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We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided. 相似文献
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Philipp M. Cromm Jochen Spiegel Dr. Tom N. Grossmann Prof. Dr. Herbert Waldmann 《Angewandte Chemie (International ed. in English)》2015,54(46):13516-13537
Small GTPases are a family of GDP‐/GTP‐binding proteins that serve as biomolecular switches inside cells to control a variety of essential cellular processes. Aberrant function and regulation of small GTPases is associated with a variety of human diseases, thus rendering these proteins highly interesting targets in drug discovery. However, this class of proteins has been considered “undruggable”, as intensive decade‐long efforts did not yield clinically relevant direct modulators of small GTPases. Recently, the targeting of small GTPases has gained fresh impetus through the discovery of novel transient cavities on the protein surfaces and the application of new targeting strategies. Besides Ras proteins, other small GTPases have attracted increased attention since improved biological insight in combination with novel targeting strategies identified them as promising targets in drug discovery. This Review gives an overview of relevant aspects of the superfamily of small GTPases and summarizes recent progress and perspectives for the direct modulation of these challenging targets. 相似文献
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Chun Y. Chow Hélène Bolvin Victoria E. Campbell Régis Guillot Jeff W. Kampf Wolfgang Wernsdorfer Frédéric Gendron Jochen Autschbach Vincent L. Pecoraro Talal Mallah 《Chemical science》2015,6(7):4148-4159
We report here the synthesis and the investigation of the magnetic properties of a series of binuclear lanthanide complexes belonging to the metallacrown family. The isostructural complexes have a core structure with the general formula [Ga4Ln2(shi3–)4(Hshi2–)2(H2shi–)2(C5H5N)4(CH3OH)x(H2O)x]·xC5H5N·xCH3OH·xH2O (where H3shi = salicylhydroxamic acid and Ln = GdIII1; TbIII2; DyIII3; ErIII4; YIII5; YIII0.9DyIII0.16). Apart from the Er-containing complex, all complexes exhibit an antiferromagnetic exchange coupling leading to a diamagnetic ground state. Magnetic studies, below 2 K, on a single crystal of 3 using a micro-squid array reveal an opening of the magnetic hysteresis cycle at zero field. The dynamic susceptibility studies of 3 and of the diluted DyY 6 complexes reveal the presence of two relaxation processes for 3 that are due to the excited ferromagnetic state and to the uncoupled DyIII ions. The antiferromagnetic coupling in 3 was shown to be mainly due to an exchange mechanism, which accounts for about 2/3 of the energy gap between the antiferro- and the ferromagnetic states. The overlap integrals between the Natural Spin Orbitals (NSOs) of the mononuclear fragments, which are related to the magnitude of the antiferromagnetic exchange, are one order of magnitude larger for the Dy2 than for the Er2 complex. 相似文献
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This work presents numerical simulations and selected results of the flow over aquatic canopies, consisting of artificial flexible rectangular blades, arranged in a well-defined order. The results obtained with three different Reynolds and Cauchy numbers are compared with experimental data achieving good agreement. The considered range of Cauchy numbers represents three different types of canopies ranging from rigid up to highly flexible plants. The transient flow data and blade positions are statistically analyzed to gain deeper understanding of the complex physical processes for this kind of fluid structure interaction. For example, the correlation of role of large scale motion of the flexible blades in conjunction with coherent vortex structures of the flow is addressed. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Jochen?DenzlerEmail author Robert J.?McCann 《Archive for Rational Mechanics and Analysis》2005,175(3):301-342
The complete spectrum is determined for the operator on the Sobolev space W1,2(Rn) formed by closing the smooth functions of compact support with respect to the norm Here the Barenblatt profile is the stationary attractor of the rescaled diffusion equation in the fast, supercritical regime m the same diffusion dynamics represent the steepest descent down an entropy E(u) on probability measures with respect to the Wasserstein distance d2. Formally, the operator H=HessE is the Hessian of this entropy at its minimum , so the spectral gap H:=2–n(1–m) found below suggests the sharp rate of asymptotic convergence: from any centered initial data 0u(0,x)L1(Rn) with second moments. This bound improves various results in the literature, and suggests the conjecture that the self-similar solution u(t,x)=R(t)–n(x/R(t)) is always slowest to converge. The higher eigenfunctions – which are polynomials with hypergeometric radial parts – and the presence of continuous spectrum yield additional insight into the relations between symmetries of Rn and the flow. Thus the rate of convergence can be improved if we are willing to replace the distance to with the distance to its nearest mass-preserving dilation (or still better, affine image). The strange numerology of the spectrum is explained in terms of the number of moments of .Dedicated to Elliott H. Lieb on the occasion of his 70th birthday. 相似文献