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991.
Sonia Mazzucchi Valter Moretti Ivan Remizov Oleg Smolyanov 《Mathematische Nachrichten》2023,296(3):1244-1284
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks. 相似文献
992.
《Journal of Functional Analysis》2023,284(1):109722
Motivated by the probabilistic methods for nonlinear differential equations introduced by McKean (1975) for the Kolmogorov-Petrovski-Piskunov (KPP) equation, and by Le Jan and Sznitman (1997) for the incompressible Navier-Stokes equations (NSE), we identify a new class of stochastic cascade models, referred to as doubly stochastic Yule cascades. We establish non-explosion criteria under the assumption that the randomization of Yule intensities from generation to generation is by an ergodic time-reversible Markov process. In addition to the cascade models that arise in the analysis of certain deterministic nonlinear differential equations, this model includes the multiplicative branching random walks, the branching Markov processes, and the stochastic generalizations of the percolation and/or cell ageing models introduced by Aldous and Shields (1988) and independently by Athreya (1985). 相似文献
993.
994.
Feliks Nüske Pter Koltai Lorenzo Boninsegna Cecilia Clementi 《Entropy (Basel, Switzerland)》2021,23(2)
The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting. 相似文献
995.
We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations. 相似文献
996.
997.
在数据驱动的建模中,通过测量或模拟得到时空数据,我们发现基于拉普拉斯先验的贝叶斯稀疏识别方法能有效地恢复时变偏微分方程的稀疏系数。本文将贝叶斯稀疏识别方法运用于各种时变偏微分方程模型(KdV方程、Burgers方程、Kuramoto-Sivashinsky方程、反应-扩散方程、非线性薛定谔方程和纳维-斯托克斯方程)的方程系数恢复,将贝叶斯稀疏恢复结果与PDE-FIND稀疏恢复算法进行比较,证实贝叶斯稀疏识别方法对偏微分方程具有非常强的稀疏恢复能力。同时,研究中发现贝叶斯稀疏方法对噪声更敏感,可以识别更多的附加项。此外,贝叶斯方法可以直接得到稀疏恢复解的误差方差,由此可以直接判定稀疏恢复的效果和可靠性。 相似文献
998.
999.
1000.
《Molecular physics》2012,110(19-20):2349-2357
The molecule [1.1.1]propellane and its neutral boron, nitrogen, oxygen, sulphur, S–O, and SO2 analogs as well as the methyl, hexafluoro, and tri-carbonyl substituted derivatives have been investigated by theoretical calculations at the coupled-cluster singles and doubles level with an augmented polarized double zeta basis set. The geometries were optimized and vibrational analysis was carried out for each species. The main objective of this study was to determine the relative strain in these systems, which in turn is a predictor of stability and reactivity providing valuable information about potentially viable synthetic targets. The systems with the least strain are the nitrogen, boron and the S–O analogs, whereas the SO2 substituted molecule and the hexafluoride and tricarbonyl substituted analogs exhibited the largest amount of strain. Geometrical features are also investigated and it is demonstrated that non-bonded repulsive interactions contribute significantly to the strain in some of the systems since cage-like structures force relatively short non-bonded distances. 相似文献