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The energy of a mass of liquid is evaluated asymptotically in powers of the range of the intermolecular potential divided by a typical dimension of the liquid. The leading term is the internal energy, proportional to the liquid volume. The second term is the energy of surface tension, proportional to the area of the liquid surface. The third term is proportional to an integral over this surface of the square of the mean curvature of the surface minus one-third of its Gaussian curvature. This new term has exactly the form of the bending energy of a thin elastic plate. Comparing it with the bending energy yields expressions for the flexural rigidity and the Poisson ratio of the liquid surface. This flexural rigidity of the surface leads to new terms in the equation of equilibrium of the liquid surface, in addition to the usual surface tension terms. 相似文献
3.
Merchant KA Noid WG Akiyama R Finkelstein IJ Goun A McClain BL Loring RF Fayer MD 《Journal of the American Chemical Society》2003,125(45):13804-13818
Spectrally resolved infrared stimulated vibrational echo data were obtained for sperm whale carbonmonoxymyoglobin (MbCO) at 300 K. The measured dephasing dynamics of the CO ligand are in agreement with dephasing dynamics calculated with molecular dynamics (MD) simulations for MbCO with the residue histidine-64 (His64) having its imidazole epsilon nitrogen protonated (N(epsilon)-H). The two conformational substate structures B(epsilon) and R(epsilon) observed in the MD simulations are assigned to the spectroscopic A(1) and A(3) conformational substates of MbCO, respectively, based on the agreement between the experimentally measured and calculated dephasing dynamics for these substates. In the A(1) substate, the N(epsilon)-H proton and N(delta) of His64 are approximately equidistant from the CO ligand, while in the A(3) substate, the N(epsilon)-H of His64 is oriented toward the CO, and the N(delta) is on the surface of the protein. The MD simulations show that dynamics of His64 represent the major source of vibrational dephasing of the CO ligand in the A(3) state on both femtosecond and picosecond time scales. Dephasing in the A(1) state is controlled by His64 on femtosecond time scales, and by the rest of the protein and the water solvent on longer time scales. 相似文献
4.
The reactions of thionyl and sulphuryl chlorides on isoflavones have been found to give a number of new chloroisoflavones and isoflavanones, whose structures have been elucidated on the basis of their spectral analytical data. 相似文献
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Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution 总被引:2,自引:0,他引:2
Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind:
where the solution (t) is assumedto have the form f(t) = x(t)+r?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme. 相似文献
8.
V.E. Merchant 《Optics Communications》1978,25(2):259-262
The time development of visible fluorescence from CO2-laser-irradiated SiF4 at various pressures is compared to the predictions of a simple model. This comparison leads to the conclusion that dissociation is a result of binary collisions between molecules that are vibrationally excited but translationally cool. 相似文献
9.
This paper describes the construction of a mathematical model and the results of its use in planning the pattern of routing in a national, complex distribution network; the model's particular feature being its ability to balance return loads on routes where two-way flow is possible. 相似文献
10.
The reaction of hexachloropropene with hydroxy-coumarins and chromones has been utilized to synthesise dichloro-benzodipyrandiones. The structures of the latter have been deduced from their spectral-analytical data. The reaction with 4-hydroxy-coumarin derivatives affords dichloropyrano-benzpyrandiones. 相似文献