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1.
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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Paul T. Marcyk Latisha R. Jefferies Deyaa I. AbuSalim Maren Pink Mu‐Hyun Baik Silas P. Cook 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2019,131(6):1741-1745
The direct, catalytic substitution of unactivated alcohols remains an undeveloped area of organic synthesis. Moreover, catalytic activation of this difficult electrophile with predictable stereo‐outcomes presents an even more formidable challenge. Described herein is a simple iron‐based catalyst system which provides the mild, direct conversion of secondary and tertiary alcohols to sulfonamides. Starting from enantioenriched alcohols, the intramolecular variant proceeds with stereoinversion to produce enantioenriched 2‐ and 2,2‐subsituted pyrrolidines and indolines, without prior derivatization of the alcohol or solvolytic conditions. 相似文献
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C. Wade Downey Grant J. Dixon Jared A. Ingersoll Claire N. Fuller Kenneth W. MacCormac Anna Takashima Rohina Sediqui 《Tetrahedron letters》2019,60(44):151192
Trimethylsilyl trifluoromethanesulfonate (TMSOTf) and a trialkylamine base promote both in situ enol silane/silyl ketene acetal formation and Mukaiyama aldol addition reactions between a variety of reaction partners in a single reaction flask. Isolation of the required enol silane or silyl ketene acetal is not necessary. For example, crossed aldol reactions between α-disubstituted aldehydes and non-enolizable aldehydes yield β-hydroxy aldehydes in good yield. In a related reaction, the common laboratory solvent ethyl acetate functions as both an enolate precursor and a green reaction solvent. When thioesters are employed as enolate precursors, high yields for additions to non-enolizable aldehydes are routinely observed. 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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In austenitic-stainless-steel weld metal, mechanical anisotropy is caused by preferred local orientation of elongated subgrains and preferred crystallographic orientation. Ultrasonic and static tensile-test methods used to determine elastic stiffness and compliance matrices, respectively, demonstrated that orthotropic symmetry exists. Inversion of this compliance matrix gave a stiffness matrix which showed general agreement between the two methods. It is suggested that the data can be used directly in finite-element analyses of weldments containing Type 308 stainless steel. 相似文献
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C. Wade Downey Sarah E. CovingtonDerek C. Obenschain Evan HallidayJames T. Rague Danielle N. Confair 《Tetrahedron letters》2014
para-Methoxybenzyl methyl ether acts as an alkylating agent for thiols in the presence of trimethylsilyl trifluoromethanesulfonate and trialkylamine base in good yields (58–96%). Aryl ketones are alkylated under similar conditions, probably through an enol silane intermediate, also in high yields (67–95%). The active alkylating species is likely a p-methoxybenzyl cation. 相似文献
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Stratospheric ozone depletion is mostly marked over the Antarctic and to a lesser extent over the Arctic, though recent reports have revealed that this also occurs at lower latitudes. Continued depletion of ozone in the lower stratosphere allows more UVR to reach the Earth's surface. Furthermore, it is projected that surface water temperatures will increase by between 0.2 and 2.0°C by the year 2060 and this will directly or indirectly influence algal growth. The interactions between environmental factors are complicated by the existence of different strains (ecotypes) of the same species that may respond differently. To understand the interactive effects of temperature and UV‐B on two strains of Anabaena circinalis, we investigated the damaging effects of UV‐B on cell numbers and photosynthetic characteristics and also examined the effect of temperature on the capacity of cells to recover from such stress. Both strains of A. circinalis responded differently in terms of survival, photosynthetic characteristics and recovery with interactions between temperature and UV‐B. This could be due to the variations in strain‐specific photoreactive mechanisms. This needs to be explored further including more strains and species before definitive conclusions can be reached about effects of global change on cyanobacteria generally. 相似文献