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101.
A coupled system known as the Drinfel'd-Sokolov-Wilson equation is reexamined. With the help of a Lax operator of fourth order, its proper Darboux transformation is constructed. Also, a nonlinear superposition formula is worked out for the associated Bäcklund transformation and some solutions are calculated. 相似文献
102.
An analytical solution of the vibration responses of biological specimens using atomic force microscopy (AFM), which often requires operation in a liquid, is developed. In this study, the modal superposition method is employed to analyze the vibration responses of AFM cantilevers in tapping mode (TM) operated in a liquid and in air. The hydrodynamic force exerted by the fluid on AFM cantilevers is approximated by additional mass and hydrodynamic damping. The tip–sample interaction forces were transformed into axial, distributed transversal, and bending loading, and then applied to the end region of the AFM through the tip holder. The effects of transverse stress and bending stress were adopted to solve the dynamic model. With this model, a number of simulations were carried out to investigate the relationship between the transient responses of the cantilever in a liquid and the parameters considered in nanoscale processing. The simulations show that the vibration of AFM cantilevers in a liquid has dramatically different dynamic characteristics from these of that in air. The liquid reduces the magnitude of the transversal response and reduces the cantilever resonances. Moreover, the magnitudes of response become larger with increasing intermolecular distances and smaller with decreasing tip length. The cantilever vibration amplitudes significantly depend on the damping constant and the mass proportionality constant. 相似文献
103.
对一类光子消灭算符aN的正交归一本征态的迭加态的振幅k次方压缩特性进行研究,结果表明一类aN的正交归一本征态的迭加态的振幅k次方压缩特性明显地区别于aN的正交归一本征态k次方压缩.无论N取奇数还是偶数迭加态均存在振幅k(k=Nt或Nt/2)次方压缩,当位相差δ=2mπ/t(m为整数)时迭加态不存在振幅k次方压缩;当δ=π时,只有N和t同时为奇数才有可能存在k次方压缩;当δ=π/2时,对应t≠4m的不同取值迭加态存在k次方压缩;因而参量的位相对振幅的k次方压缩起着关键性的作用. 相似文献
104.
105.
We report the basis set dependencies and the basis set superposition errors for the hydrated complexes of K+ and Na+ ions in relation to the recent studies of the KcsA potassium channel. The basis set superposition errors are estimated by the geometry optimizations at the counterpoise-corrected B3LYP level. The counterpoise optimizations alter the hydration distances by about 0.02–0.03 Å. The enthalpies and free energies for K+ + n(H2O) → [K(H2O)n]+ and Na+ + n(H2O) → [Na(H2O)n]+ (n = 1–6) are compared between the theoretical and experimental values. The results show that the addition of diffuse functions to K, Na, and O species are effective. However, it is also found that the counterpoise corrections using diffuse functions work so as to underestimate the free energies for the complexes with increasing the hydration number. The stabilization energies in aqueous solution are larger for a Na+ ion than for a K+ ion, suggesting the contributions of their dehydration processes to the ion selectivity of the KcsA potassium channel. The changes in coordination distance between the isolated [K(H2O)8]+ and the [K(H2O)8]+ in the KcsA potassium channel indicate the importance of hydrogen bondings between the first hydration shell and the outer hydration shells. 相似文献
106.
Gang Lv Fadong Wei Hui Jiang Yanyan Zhou Xuemei Wang 《Journal of Molecular Structure》2009,915(1-3):98-104
Density functional B3LYP method with 6-31++G** basis set is applied to optimize the geometries of the luteolin, water and luteolin–(H2O)n complexes. The vibrational frequencies are also studied at the same level to analyze these complexes. We obtained four steady luteolin–H2O, nine steady luteolin–(H2O)2 and ten steady luteolin–(H2O)3, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) are used to investigate the hydrogen bonds involved in all the systems. The interaction energies of all the complexes corrected by basis set superposition error, are within −13.7 to −82.5 kJ/mol. The strong hydrogen bonding mainly contribute to the interaction energies, Natural bond orbital analysis is performed to reveal the origin of the interaction. All calculations also indicate that there are strong hydrogen bonding interactions in luteolin–(H2O)n complexes. The OH stretching modes of complexes are red-shifted relative to those of the monomer. 相似文献
107.
Wen-Xiu MA 《Frontiers of Mathematics in China》2013,8(5):1139-1156
A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables. 相似文献
108.
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110.
We discuss a parameter estimation problem using quantum decoherence in the double-slit interferometer. We consider a particle coupled to a massive scalar field after the particle passing through the double slit and solve the dynamics non-perturbatively for the coupling by the WKB approximation. This allows us to analyze the estimation problem which cannot be treated by master equation used in the research of quantum probe. In this model, the scalar field reduces the interference fringes of the particle and the fringe pattern depends on the field mass and coupling. To evaluate the contrast and the estimation precision obtained from the pattern, we introduce the interferometric visibility and the Fisher information matrix of the field mass and coupling. For the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the Fisher matrix. Also, focusing on the estimation precision of the mass, we find that the Fisher information characterizes the wave-particle duality in the double-slit interferometer. 相似文献