随管径的演变规律. 结果表明, 在容器宽度与粒径比为40、管振幅与粒径比为14.33、管振动频率为12 Hz情况下, 管径与粒径比$D/d = 3.33$时, 管内颗粒堵塞严重, 使得颗粒上升缓慢,并造成颗粒柱中断; $D/d = 8.33$时, 起初毛细上升高度增加迅速, 随后毛细上升高度的增大逐渐减缓, 管内颗粒在管径方向几乎不存在速度梯度; $D/d =15$时, 随着颗粒毛细上升高度的增大, 管内颗粒柱分离为速度截然不同的两层, 上层颗粒在管径方向几乎不存在速度梯度, 而下层颗粒存在明显的速度梯度.研究还发现, 在毛细效应能够发生的管径范围内, 存在一个对应于颗粒最终毛细上升高度最大值的临界管径, 当管径小于临界管径时, 颗粒最终毛细上升高度随管径的增大而增大, 当管径大于临界管径时, 颗粒最终毛细上升高度随管径的增大而趋于减小; 增大容器宽度,临界管径有所增大; 增大振幅、适当提高频率能够有效促进临界管径的增大. 相似文献
99.
ShiJun Liao 《中国科学:物理学 力学 天文学(英文版)》2020,(3):70-81
A new non-perturbative approach is proposed to solve time-independent Schr?dinger equations in quantum mechanics.It is based on the homotopy analysis method(HAM)that was developed by the author in 1992 for highly nonlinear equations and has been widely applied in many fields.Unlike perturbative methods,this HAM-based approach has nothing to do with small/large physical parameters.Besides,convergent series solution can be obtained even if the disturbance is far from the known status.A nonlinear harmonic oscillator is used as an example to illustrate the validity of this approach for disturbances that might be one thousand times larger than the possible superior limit of the perturbative approach.This HAM-based approach could provide us rigorous theoretical results in quantum mechanics,which can be directly compared with experimental data.Obviously,this is of great benefit not only for improving the accuracy of experimental measurements but also for validating physical theories. 相似文献
100.
The complex-scaled Green's function(CGF)method is employed to explore the single-proton resonance in 15F.Special attention is paid to the first excited resonant state 5/2+,which has been widely studied in both theory and experiments.However,past studies generally overestimated the width of the 5/2+state.The predicted energy and width of the first excited resonant state 5/2+by the CGF method are both in good agreement with the experimental value and close to Fortune's new estimation.Furthermore,the influence of the potential parameters and quadruple deformation effects on the resonant states are investigated in detail,which is helpful to the study of the shell structure evolution. 相似文献