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991.
Elena Almaraz Antonio Gmez‐Corral 《Mathematical Methods in the Applied Sciences》2019,42(12):4318-4330
We study a stochastic model for the spread of two pathogen strains—termed type 1 and type 2—among a homogeneously mixing community consisting of a finite number of individuals. In the model, we assume partial cross‐immunity, exogenous streams of infection, and that the degree of severity of a newly infective individual depends on who this infective individual was infected by. The aim is to characterize the joint probability distribution of the numbers M1 and M2 of type‐1 and type‐2 infections suffered by a focal individual during an outbreak of the disease. We present iterative procedures for computing the probability mass function of (M1,M2) under the assumption that the initial state of the focal individual is known, and a numerical study of the model is performed to investigate the influence of certain key parameters on the spread of resistant bacteria in hospitals. 相似文献
992.
Boumedine Chentouf Aissa Guesmia 《Mathematical Methods in the Applied Sciences》2019,42(13):4584-4605
This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems. 相似文献
993.
Pavel ehk 《Mathematical Methods in the Applied Sciences》2019,42(18):6009-6020
We introduce a new class of the so‐called regularly varying sequences with respect to τ and state its properties. This class, on one hand, generalizes regularly varying sequences. On the other hand, it refines them and makes it possible to do a more sophisticated analysis in applications. We show a close connection with regular variation on time scales; thanks to this relation, we can use the existing theory on time scales to develop discrete regular variation with respect to τ. We reveal also a connection with generalized regularly varying functions. As an application, we study asymptotic behavior of solutions to linear difference equations; we obtain generalization and extension of known results. The theory also yields, in some way, a new view on the tests for convergence and divergence of series; we establish the statement that generalizes Raabe test and Bertrand test. 相似文献
994.
This paper firstly deals with finite time stability (FTS) of Riemann‐Liouville fractional delay differential equations via giving a series of properties of delayed matrix function of Mittag‐Leffler. We secondly study relative controllability of such type‐controlled system. With the help of the representation of solution, both Gram‐like type matrix and rank criterion are derived, which extend the corresponding results for linear systems. 相似文献
995.
《Stochastic Processes and their Applications》2019,129(6):1993-2009
A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate) time series such that all finite dimensional distributions are multivariate regularly varying. The extremal behavior of such a process can then be described by the index of regular variation and the so-called spectral tail process, which is the limiting distribution of the rescaled process, given an extreme event at time 0. As shown in Basrak and Segers (2009), the stationarity of the underlying time series implies a certain structure of the spectral tail process, informally known as the “time change formula”. In this article, we show that on the other hand, every process which satisfies this property is in fact the spectral tail process of an underlying stationary max-stable process. The spectral tail process and the corresponding max-stable process then provide two complementary views on the extremal behavior of a multivariate regularly varying stationary time series. 相似文献
996.
Quoc Thong Nguyen Kim Phuc Tran Henri L. Heuchenne Thi Hien Nguyen Huu Du Nguyen 《商业与工业应用随机模型》2019,35(5):1253-1268
In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data. 相似文献
997.
We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary rigidity problem is whether we can determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points. The lens rigidity problem problem is to determine a Riemannian metric of a Riemannian manifold with boundary by measuring for every point and direction of entrance of a geodesic the point of exit and direction of exit and its length. The linearization of these two problems is tensor tomography. The question is whether one can determine a symmetric two-tensor from its integrals along geodesics. We emphasize recent results on boundary and lens rigidity and in tensor tomography in the partial data case, with further applications. 相似文献
998.
Let X be a standard Markov process. We prove that a space inversion property of X implies the existence of a Kelvin transform of X‐harmonic, excessive and operator‐harmonic functions and that the inversion property is inherited by Doob h‐transforms. We determine new classes of processes having space inversion properties amongst transient processes satisfying the time inversion property. For these processes, some explicit inversions, which are often not the spherical ones, and excessive functions are given explicitly. We treat in details the examples of free scaled power Bessel processes, non‐colliding Bessel particles, Wishart processes, Gaussian Ensemble and Dyson Brownian Motion. 相似文献
999.
In this paper, we prove the results on existence and uniqueness of the maximal solutions for measure differential equations, considering more general conditions on functions f and g by using the correspondence between the solutions of these equations and the solutions of generalized ODEs. Moreover, we prove these results for the dynamic equations on time scales, using the correspondence between the solutions of these last equations and the solutions of the measure differential equations. 相似文献
1000.