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This paper concentrates on considering the down/up crossing property of weighted Markov collision processes. The joint probability generating function of down crossing and up crossing numbers of weighted Markov collision processes until its extinction are obtained by constructing and studying a related multi-dimensional Markov chain. Hence, the joint probability distribution of down crossing and up crossing numbers and the mean numbers are obtained. 相似文献
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The existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping. 相似文献
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《Stochastic Processes and their Applications》2019,129(9):3319-3359
For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a deterministic limit and a central limit theorem around it have already been proven in Kang and Kurtz (2013) and Kang et al. (2014). We present here a general approach to proving a large deviation principle in path space for such multi-scale Markov processes. Motivated by models arising in systems biology, we apply these large deviation results to general chemical reaction systems which exhibit multiple time-scales, and provide explicit calculations for several relevant examples. 相似文献
6.
《Stochastic Processes and their Applications》2019,129(12):5278-5311
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly overdamped) Langevin diffusion and establish guarantees on its error measured in the Wasserstein-2 distance. Our guarantees improve or extend the state-of-the-art results in three directions. First, we provide an upper bound on the error of the first-order Langevin Monte Carlo (LMC) algorithm with optimized varying step-size. This result has the advantage of being horizon free (we do not need to know in advance the target precision) and to improve by a logarithmic factor the corresponding result for the constant step-size. Second, we study the case where accurate evaluations of the gradient of the log-density are unavailable, but one can have access to approximations of the aforementioned gradient. In such a situation, we consider both deterministic and stochastic approximations of the gradient and provide an upper bound on the sampling error of the first-order LMC that quantifies the impact of the gradient evaluation inaccuracies. Third, we establish upper bounds for two versions of the second-order LMC, which leverage the Hessian of the log-density. We provide non asymptotic guarantees on the sampling error of these second-order LMCs. These guarantees reveal that the second-order LMC algorithms improve on the first-order LMC in ill-conditioned settings. 相似文献
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Randomize-then-optimize (RTO) is widely used for sampling from posterior distribu-tions in Bayesian inverse problems.However,RTO can be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient.In this work,we present a novel goal-oriented deep neural networks (DNN) sur-rogate approach to substantially reduce the computation burden of RTO.In particular,we propose to drawn the training points for the DNN-surrogate from a local approximated posterior distribution-yielding a flexible and efficient sampling algorithm that converges to the direct RTO approach.We present a Bayesian inverse problem governed by elliptic PDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO ap-proach,which shows that DNN-RTO can significantly outperform the traditional RTO. 相似文献
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We investigate Hoeffding's inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and the explicit upper bounds in the inequalities are obtained via the solution of Poisson's equation. The results are further illustrated with applications to queueing theory and reective diffusion processes. 相似文献
9.
Stephen Fox 《Entropy (Basel, Switzerland)》2021,23(2)
Active inference is a physics of life process theory of perception, action and learning that is applicable to natural and artificial agents. In this paper, active inference theory is related to different types of practice in social organization. Here, the term social organization is used to clarify that this paper does not encompass organization in biological systems. Rather, the paper addresses active inference in social organization that utilizes industrial engineering, quality management, and artificial intelligence alongside human intelligence. Social organization referred to in this paper can be in private companies, public institutions, other for-profit or not-for-profit organizations, and any combination of them. The relevance of active inference theory is explained in terms of variational free energy, prediction errors, generative models, and Markov blankets. Active inference theory is most relevant to the social organization of work that is highly repetitive. By contrast, there are more challenges involved in applying active inference theory for social organization of less repetitive endeavors such as one-of-a-kind projects. These challenges need to be addressed in order for active inference to provide a unifying framework for different types of social organization employing human and artificial intelligence. 相似文献
10.
重金属污染农作物后可通过食物链进入人体从而严重危害身体健康。如何快速准确地监测农作物中重金属含量已成为当今生态与粮食安全等领域的重要研究内容。常规的生化监测方法存在操作繁琐、过程长、具有破坏性等缺点,而高光谱遥感具有光谱分辨率高、信息量大、生化反演能力强、方便快捷、对监测对象无损伤等优势,因此利用高光谱遥感技术监测农作物中重金属含量已成为遥感领域的热点研究之一。以不同浓度Pb(NO3)2溶液胁迫下盆栽玉米植株为研究对象,基于不同铅离子(Pb2+)胁迫梯度下玉米叶片的反射光谱及其中Pb2+含量的测定数据,结合奇异值分解(SVD)理论和自适应模糊神经网络推理系统(ANFIS)结构,建立了一种Pb2+含量预测的SVD-ANFIS模型。首先对各胁迫梯度下玉米的老叶(O)、中叶(M)、新叶(N)三种叶片的反射光谱数据进行SVD处理,获取原始光谱信息的奇异值;然后选择O,M和N叶片对应的奇异值来寻求ANFIS结构的最佳输入组合,最终选定O-M(双输入)组合作为ANFIS结构的输入量,通过训练和学习获得最优模糊规则库后,ANFIS结构的输出量即为叶片中Pb2+含量,从而实现了SVD-ANFIS模型的预测性能。研究结果表明,该模型的输出误差值较小,精度较高,在模糊训练过程中隶属函数选为钟型函数时预测效果最佳。利用多参数的反向传播(BP)神经网络预测模型对SVD-ANFIS模型的预测优越性进行验证时,得到BP模型和SVD-ANFIS模型的决定系数(R2)分别为0.977 6和0.988 7,均方根误差(RMSE)分别为2.455 9和0.601 3,可见SVD-ANFIS模型的拟合度更高,预测效果更好。同时选取不同年份的Pb污染玉米叶片等光谱数据对SVD-ANFIS模型进行可行性检验,其R2和RMSE分别为0.986 4和0.887 4,说明SVD-ANFIS模型能较好的用于玉米叶片中Pb2+含量预测且具有较高的鲁棒性,可作为预测玉米叶片中重金属含量的一种方法。 相似文献