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971.
Manuel del Pino Konstantinos T. Gkikas 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(1):187-215
We consider the parabolic Allen–Cahn equation in , , We construct an ancient radially symmetric solution with any given number k of transition layers between ?1 and +1. At main order they consist of k time-traveling copies of w with spherical interfaces distant one to each other as . These interfaces are resemble at main order copies of the shrinking sphere ancient solution to mean the flow by mean curvature of surfaces: . More precisely, if denotes the heteroclinic 1-dimensional solution of given by we have where 相似文献
972.
Many results in the theory of Gaussian processes rely on the eigenstructure of the covariance operator. However, eigenproblems are notoriously hard to solve explicitly and closed form solutions are known only in a limited number of cases. In this paper we set up a framework for the spectral analysis of the fractional type covariance operators, corresponding to an important family of processes, which includes the fractional Brownian motion and its noise. We obtain accurate asymptotic approximations for the eigenvalues and the eigenfunctions. Our results provide a key to several problems, whose solution is long known in the standard Brownian case, but was missing in the more general fractional setting. This includes computation of the exact limits of -small ball probabilities and asymptotic analysis of singularly perturbed integral equations, arising in mathematical physics and applied probability. 相似文献
973.
We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely near-monotonicity, and show that there always exists a solution to the risk-sensitive Hamilton–Jacobi–Bellman (HJB) equation, and that any minimizer in the Hamiltonian is optimal in the class of stationary Markov controls. Under the additional hypothesis that the coefficients of the diffusion are bounded, and satisfy a condition that limits (even though it still allows) transient behavior, we show that any minimizer in the Hamiltonian is optimal in the class of all admissible controls. In addition, we present a sufficient condition, under which the solution of the HJB is unique (up to a multiplicative constant), and establish the usual verification result. We also present some new results concerning the multiplicative Poisson equation for elliptic operators in . 相似文献
974.
Mitsuhiro Nakao 《Journal of Differential Equations》2018,264(1):134-162
We prove the global existence of weak solution pair to the initial boundary value problem for a system of m-Laplacian type diffusion equation and nonlinear wave equation. The interaction of two equations is given through nonlinear source terms and . 相似文献
975.
M. Daoulatli 《Journal of Differential Equations》2018,264(7):4260-4302
In this paper we study the behaviors of the energy of solutions of the wave equations with localized nonlinear damping in exterior domains. 相似文献
976.
Haibo Cui Haiyan Yin Jinshun Zhang Changjiang Zhu 《Journal of Differential Equations》2018,264(7):4564-4602
In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. . Our proof is based on the classical energy method. 相似文献
977.
Levenberg-Marquardt method with a general LM parameter and a nonmonotone trust region technique 下载免费PDF全文
We propose a new Levenberg-Marquardt (LM) method for solving the nonlinear equations. The new LM method takes a general LM parameter \lambda_k=\mu_k[(1-\theta)\|F_k\|^\delta+\theta\|J_k^TF_k\|^\delta] where \theta\in[0,1] and \delta\in(0,3) and adopts a nonmonotone trust region technique to ensure the global convergence.
Under the local error bound condition, we prove that the new LM method has at least superlinear convergence rate with the order \min\{1+\delta,4-\delta,2\}.
We also apply the new LM method to solve the nonlinear equations arising from the weighted linear complementarity problem. Numerical experiments indicate that the new LM method is efficient and promising. 相似文献
978.
Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications. 相似文献
979.
《Stochastic Processes and their Applications》2020,130(2):806-823
The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties, such as continuity and various bounds of the value function, are established. However, structural properties of the optimal stopping region are shown to crucially depend on the prior, and we provide a general condition for a one-sided stopping region. Moreover, a detailed analysis is conducted in the cases of the two-point and the mixed Gaussian priors, revealing a rich structure present in the problem. 相似文献
980.
Yongyong Cai & Yan Wang 《数学研究》2020,53(2):125-142
We consider the nonlinear Dirac equation (NLD) with time dependent external electro-magnetic potentials, involving a dimensionless parameter $ε\in(0,1]$ which is inversely proportional to the speed of light. In the nonrelativistic limit regime $ε\ll1$ (speed of light tends to infinity), we decompose the solution into the eigenspaces associated with the 'free Dirac operator' and construct an approximation to the NLD with $O(ε^2)$ error. The NLD converges (with a phase factor) to a coupled nonlinear Schrödinger system (NLS) with external electric potential in the nonrelativistic limit as $ε\to0^+$, and the error of the NLS approximation is first order $O(ε)$. The constructed $O(ε^2)$ approximation is well-suited for numerical purposes. 相似文献