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1.
Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems. 相似文献
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多孔液体(Porous Liquids, PLs)是一类结合了多孔固体永久性孔隙与液态流动性优势的新材料. 自2007年, PLs的概念被首次提出以来, 其在合成策略与应用领域方面均取得了较大的突破. 然而, 传统的PLs因高黏度、高密度、高熔点与高原材料成本等缺陷极大程度制约了其在流动工业系统中的大规模应用. 因此, 迫切需要寻求理想的位阻溶剂用于制备先进的多孔液体. 离子液体(Ionic Liquids, ILs)因独特的可调节物理特性、非挥发性、高稳定性、易获得、经济性高、低再生能耗等特性, 使其成为构筑PLs中最具有应用前景的理想溶剂之一. 在过去的5年间, 基于多种ILs与先进多孔固体(如有机笼、金属有机框架、中空碳、沸石、多孔聚合物等)制备的多孔离子液体(Porous Ionic Liquids, PILs)被陆续报道. PILs独特的永久性孔隙、无溶剂挥发、再生能力强、黏度可调、低熔点、高稳定性等特性加快了其在气体吸附、分离、催化、萃取、分子分离等领域的快速发展. 本综述围绕PILs的构筑策略、特性、应用领域等阐述了其研究进展. 最后, 对PILs在制备中存在的挑战与未来的研究方向进行了归纳与展望. 相似文献
5.
Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of reaction–diffusion–convection equations coupled with ordinary differential equations, which models a combustion front moving through a porous medium with parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function. 相似文献
6.
Aiming at training the feed-forward threshold neural network consisting of nondifferentiable activation functions, the approach of noise injection forms a stochastic resonance based threshold network that can be optimized by various gradient-based optimizers. The introduction of injected noise extends the noise level into the parameter space of the designed threshold network, but leads to a highly non-convex optimization landscape of the loss function. Thus, the hyperparameter on-line learning procedure with respective to network weights and noise levels becomes of challenge. It is shown that the Adam optimizer, as an adaptive variant of stochastic gradient descent, manifests its superior learning ability in training the stochastic resonance based threshold network effectively. Experimental results demonstrate the significant improvement of performance of the designed threshold network trained by the Adam optimizer for function approximation and image classification. 相似文献
7.
Masaaki Kijima 《商业与工业应用随机模型》2021,37(1):17-20
In this note, some point of views on virtual ages are presented in terms of the discussion paper written by Finkelstein and Cha, which include generalized stochastic order‐based virtual ages, system‐level virtual ages, virtual ages in Weibull distribution and repair degrees with virtual ages. Finally, some possible future researches on virtual ages are described. 相似文献
8.
Tatsuya Iioka Satoshi Takahashi Yuichiro Yoshida Yoshihiro Matsumura Shuichi Hiraoka Hirofumi Sato 《Journal of computational chemistry》2019,40(1):279-285
The kinetics on a basic ligand substitution reaction on dinuclear platinum complexes [Pt(PEt3)2PhPt(PEt3)2]2+ and [Pt(PEt3)2PhCOPhPt(PEt3)2]2+ , with the ligands pyridine and 3-chloropyridine, is studied. This is a fundamental step in a self-assembly, and the time evolution has been observed with a new experimental technique, QASAP (quantitative analysis of self-assembly process), which is recently developed by Hiraoka's group. As a result of numerical calculations based on master equation, we succeed in specifying the reaction rate constants with a simple reaction model. In addition, the time evolutions of all the intermediate components produced and consumed in chemical reaction are revealed, including those unobserved in the experiments. The convergence behavior of the existence ratios of specific chemical species calculated with the stochastic algorithm method is compared with those obtained from deterministic formalism based on rate equations, revealing a clear dependence on the number of constituent molecules. © 2018 Wiley Periodicals, Inc. 相似文献
9.
Eugene O. Kamenetskii 《Annalen der Physik》2020,532(3):1900423
The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the electromagnetic (EM) field in a magnetoelectric (ME) medium is not a trivial problem. The question of whether electromagnetism and magnetoelectricity can coexist without an extension of Maxwell's theory arises when the effects of EM energy propagation are studied and the group velocity of the waves in an ME medium is considered. The energy balance equation reveals unusual topological structure of fields in ME materials. Together with certain constraints on the constitutive parameters of a medium, definite constraints on the local field structure should be imposed. Analyzing the EM phenomena inside an ME material, the question “what kind of the near fields arising from a sample of such a material can be measured?” should be answered. The visualization of the ME states requires an experimental technique that is based on an effective coupling to the violation of spatial as well as temporal inversion symmetry. To observe the ME energy in a subwavelength region, it is necessary to assume the existence of first-principle near fields—the ME fields. These are non-Maxwellian near fields with specific properties of violation of spatial and temporal inversion symmetry. A particular interest to the ME fields arises in studies of metamaterials with “artificial-atoms” ME elements. 相似文献
10.
《Stochastic Processes and their Applications》2020,130(6):3753-3801
We analyse convergence of a micro–macro acceleration method for the simulation of stochastic differential equations with time-scale separation. The method alternates short bursts of path simulations with the extrapolation of macroscopic state variables forward in time. After extrapolation, a new microscopic state is constructed, consistent with the extrapolated macroscopic state, that minimises the perturbation caused by the extrapolation in a relative entropy sense. We study local errors and numerical stability of the method to prove its convergence to the full microscopic dynamics when the extrapolation time step tends to zero and the number of macroscopic state variables tends to infinity. 相似文献