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1.
The treatment of the non-linear isotherm in chromatography by one of the authors [1] is extended to other cases of practical interest. The original paper dealt with the case of an initially thin zone resulting in a Poisson distribution the asymmetry of which is a function of the plate number and the non-linearity constant. The present work shows that the same relations apply to initially thick zones and to the cases of washing and deposition leading to simple relations for breakthrough curves. For significantly non-linear isotherms other quasi-Gaussian distributions can give a better fit. 相似文献
2.
Hua‐Wei Li Sabyasachi Kar Pinghui Jiang 《International journal of quantum chemistry》2013,113(10):1493-1497
The effects of Debye plasma on the frequency‐dependent polarizabilities of Li and Na atoms are investigated using symplectic algorithm within the framework of the pseudostate summation technique. Dynamic dipole polarizabilities of Li (2s 2S) and Na(3s 2S) as functions of scaled number density of the plasma electrons for arbitrary plasma temperature are presented. Screening effects on the resonance frequencies are also presented. In free‐atomic cases, our calculated results are comparable with the reported theoretical and experimental predictions. © 2012 Wiley Periodicals, Inc. 相似文献
3.
Building on the pioneering work of Jean-Marie André and working in the laboratory he founded, the authors have developed a code called FT-1D to make Hartree-Fock electronic structure computations for stereoregular polymers using Ewald-type convergence acceleration methods. That code also takes full advantage of all line-group symmetries to calculate only the minimal set of two-electron integrals and to optimize the computation of the Fock matrix. The present communication reports a benchmark study of the FT-1D code using polytetrafluoroethylene(PTFE) as a test case. Our results not only confirm the algorithmic correctness of the code through agreement with other studies where they are applicable, but also show that the use of convergence acceleration enables accurate results to be obtained in situations where other widely-used codes(e.g., PLH and Crystal) fail. It is also found that full attention to the line-group symmetry of the PTFE polymer leads to an increase of between one and two orders of magnitude in the speed of computation. The new code can therefore be viewed as extending the range of electronic-structure computations for stereoregular polymers beyond the present scope of the successful and valuable code Crystal. 相似文献
4.
A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.
5.
Zhi-Guo Liu 《The Ramanujan Journal》2002,6(4):429-447
In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers–Fine identity, the nonterminating 65 summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed. 相似文献
6.
Necessary and sufficient conditions for an orthogonal series to be the Fourier series of a function in the space
,
, are obtained. In the special case of regular summation methods we recover the classical results of Orlicz and Lomnicki. 相似文献
7.
Grand Canonical Monte Carlo (GCMC) was used to study the sorption thermodynamics of carbon dioxide in model graphite slit-like pores and nanotubes by means of the Ewald technique, suitably adapted for the computation of long range (electrostatic) interactions of sorbates confined in pore systems exhibiting reduced periodicity in space. The computed thereby micropore size distributions extracted via mathematical elaboration of the simulation results with respect to real graphitic materials, reproduced successfully the experimentally measured isotherms of carbon dioxide in these materials at various temperatures. In the case of nanotubes, a direct Coulomb summation over a large number of periodic images proved to be a sufficient approximation leading to excellent agreement between the simulated and measured isotherms. 相似文献
8.
9.
We propose a new method of summation to any accuracy for a wide class of divergent series, using only a finite number of terms
of the series.
Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 24–35, July, 2000. 相似文献
10.
主要论述n次单位根在一些组合数求和、多项式的整除、因式分解中的应用,说明了n次单位根法可拓宽解题思路,是一种方便、快捷的数学解题方法. 相似文献