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1.
We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.  相似文献   
2.
Let F ∈ C[x, y, s, t] be an irreducible constant-degree polynomial, and let A,B,C,D ? C be finite sets of size n. We show that F vanishes on at most O(n8/3) points of the Cartesian product A × B × C × D, unless F has a special group-related form. A similar statement holds for A,B,C,D of unequal sizes, with a suitably modified bound on the number of zeros. This is a four-dimensional extension of our recent improved analysis of the original Elekes–Szabó theorem in three dimensions. We give three applications: an expansion bound for three-variable real polynomials that do not have a special form, a bound on the number of coplanar quadruples on a space curve that is neither planar nor quartic, and a bound on the number of four-point circles on a plane curve that has degree at least five.  相似文献   
3.
4.
NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .  相似文献   
5.
The direct conversion of syngas to ethanol, typically using promoted Rh catalysts, is a cornerstone reaction in CO2 utilization and hydrogen storage technologies. A rational catalyst development requires a detailed structural understanding of the activated catalyst and the role of promoters in driving chemoselectivity. Herein, we report a comprehensive atomic‐scale study of metal–promoter interactions in silica‐supported Rh, Rh–Mn, and Rh–Mn–Fe catalysts by aberration‐corrected (AC) TEM. While the catalytic reaction leads to the formation of a Rh carbide phase in the Rh–Mn/SiO2 catalyst, the addition of Fe results in the formation of bimetallic Rh–Fe alloys, which further improves the selectivity and prevents the carbide formation. In all promoted catalysts, Mn is present as an oxide decorating the metal particles. Based on the atomic insight obtained, structural and electronic modifications induced by promoters are revealed and a basis for refined theoretical models is provided.  相似文献   
6.
Flow injection analysis with amperometric detection (FIA‐AD) at screen‐printed carbon electrodes (SPCEs) in optimum medium of Britton‐Robinson buffer (0.04 mol ? L?1, pH 2.0) was used for the determination of three tumor biomarkers (homovanillic acid (HVA), vanillylmandelic acid (VMA), and 5‐hydroxyindole‐3‐acetic acid (5‐HIAA)). Dependences of the peak current on the concentration of biomarkers were linear in the whole tested concentration range from 0.05 to 100 μmol ? L?1, with limits of detection (LODs) of 0.065 μmol ? L?1 for HVA, 0.053 μmol ? L?1 for VMA, and 0.033 μmol ? L?1 for 5‐HIAA (calculated from peak heights), and 0.024 μmol ? L?1 for HVA, 0.020 μmol ? L?1 for VMA, and 0.012 μmol ? L?1 for 5‐HIAA (calculated from peak areas), respectively.  相似文献   
7.
Four bis(dioxane) adducts of mixed‐metal trifluoroacetates, M[M′(O2CCF3)4(C4H8O2)2] (M = Na, K, Cs, M′ = In and M = Cs, M′ = Ga) were synthesized by reaction of alkali metal trifluoroacetate and group 13 element trifluoroacetate in 1,4‐dioxane and completely characterized including X‐ray structure determination. Geometric parameters, empirical bond valences and frequencies of the symmetric C=O stretching vibrations show that the moisture sensitive solids are composed of dimeric structural moieties with site symmetry 1 , containing alkali metal ions and bis(dioxane)tetrakis(trifluoroacetato)indate or ‐gallate ions. The dimeric units are further connected by weaker “intermolecular” dioxane interactions to neighboring alkali metal ions. Closer inspection of space group symmetry, unit cell parameters and atom sites allows to rationalize the compounds as members of two isotypic pairs that are further closely related due to the group‐subgroup relation of their monoclinc space groups to a common orthorhombic supergroup.  相似文献   
8.
A series of potentially useful lithium amidinates and guanidinates were prepared and fully characterized. Treatment of N,N′‐diisopropylcarbodiimide with phenyllithium in diethyl ether afforded the lithium amidinate [PhC(NiPr)2Li(OEt2)]2 ( 1 ). Similar treatment of N,N′‐diorganocarbodiimides R′–N=C=N–R′ [R′ = iPr, cyclohexyl (Cy)] with secondary lithium amides LiNR2 [R2 = Et2, iPr2, (CH2)4] followed by crystallization from THF or 1,4‐dioxane gave the lithium guanidinates [R2NC(NR′)2Li(S)]2 [ 2 : R = Et, R′ = iPr, S = THF; 3 : R2 = (CH2)4, R′ = iPr, S = THF; 4 : R = R′ = iPr, S = ½ 1,4‐dioxane; 5 : R2 = (CH2)4, R′ = Cy, S = 1,4‐dioxane] as crystalline solids. Reaction of N‐lithioaziridine with the corresponding carbodiimides afforded solvent‐deficient [{C2H4NC(NiPr2)2}2Li2(THF)]2 ( 6 ), and [C2H4NC(NEt)(NtBu)Li(THF)]2 ( 7 ). Crystal structure determination revealed the presence of common ladder‐type dimeric structures for 1 – 5 . Compound 6 exists as a dimer of two ladder‐type dimers in the crystal, and 7 exhibits an unusual dimeric structure comprising an eight‐membered C2N4Li2 ring.  相似文献   
9.
The use of additive correction schemes to obtain structures and vibrational frequencies of increasingly larger molecules is becoming more common. Such approaches, based on the cubic extrapolation formula applied directly to the quantity of interest, have been successfully validated only at the highest levels of computational accuracy: for coupled cluster methods with comparably large basis sets. Here, a systematic validation of geometries and vibrational frequencies is carried out, including more affordable and relevant levels of theory, such as the Møller-Plesset perturbation theory applied with smaller basis sets. Comparisons of such additive schemes against the more rigorous gradient-based extrapolation are presented. The cbs () routine of the open-source quantum-chemistry package Psi4 has been extended for this purpose. The results confirm that geometries and frequencies of covalently bound species obtained with additive correction schemes are in an excellent agreement with the results of gradient-based extrapolations. However, when applied to systems involving noncovalent interactions, the errors due to such schemes are significantly larger. In general, we propose the application of gradient-based extrapolations, as they incur no extra cost compared to additive schemes.  相似文献   
10.
Probabilistic predictions with machine learning are important in many applications. These are commonly done with Bayesian learning algorithms. However, Bayesian learning methods are computationally expensive in comparison with non-Bayesian methods. Furthermore, the data used to train these algorithms are often distributed over a large group of end devices. Federated learning can be applied in this setting in a communication-efficient and privacy-preserving manner but does not include predictive uncertainty. To represent predictive uncertainty in federated learning, our suggestion is to introduce uncertainty in the aggregation step of the algorithm by treating the set of local weights as a posterior distribution for the weights of the global model. We compare our approach to state-of-the-art Bayesian and non-Bayesian probabilistic learning algorithms. By applying proper scoring rules to evaluate the predictive distributions, we show that our approach can achieve similar performance as the benchmark would achieve in a non-distributed setting.  相似文献   
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