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Let PN be a uniform random N × N permutation matrix and let χN(z) = det(zIN − PN) denote its characteristic polynomial. We prove a law of large numbers for the maximum modulus of χN on the unit circle, specifically, with probability tending to 1 as N → ∞ , for a numerical constant x0 ≈ 0.652 . The main idea of the proof is to uncover a logarithmic correlation structure for the distribution of (the logarithm of) χN , viewed as a random field on the circle, and to adapt a well-known second-moment argument for the maximum of the branching random walk. Unlike the well-studied CUE field in which PN is replaced with a Haar unitary, the distribution of χN(e2πit) is sensitive to Diophantine properties of the point t . To deal with this we borrow tools from the Hardy-Littlewood circle method. © 2020 Wiley Periodicals LLC 相似文献
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Patrick E. Hartnett Scott M. Dyar Eric A. Margulies Leah E. Shoer Andrew W. Cook Samuel W. Eaton Tobin J. Marks Michael R. Wasielewski 《Chemical science》2015,6(1):402-411
The photophysics of a covalently linked perylenediimide–diketopyrrolopyrrole–perylenediimide acceptor–donor–acceptor molecule (PDI–DPP–PDI, 1) were investigated and found to be markedly different in solution versus in unannealed and solvent annealed films. Photoexcitation of 1 in toluene results in quantitative charge separation in τ = 3.1 ± 0.2 ps, with charge recombination in τ = 340 ± 10 ps, while in unannealed/disordered films of 1, charge separation occurs in τ < 250 fs, while charge recombination displays a multiexponential decay in ∼6 ns. The absence of long-lived, charge separation in the disordered film suggests that few free charge carriers are generated. In contrast, upon CH2Cl2 vapor annealing films of 1, grazing-incidence X-ray scattering shows that the molecules form a more ordered structure. Photoexcitation of the ordered films results in initial formation of a spin-correlated radical ion pair (electron–hole pair) as indicated by magnetic field effects on the formation of free charge carriers which live for ∼4 μs. This result has significant implications for the design of organic solar cells based on covalent donor–acceptor systems and shows that long-lived, charge-separated states can be achieved by controlling intramolecular charge separation dynamics in well-ordered systems. 相似文献
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Electron spin resonance spectroscopy has been used to investigate radiation damage in an irradiated single crystal of maleic acid. At least two stable radicals are produced by the radiation. One of these radicals is probably HOOC-H2C-CH-COOH. Another species, possibly of the form HOOC-RCH-CH-COOH, has also been observed. Radical yields have been measured for the isomeric maleic and fumaric acids. The G-values are 0.1 for maleic acid and 0.06 for fumaric acid. 相似文献
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Reallocation of input resources (RIR) is a process by which certain decision making units (DMUs) reallocate resources among themselves; a process that occurs frequently in many enterprises. In this paper, a new data envelopment analysis (DEA) approach is developed to select the best cooperative partner DMU. Context-dependent DEA is used to identify the different levels of best-practice frontiers. Two DEA-based models are established for two cooperative scenarios, namely, resources pooling only and best-practice sharing. A cooperative method is applied to determine how to reallocate the input resources, and Shapley value is used to estimate the revenue changes that the various DMUs should expect after RIR. Two different situations with different objectives are considered. One objective is to maximize total revenue for the partnership, while the other is to maximize the Shapley value. The proposed approaches are illustrated with two examples. 相似文献
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Vincent Besse Loïc Le Pluart Wayne D. Cook Thi‐Nhàn Pham Pierre‐Jean Madec 《Journal of polymer science. Part A, Polymer chemistry》2013,51(23):5046-5055
Phosphonic acids are known to be useful monomers in dental restorative materials because of their good potential to provide enhanced adhesion to hydroxyapatite and their high hydrolytic stability. In this study, the photopolymerization of phosphonic acid‐based monomer via the camphorquinone (CQ)/ethyl‐4‐(dimethylaminobenzoate) (EDAB) photoredox system is compared with a ternary system composed of iodonium hexafluorophosphate and CQ/EDAB. Photocalorimetry shows that the ternary system does not provide a significant acceleration of the polymerization with either acrylamide or methacrylate phosphonic acids. The complexation of the iodonium by the phosphonic moiety of the acidic monomers leads to a lowered iodonium reactivity and reduced polarizability of the medium and as a consequence limits the rate enhancement effect normally observed by phosphonic acids on the polymerization rate. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 5046–5055 相似文献