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981.
Avy?Soffer Jianguo?XiaoEmail authorView authors OrcID profile 《Mathematical Physics, Analysis and Geometry》2016,19(4):22
We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is the repulsiveness or nontrapping conditions on the flow corresponding to the wave equation. Thus this method is limited to potential perturbations which are repulsive, that is the radial derivative pointing away from the origin. In this work, we generalize this method to include potentials which are repulsive relative to a line in space (in three or higher dimensions), among other cases. This method is based on constructing multi-centered vector fields as multipliers, cancellation lemmas and energy localization. 相似文献
982.
983.
Yahya A Gino Fallone B 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2007,188(1):111-121
A proton spectral editing pulse sequence for the detection of metabolites with spin systems that involve weak coupling is presented. The sequence is based on homonuclear polarization transfer incorporated into the standard PRESS (Point RESolved Spectroscopy) sequence, which is a volume-selective double spin echo method, to enable spatial localization. All peaks in the region of interest are initially suppressed whether they are peaks from the target metabolite or from contaminating background. The target signal is then restored by polarization transfer from a proton that has a resonance outside the suppressed region and to which the target spins are weakly coupled. This is achieved by the application of a 90 degrees hard pulse with phase orthogonal to that of the PRESS excitation pulse at the location of the first echo in PRESS and by optimizing the two PRESS timings, TE(1) and TE(2), for most efficient yield. Background signal not coupled to any protons outside the initially saturated region remains suppressed. The advantage of this sequence compared to multiple quantum filters is that signal from singlet peaks outside the suppressed area are preserved and can thus be used as a reference. The efficacy of the sequence was verified experimentally on phantom solutions of lactate and glutathione at 3.0 T. For the AX(3) spin system of lactate, the sequence timings were optimized by product operator calculations whereas for the ABX spin system of the cysteinyl group of glutathione numerical calculations were performed for sequence timing optimization. 相似文献
984.
Yuanyuan?Zhu Rongjuan?Wang Li?Wang Yong?LiuEmail author Rui?XiongEmail author Jing?Shi 《Applied magnetic resonance》2015,46(5):505-513
We report the electron paramagnetic resonance (EPR) studies of MgTi2O4 in the 300–140 K range. Above the transition temperature T t (~258 K), the EPR results indicate that MgTi2O4 is paramagnetic. The parameters of the EPR spectra show an anomalous change at T t. The clear EPR lines can be observed in temperature between T t and 220 K. Besides that the EPR intensity, g value, and EPR linewidth increase with decreasing temperature; in temperature range below 220 K, no clear EPR line can be detected. The EPR spectra results demonstrate that magnetic spin-singlet state and the orbital density wave of MgTi2O4 system are formed gradually with decreasing temperature at low temperature range. 相似文献
985.
Camilla?Terenzi Cinzia?CasieriEmail author Francesco?De?Luca Raimondo?Quaresima Giovanni?Quarta Valentina?Tudisca 《Applied magnetic resonance》2015,46(10):1159-1178
This study deals with the application of two-dimensional proton nuclear magnetic resonance relaxometry (2D 1H NMR-R) to the characterization of porous ceramics nearly free of magnetic compounds. Different microstructural properties were obtained by firing a diamagnetic mixture of kaolin, calcium, and magnesium carbonate over a wide range of maximum temperatures (600–1100 °C) and firing times at the maximum temperature (soaking times) (0–10 h). The 2D 1H NMR-R method relies on the correlated measurement of 1H longitudinal (T 1) and transverse (T 2) relaxation times of pore-filling water by which the properties of the interconnected pore space may be investigated. In the absence of significant magnetic susceptibility effect due to para- and ferro-magnetic compounds, the 2D 1H NMR-R maps allow studying the conjoint effects on pore size distribution and inter-pore coupling due to the variations in both time and temperature of firing. The NMR experiments were performed with a low-field 1H NMR sensor, which allows non-destructive and in situ analysis. For ceramic specimens fired at 600 and 700 °C, the fraction of smallest pores increases with firing time at the expenses of those with intermediate size. The pore shrinkage occurring at this stage, and likely associated with the transformation of kaolinite in metakaolinite, is affected in a similar way by soaking time and firing temperature, in line with the concept of equivalent firing temperature. At temperatures from 800 to 1100 °C, the structural modifications involving interconnectivity and average pore size are driven primarily by firing temperature and, secondarily, by soaking time. The 2D 1H NMR-R results are confirmed by more traditional, but destructive, mineralogical, and structural analyses like X-ray powder diffraction, helium pycnometry, mercury intrusion porosimetry, and nitrogen adsorption/desorption method. 相似文献
986.
