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1.
We report our investigation of the dependence of the profile extracted from ARXPS data on the value of the regularization parameter α. We argue that a choice based upon the L-curve criterion, which does not require knowledge of the variances in the data, is less satisfactory than an approach based on choosing α such that χ2/N = 1. 相似文献
2.
We develop a self-adaptive algebraic tomography algorithm (SAATA) to investigate the simultaneons reconstruction of concentration and temperature distributions in larger temperature range from two views. The simplified optical arrangement with fewer projections is realized by extension of spectral information at multiple wavelengths, resulting in great potential in applications of practical combustion diagnosis. Tile results show SAATA can perform much better reconstructions in 300 3000 K temperature range than genetic simulated annealing algorithm and least-square orthogonal-triangular decomposition method with two- wavelength scheme. More phantoms are created to demonstrate the capability of SAATA to capture the peaks and adapt for both flat and sharp temperature distributions. Meanwhile, the advantage of high stability ensures better reconstruction performance at noise levels from 0.1% to 10% in projections. 相似文献
3.
The technique we propose for solving ill-conditioned linear systems consists of two steps. First we compute the regularized solution on some values of the regularization parameter . Then we use these solutions either to extrapolate at =0 or to estimate the regularized solution with determined by the generalized cross validation or by the L-curve method. 相似文献
4.
We propose a new method for the nonperturbative solution of quantum field theories and illustrate its use in the context of a light-front analog to the Greenberg–Schweber model. The method is based on light-front quantization and uses the exponential-operator technique of the many-body coupled-cluster method. The formulation produces an effective Hamiltonian eigenvalue problem in the valence Fock sector of the system of interest, combined with nonlinear integral equations to be solved for the functions that define the effective Hamiltonian. The method avoids the Fock-space truncations usually used in nonperturbative light-front Hamiltonian methods and, therefore, does not suffer from the spectator dependence, Fock-sector dependence, and uncanceled divergences caused by such truncations. 相似文献
5.
C. Brezinski 《Journal of Computational and Applied Mathematics》2012,236(8):2063-2077
For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix. In this sense, the method can be referred to as an iterative refinement process. Numerical experiments arising from integral equations and interpolation theory are presented. Finally, the method is extended to work in connection with the standard Tikhonov regularization with the right-hand side contaminated by noise. 相似文献
6.
探讨了一维对流弥散方程的时间依赖反应系数函数的反演问题及其在一个土柱渗流试验中的应用.借助一个积分恒等式,讨论了正问题单调解的存在条件及反问题的数据相容性.进一步考虑一个扰动土柱试验模型模拟问题,应用一种最佳摄动量正则化算法,对反应系数函数进行了数值反演模拟,并应用于实际试验数据的反分析,反演重建结果不仅与相容性分析一致,而且与实际观测数据基本吻合. 相似文献
7.
A mesh-independent, robust, and accurate multigrid scheme to solve a linear state-constrained
parabolic optimal control problem is presented. We first consider a Lavrentiev regularization of the
state-constrained optimization problem. Then, a multigrid scheme is designed for the numerical
solution of the regularized optimality system. Central to this scheme is the construction of an
iterative pointwise smoother which can be formulated as a local semismooth Newton iteration. Results
of numerical experiments and theoretical two-grid local Fourier analysis estimates demonstrate that
the proposed scheme is able to solve parabolic state-constrained optimality systems with textbook
multigrid efficiency. 相似文献
8.
Frank Pörner 《Optimization》2016,65(12):2195-2215
We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition and a regularity condition on the active sets. We do not assume attainability of the desired state. Furthermore, a priori regularization error estimates are obtained. 相似文献
9.
Nahid Akhtar 《Applicable analysis》2013,92(12):2105-2132
To solve the inverse gravimetric problem, i.e. to reconstruct the Earth's mass density distribution by using the gravitational potential, we introduce a spline interpolation method for the ellipsoidal Earth model, where the ellipsoid has a rotational symmetry. This problem is ill-posed in the sense of Hadamard as the solution may not exist, it is not unique and it is not stable. Since the anharmonic part (orthogonal complement) of the density function produces a zero potential, we restrict our attention only to reconstruct the harmonic part of the density function by using the gravitational potential. This spline interpolation method gives the existence and uniqueness of the unknown solution. Moreover, this method represents a regularization, i.e. every spline continuously depends on the given gravitational potential. These splines are also combined with a multiresolution concept, i.e. we get closer and closer to the unknown solution by increasing the scale and adding more and more data at each step. 相似文献
10.
Nguyen Buong 《数学学报(英文版)》2010,26(3):587-594
The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces. 相似文献