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41.
Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group 下载免费PDF全文
Hajer Bahouri & Isabelle Gallagher 《数学研究通讯:英文版》2023,39(1):1-35
It was proved by Bahouri et al. [9] that the Schrödinger equation on
the Heisenberg group $\mathbb{H}^d,$ involving the sublaplacian, is an example of a totally
non-dispersive evolution equation: for this reason global dispersive estimates
cannot hold. This paper aims at establishing local dispersive estimates on $\mathbb{H}^d$ for the linear Schrödinger equation, by a refined study of the Schrödinger kernel $S_t$ on $\mathbb{H}^d.$ The sharpness of these estimates is discussed through several
examples. Our approach, based on the explicit formula of the heat kernel on $\mathbb{H}^d$ derived by Gaveau [19], is achieved by combining complex analysis and
Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel $S_t$ concentrates on quantized horizontal hyperplanes of $\mathbb{H}^d.$ 相似文献
42.
Nash constructible functions on a real algebraic set V are defined as linear combinations, with integer coefficients, of Euler characteristic of fibres of proper regular morphisms restricted to connected components of algebraic sets. We prove that if V is compact, these functions are sums of signs of semialgebraic arc-analytic functions (i.e. functions which become analytic when composed with any analytic arc). We also give a sharp upper bound to the number of semialgebraic arc-analytic functions which are necessary to define any given Nash constructible functions. 相似文献
43.
Vijay Singh R.P.S. Chakradhar Isabelle Ledoux-Rak Laurent Badie Fabienne Pelle Svetlana Ivanova 《Journal of luminescence》2009,129(11):1375-1380
New near-infrared luminescent, monoclinic CaAl2O4:Er3+ phosphor was prepared by using the combustion route at furnace temperatures as low as 500 °C in a few minutes. Combustion synthesized phosphor has been well characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy-dispersive analysis of X-ray (EDAX) mapping studies. The luminescence spectra of Er3+-doped calcium aluminate were studied at UV (380 nm), vis (488 nm) and IR (980 nm) excitation. Upon UV and vis excitation, the CaAl2O4:Er3+ phosphor exhibits emission bands at ~523 nm and at ~547 nm, corresponding to transitions from the 2H11/2 and 4S3/2 erbium levels to the 4I15/2 ground state. A strong luminescence at 1.55 μm in the infrared (IR) region due to 4I13/2→4I15/2 transition has been observed in CaAl2O4:Er3+ phosphor upon 980 nm CW pumping. In the spectrum of IR-excited up-conversion luminescence, green (~523 and ~547 nm) and red (662 nm) luminescence bands were present, the latter associated with the 4F9/2→4I15/2 transitions of Er3+ ions. Both excited state absorption and energy transfer may be proposed as processes responsible for the population of the 4S3/2 and 4F9/2 erbium levels upon IR excitation. The mechanisms responsible for the up-conversion luminescence are discussed. 相似文献
44.
Vijay Singh Vineet Kumar Rai S. Watanabe T. K. Gundu?Rao Isabelle Ledoux-Rak Ho-Young Kwak 《Applied Physics A: Materials Science & Processing》2010,100(4):1123-1130
YAG phosphor powders doped/codoped with Er3+/(Er3+ + Yb3+) have been synthesised by using the solution combustion method. The effect of direct pumping into the 4I11/2 level under 980 nm excitation of doped/codoped Er3+/Yb3+−Er3+ in Y3Al5O12 (YAG) phosphor responsible for an infrared (IR) emission peaking at ∼1.53 μm corresponding to the 4I13/2→4I15/2 transition has been studied. YAG exhibits three thermally-stimulated luminescence (TSL) peaks at around 140°C, 210°C and
445°C. Electron spin resonance (ESR) studies were carried out to identify the centres responsible for the TSL peaks. The room
temperature ESR spectrum of irradiated phosphor appears to be a superposition of two distinct centres. One of the centres
(centre I) with principal g-value 2.0176 is identified as O− ion, while centre II with an isotropic g-factor 2.0020 is assigned to an F+ centre (singly ionised oxygen vacancy). An additional defect centre is observed during thermal-annealing experiments and
this centre (assigned to F+ centre) seems to originate from an F-centre (oxygen vacancy with two electrons) and these two centres appear to correlate
with the observed high-temperature TSL peak in YAG phosphor. 相似文献
45.
Sebastian Scheidel Laurina Östreicher Isabelle Mark Ann-Christin Pöppler 《Magnetic resonance in chemistry : MRC》2022,60(6):572-582
Although solid-state nuclear magnetic resonance (NMR) is a versatile analytical tool to study polymorphs and phase transitions of pharmaceutical molecules and products, this work summarizes examples of spontaneous and unexpected (and unwanted) structural rearrangements and phase transitions (amorphous-to-crystalline and crystalline-to-crystalline) under magic angle spinning (MAS) conditions, some of them clearly being due to the pressure experienced by the samples. It is widely known that such changes can often be detected by X-ray powder diffraction (XRPD); here, the capability of solid-state NMR experiments with a special focus on 1H-13C frequency-switched Lee–Goldburg heteronuclear correlation (FSLG HETCOR)/MAS NMR experiments to detect even subtle changes on a molecular level not observable by conventional 1D NMR experiments or XRPD is presented. Furthermore, it is shown that a polymorphic impurity combined with MAS can induce a crystalline-to-crystalline phase transition. This showcases that solid-state NMR is not always noninvasive and such changes upon MAS should be considered in particular when compounds are studied over longer time spans. 相似文献
46.