Saipeng?Huang Zhao?Chen Libo?Du Qiu?Tian Yangping?Liu Yuansuo?Zheng Yang?LiuEmail author 《Applied magnetic resonance》2015,46(5):489-504
The detection of free radicals and related species has attracted considerable attention in recent years due to their critical roles in physiological and pathological processes. Among the various methods for the detection of free radicals, electron spin resonance coupled with spin-trapping technique has been an effective approach for the characterization and quantification of free radicals due to its high specificity. In this study, we designed and synthesized a novel amphiphilic spin trap, 2-(diethoxyphosphoryl)-2-heptadecanyl-3,4-dihydro-2H-pyrrole-1-oxide (DEPHdPO), from 5-(diethoxyphosphoryl)-5-methyl-1-pyrroline-N-oxide with a long hydrocarbon chain at the C-5 position of the pyrroline ring, providing the amphiphilic character. The free-radical-trapping ability of DEPHdPO was evaluated by capturing hydroxyl radicals (·OH), superoxide anions (\( {\text{O}}_{2}^{ \cdot - } \)), and carbon-centered free radicals in a model membrane prepared from sodium dodecyl sulfate (SDS). The results indicate that the hydrophobic hydrocarbon chain of DEPHdPO can be inserted into the inner core of SDS micelles, and the hydrophilic nitronyl functional moiety is located on the surface layer. Thus, various free radicals, including ·OH radicals, \( {\text{O}}_{2}^{ \cdot - } \) anions, and carbon-centered radicals could be site-specifically detected near the membrane surface. Moreover, DEPHdPO could be successfully located on the surface of thylakoid membranes, and the nearby photo-initiated \( {\text{O}}_{2}^{ \cdot - } \) anions could be trapped site-specifically. 相似文献
987.
We discuss the discrete p-Laplacian eigenvalue problem, where T > 1 is a given positive integer and φ p (x):= |x| p?2 x, p > 1. First, the existence of an unbounded continuum C of positive solutions emanating from (λ, u) = (0, 0) is shown under suitable conditions on the nonlinearity. Then, under an additional condition, it is shown that the positive solution is unique for any λ > 0 and all solutions are ordered. Thus the continuum C is a monotone continuous curve globally defined for all λ > 0.
相似文献
$$\left\{ \begin{gathered} \Delta (\phi _p (\Delta u(k - 1))) + \lambda a(k)g(u(k)) = 0,k \in \{ 1,2,...,T\} , \hfill \\ u(0) = u(T + 1) = 0, \hfill \\ \end{gathered} \right.$$
988.
The numerical approximation of one-dimensional relativistic Dirac wave equations is considered within the recent framework consisting in deriving local scattering matrices at each interface of the uniform Cartesian computational grid. For a Courant number equal to unity, it is rigorously shown that such a discretization preserves exactly the \(L^2\) norm despite being explicit in time. This construction is well-suited for particles for which the reference velocity is of the order of \(c\), the speed of light. Moreover, when \(c\) diverges, that is to say, for slow particles (the characteristic scale of the motion is non-relativistic), Dirac equations are naturally written so as to let a “diffusive limit” emerge numerically, like for discrete 2-velocity kinetic models. It is shown that an asymptotic-preserving scheme can be deduced from the aforementioned well-balanced one, with the following properties: it yields unconditionally a classical Schrödinger equation for free particles, but it handles the more intricate case with an external potential only conditionally (the grid should be such that \(c \Delta x\rightarrow 0\)). Such a stringent restriction on the computational grid can be circumvented easily in order to derive a seemingly original Schrödinger scheme still containing tiny relativistic features. Numerical tests (on both linear and nonlinear equations) are displayed. 相似文献
989.
Our purpose is to provide an affirmative answer to Moszner’s problem [cf. Moszner (Ann Univ Paed Crac Stud Math XI:69–94, 2012), p. 93] concerning the superstability of the Cauchy equation with squaresin the class of functions mapping an Abelian semigroup into a finite-dimensional normed algebra without divisors of zero.
相似文献
$$f(x + y)^2 = (f(x) + f(y))^2$$
990.
Given a sequence A = (a 1, …, a n ) of real numbers, a block B of A is either a set B = {a i , a i+1, …, a j } where i ≤ j or the empty set. The size b of a block B is the sum of its elements. We show that when each a i ∈ [0, 1] and k is a positive integer, there is a partition of A into k blocks B 1, …, B k with |b i ?b j | ≤ 1 for every i, j. We extend this result in several directions. 相似文献