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991.
In this paper we define the structural information content of graphs as their corresponding graph entropy. This definition is based on local vertex functionals obtained by calculating j-spheres via the algorithm of Dijkstra. We prove that the graph entropy and, hence, the local vertex functionals can be computed with polynomial time complexity enabling the application of our measure for large graphs. In this paper we present numerical results for the graph entropy of chemical graphs and discuss resulting properties. 相似文献
992.
Changes in the configurational entropies of molecules make important contributions to the free energies of reaction for processes such as protein-folding, noncovalent association, and conformational change. However, obtaining entropy from molecular simulations represents a long-standing computational challenge. Here, two recently introduced approaches, the nearest-neighbor (NN) method and the mutual-information expansion (MIE), are combined to furnish an efficient and accurate method of extracting the configurational entropy from a molecular simulation to a given order of correlations among the internal degrees of freedom. The resulting method takes advantage of the strengths of each approach. The NN method is entirely nonparametric (i.e., it makes no assumptions about the underlying probability distribution), its estimates are asymptotically unbiased and consistent, and it makes optimum use of a limited number of available data samples. The MIE, a systematic expansion of entropy in mutual information terms of increasing order, provides a well-characterized approximation for lowering the dimensionality of the numerical problem of calculating the entropy of a high-dimensional system. The combination of these two methods enables obtaining well-converged estimations of the configurational entropy that capture many-body correlations of higher order than is possible with the simple histogramming that was used in the MIE method originally. The combined method is tested here on two simple systems: an idealized system represented by an analytical distribution of six circular variables, where the full joint entropy and all the MIE terms are exactly known, and the R,S stereoisomer of tartaric acid, a molecule with seven internal-rotation degrees of freedom for which the full entropy of internal rotation has been already estimated by the NN method. For these two systems, all the expansion terms of the full MIE of the entropy are estimated by the NN method and, for comparison, the MIE approximations up to third order are also estimated by simple histogramming. The results indicate that the truncation of the MIE at the two-body level can be an accurate, computationally nondemanding approximation to the configurational entropy of anharmonic internal degrees of freedom. If needed, higher-order correlations can be estimated reliably by the NN method without excessive demands on the molecular-simulation sample size and computing time. 相似文献
993.
With more and more RNA secondary structures accumulated, the need for comparing different RNA secondary structures often arises in function prediction and evolutionary analysis. Numerous efficient algorithms were developed for comparing different RNA secondary structures, but challenges remain. In this article, a new statistical measure extending the notion of relative entropy based on the proposed stochastic model is evaluated for RNA secondary structures. The results obtained from several experiments on real datasets have shown the effectiveness of the proposed approach. Moreover, the time complexity of our method is favorable by comparing with that of the existing methods which solve the similar problem. 相似文献
994.
为了预测二元无机物的标准熵,基于分子图的连接矩阵和离子参数gi、qi,提出了一种新的连接性指数mQ, mG及其逆指数mQ’, mG’。 qi、gi定义为:qi=(1.1+Zi1.1) /(1.7+ni), gi=(1.4+Zi) /(0.9+ri+ri-1),其中Zi 、ni和 ri分别代表离子i的电荷数、最外层主量子数和半径。从0Q, 0Q’, 1G,和1G’,利用多元线性回归分析方法和人工神经网络方法,可以构建优良的QSPR模型。对371个二元无机物,其多元线性模型及神经网络模型的相关系数、标准偏差和平均绝对偏差分别是:0.9905, 8.29 J.K-1.mol-1, 6.48 J. K-1.mol-1, 0.9960, 5.37 J.K-1.mol-1 和 3.90 J.K-1.mol-1。留一法交叉验证表明,其多元线性模型具有良好的稳定性。两个模型对187个未进入模型的二元无机物的标准熵的预测值和实验值之间的相关系数、标准偏差和平均绝对偏差分别是:0.9897, 8.64 J. K-1.mol-1, 6.84 J. K-1.mol-1, 0.9957, 5.63 J.K-1.mol-1, 和 4.18 J.K-1.mol-1。研究表明,本文方法在预测二元无机物标准熵时比文献方法更有效,两种模型均能较精确的预测二元无机物的标准熵,且神经网络模型的预测结果更精确。 相似文献
995.
996.
We investigate the approximation rate for certain centered Gaussian fields by a general approach. Upper estimates are proved in the context of so–called Hölder operators and lower estimates follow from the eigenvalue behavior of some related self–adjoint integral operator in a suitable L 2(μ)–space. In particular, we determine the approximation rate for the Lévy fractional Brownian motion X H with Hurst parameter H∈(0,1), indexed by a self–similar set T?? N of Hausdorff dimension D. This rate turns out to be of order n ?H/D (log?n)1/2. In the case T=[0,1] N we present a concrete wavelet representation of X H leading to an approximation of X H with the optimal rate n ?H/N (log?n)1/2. 相似文献
997.
Manav Das 《Proceedings of the American Mathematical Society》2008,136(1):273-278
For a stochastic process on a finite state space, we define the notion of a packing measure based on the naturally defined cylinder sets. For any two measures , , corresponding to the same stochastic process, if then we prove that
998.
Ming-Chang Kang 《Proceedings of the American Mathematical Society》2008,136(3):809-813
Let be an arbitrary field and a finite group. We will denote by the essential dimension of over . A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained.
999.
The paper is related to the norm estimate of Mercer kernel matrices.The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on[0,1]×[0,1]based on the Bernstein-Durrmeyer operator kernel ale obtained,with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2-norm for general Mercer kernel matrices on[0,1]×[0,1]are provided. 相似文献
1000.
Matrimid/polysulfone (PSf) dual-layer hollow fiber membranes were fabricated by using co-extrusion and dry-jet wet-spinning phase-inversion techniques. The effects of the spinning dope composition, spinneret dimension, spinneret temperature and the air gap distance on the hollow fiber membranes separation performance were studied. Aging phenomenon was also studied. After coated by 3 wt% silicon solution, the hollow fiber membranes have an O2/N2 selectivity of 7.55 at 25 °C, 506.625 kPa which exceeds the intrinsic value of Matrimid. The membranes have an O2 permeance of 9.36 GPU with an apparent dense-layer thickness of 1421 Å calculated from the O2 permeability. SEM images show the high porosity underneath the dense skin. It indicates that non-solvent addition is not necessary in the inner spinning dope to induce the macroviod formation. The binodals of the Matrimid/solvent/H2O and PSf/solvent/H2O indicate that the composition of the spinning dope plays an important role in the structure and the gas separation performance of the dual-layer hollow fiber membranes. The delayed demixing of the inner spinning dope may fabricate low resistance support layers in the dual-layer hollow fiber membranes. 相似文献