Base-catalyzed tandem carbon-carbon followed by nitrogen-nitrogen bond formations quantitatively converted N-alkyl-2-nitro-N-(2-oxo-2-aryl-ethyl)-benzenesulfonamides to 2H-indazoles 1-oxides under mild conditions. Triphenylphosphine or mesyl chloride/triethylamine-mediated deoxygenation afforded 2H-indazoles. 相似文献
47.
Ohkoshi S Tokoro H Hozumi T Zhang Y Hashimoto K Mathonière C Bord I Rombaut G Verelst M Cartier dit Moulin C Villain F 《Journal of the American Chemical Society》2006,128(1):270-277
This article describes the studies of a photomagnetic cyanide-bridged Cu-Mo bimetallic assembly, Cu(II)(2)[Mo(IV)(CN)(8)].8H(2)O (Cu(II), S = (1)/(2); Mo(IV), S = 0) (1), which has an intervalence transfer (IT) band from Mo(IV)-CN-Cu(II) to Mo(V)-CN-Cu(I) around 480 nm. Wide-angle X-ray scattering and X-ray spectroscopic studies provide precise information about the 3D connectivity and the local environment of the transition metal ions. Irradiating with blue light causes solid 1 to exhibit a spontaneous magnetization (Curie temperature = 25 K). The thermal reversibility is carefully studied and shows the long-time stability of the photoinduced state up to 100 K. Photoreversibility is also observed; i.e., the magnetization is induced by irradiation with light below 520 nm, while the magnetization is reduced by irradiation with light above 520 nm. The UV-vis absorption spectrum after irradiation shows a decrease of the IT band and the appearance of the reverse-IT band in the region of 600-900 nm (lambda(max) = 710 nm). This UV-vis absorption spectrum is recovered to the original spectrum by irradiation with 658-, 785-, and 840-nm light. In this photomagnetic effect, the excitation of the IT band causes an electron transfer from Mo(IV) to Cu(II), producing a ferromagnetic mixed-valence isomer of Cu(I)Cu(II)[Mo(V)(CN)(8)].8H(2)O (Cu(I), S = 0; Cu(II), S = (1)/(2); Mo(V), S = (1)/(2)) (1'). 1' returns to 1 by irradiation of the reverse-IT band, which obeys the scheme for the potential energy surface in mixed-valence class II compounds. 相似文献
48.
A comprehensive normal phase system LC-reversed phase LC (NPLC x RPLC) was evaluated for the separation of a pharmaceutical mixture and citrus oil extracts. NPLC was performed on a 25 cm x 1 mm ID x 5 microm dp diol phase. In the second dimension, an RP 18 monolithic column (10 cm L x 4.6 mm ID x 2 microm macropore size) and an octadecyl silicagel-packed column (5 cm L x 4.6 mm ID x 3.5 microm dp) were applied for the analyses of the pharmaceutical sample and the citrus oil extracts, respectively. A two-position/ten-port switching valve was used as interface. Under optimised LC conditions, the high degree of orthogonality between NP and RP resulted in peak capacities of 300 for the pharmaceutical sample and of 450 for the citrus oil extract composed of lemon and orange oil. Despite the features of NPLC x RPLC, several shortcomings related with the solvent incompatibility between the two LC modes were identified and the practical consequences were discussed. 相似文献
49.
Consola S Blanzat M Perez E Garrigues JC Bordat P Rico-Lattes I 《Chemistry (Weinheim an der Bergstrasse, Germany)》2007,13(11):3039-3047
A new kind of catanionic assembly was developed that associates a sugar-based surfactant with a non-steroidal anti-inflammatory drug (NSAID). Three different assemblies using indomethacin, ibuprofen and ketoprofen as NSAIDs were easily obtained in water by an acid-base reaction. These assemblies formed new amphiphilic entities because of electrostatic and hydrophobic effects in water and led to the spontaneous formation of vesicles. These catanionic vesicles were then tested as potential NSAID delivery systems for dermatological application. The anti-inflammatory activity was evaluated in vivo, and this study clearly showed an improved therapeutic effect for NSAIDs that were formulated as catanionic vesicles. These vesicles ensured a slower diffusion of the NSAID through the skin. This release probably increased the time of retention of the NSAID in the targeted strata of the skin. Thus, the present study suggests that this catanionic bioactive formulation could be a promising dermal delivery system for NSAIDs in the course of skin inflammation treatment. 相似文献
50.
Lisiecki I 《The journal of physical chemistry. B》2005,109(25):12231-12244
In this review, we show that chemical reduction in colloidal assemblies favors the formation of size- and shape-controlled metallic nanoparticles. The key parameters that make possible the size control of spherical nanoparticles produced in spherical reverse micelles are the degree of hydration of the reactants, the dynamic character of the micelles, the capping with the surfactant, and the reducing agent concentration. The particle shape can be controlled by combining the strategy of the surfactant-based template and the capping of salts or molecules. Proof of the quality of the samples is given by the observation of two- and three-dimensional spontaneous self-organizations. 相似文献