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991.
近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用. 相似文献
992.
《Integral Transforms and Special Functions》2012,23(3):233-256
The extended hypergeometric equation is a generalization of the Gaussian hypergeometric equation (Section 1), which is distinct from the generalized hypergeometric equation, because it remains of the second-order, but has an irregular singularity at infinity, of degree intermediate between those of Mathieu and Hill equations (Section 2). The solutions in the neighbourhood of the regular singularities (Section 3) at the origin (Subsections 3.1, 3.2) and point unity (Subsection 3.3), can be obtained by the Frobenius- Puchs method, in terms of power series with power (Subsection 3.1) or logarithmic (Subsection 3.2) singularities, with the difference that the recurrence formulas for the coefficients are multiple. The point at infinity is an irregular singularity (Section 4) of the extended hypergeometric equation. Because the corresponding solutions for this equation involve an essential singularity, the Frobenius-Fuchs method (Subsection 4.1) fails to give the solution in the neighbourhood of this point. The method of normal integrals (Subsection 4.2) yields the asymptotic expansions for extended hypergeometric functions only in the cases of lower degree, e.g. in the case of the first degree they generalize the asymptotic expansions of Mathieu functions. The solution of the extended hypergeometric equation in the neighbourhood of the irregular singularity at infinity, for any degree, is formally expressible as a Laurent series multiplied by a complex power, whose exponent on index is the root of an infinite determinant, and whose coefficients are determined from infinite linear systems of equations (Subsection 4.3). The method is similar to that used to solve Hill's equation, into which the extended hypergeometric type can be transformed (Section 5). The conclusion (Section 6) indicates some physical problems leading to differential equations with irregular singularities, and the cases in which the corresponding solutions are specified by extended hypergeometric functions. 相似文献
993.
《Integral Transforms and Special Functions》2012,23(10):751-755
The purpose of this study is to establish an expressions formula of sums of products of the degenerate Bernoulli numbers in terms of the degenerate Bernoulli numbers. 相似文献
994.
《Integral Transforms and Special Functions》2012,23(3):203-214
In terms of the telescoping method, a simple binomial sum is given. By applying the derivative operators to the equation just mentioned, we establish several general harmonic number identities including some known results. 相似文献
995.
《Integral Transforms and Special Functions》2012,23(4):324-330
By applying the derivative operators to Chu–Vandermonde convolution, several general harmonic number identities are established. 相似文献
996.
997.
Pan Zhou Haiyu Zhou Yingchun Xia Qingqing Feng Xian Kong Wen-hui Hou Yu Ou Xuan Song Hang-yu Zhou Weili Zhang Yang Lu Fengxiang Liu Qingbin Cao Hao Liu Shuaishuai Yan Kai Liu 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2024,136(19):e202316717
The electrolytes for lithium metal batteries (LMBs) are plagued by a low Li+ transference number (T+) of conventional lithium salts and inability to form a stable solid electrolyte interphase (SEI). Here, we synthesized a self-folded lithium salt, lithium 2-[2-(2-methoxy ethoxy)ethoxy]ethanesulfonyl(trifluoromethanesulfonyl) imide (LiETFSI), and comparatively studied with its structure analogue, lithium 1,1,1-trifluoro-N-[2-[2-(2-methoxyethoxy)ethoxy)]ethyl]methanesulfonamide (LiFEA). The special anion chemistry imparts the following new characteristics: i) In both LiFEA and LiETFSI, the ethylene oxide moiety efficiently captures Li+, resulting in a self-folded structure and high T+ around 0.8. ii) For LiFEA, a Li−N bond (2.069 Å) is revealed by single crystal X-ray diffraction, indicating that the FEA anion possesses a high donor number (DN) and thus an intensive interphase “self-cleaning” function for an ultra-thin and compact SEI. iii) Starting from LiFEA, an electron-withdrawing sulfone group is introduced near the N atom. The distance of Li−N is tuned from 2.069 Å in LiFEA to 4.367 Å in LiETFSI. This alteration enhances ionic separation, achieves a more balanced DN, and tunes the self-cleaning intensity for a reinforced SEI. Consequently, the fast charging/discharging capability of LMBs is progressively improved. This rationally tuned anion chemistry reshapes the interactions among Li+, anions, and solvents, presenting new prospects for advanced LMBs. 相似文献
998.
《Mendeleev Communications》2023,33(2):279-281
It has been experimentally shown that a complex obstacle consisting of two confusers oriented in opposite directions of a cylindrical vessel completely prevents the propagation of diluted methane – oxygen flames, i.e., the obstacle is the most effective flame arrester; the theoretical predictions are consistent with the experiments. 相似文献
999.
1000.
Angélica Garzon-Fontecha Harvi Castillo Daniel Escobar-Rincón Elisabeth Restrepo-Parra Wencel De La Cruz 《Surface and interface analysis : SIA》2019,51(9):906-913
Cr, Nb, Cr/Nb, CrNx, NbNx, CrNbN, and (CrN/NbN)n structures were produced on Si and glass substrates, using the d.c. magnetron sputtering technique. Compositional analysis, based on binding energies of Cr, Nb, and N, was carried out by means of X-ray photoelectron spectroscopy (XPS). Through Auger electron spectroscopy (AES), depth profiles were obtained, allowing to demonstrate the multilayers production. Surface morphological characteristics, as roughness and grain size, were evaluated by atomic force microscopy (AFM), revealing very smooth surfaces, that is a consequence of the deposition parameters used in the synthetization experiments. Finally, for different configurations, conductivity measurements were carried out, revealing the influence of nitrogen content and temperature on electron transport. It was found that substoichiometric nitrides (CrN0.35 and NbN0.12) exhibited the highest conductivity, because the nitrogen atoms act as donor of electrons. 相似文献