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991.
《国际计算机数学杂志》2012,89(5):745-758
This paper considers a 2D Ginzburg–Landau equation with a periodic initial-value condition. A fully discrete Galerkin–Fourier spectral approximation scheme, which is a linear scheme, is constructed and the dynamical behaviour of the discrete system is then analysed. First, the existence and convergence of global attractors of the discrete system are obtained by a priori estimates and the error estimates of the discrete solution without any restriction on the time step, and the convergence of the discrete scheme is then obtained. The numerical stability of the discrete scheme is proved. 相似文献
992.
《国际计算机数学杂志》2012,89(10):2188-2201
The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results. 相似文献
993.
994.
《国际计算机数学杂志》2012,89(17):3762-3779
In order to solve the large sparse systems of linear equations arising from numerical solutions of two-dimensional steady incompressible viscous flow problems in primitive variable formulation, Ran and Yuan [On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems, Appl. Math. Comput. 217 (2010), pp. 3050–3068] presented the block symmetric successive over-relaxation (BSSOR) and the modified BSSOR iteration methods based on the special structures of the coefficient matrices. In this study, we present the modified alternating direction-implicit (MADI) iteration method for solving the linear systems. Under suitable conditions, we establish convergence theorems for the MADI iteration method. In addition, the optimal parameter involved in the MADI iteration method is estimated in detail. Numerical experiments show that the MADI iteration method is a feasible and effective iterative solver. 相似文献
995.
《国际计算机数学杂志》2012,89(4):543-560
In this paper, based on the Kanzow-Kleinmichel (KK) function, we introduce a new nonlinear complementarity problem (NCP) function: penalized KK function. We show that the function possesses desirable properties similar to those of the KK function. Based on this new NCP function, we reformulate the NCP to a system of semismooth equations. We also propose a new semismooth Levenberg–Marquardt method to solve the system of semismooth equations that employs both trust region techniques and line searches. The global and quadratic convergence properties can be established under very mild assumptions. Numerical results show the effectiveness of the proposed algorithm and also indicate that superior behaviour of the proposed new NCP function. 相似文献
996.
《国际计算机数学杂志》2012,89(5):691-700
New splitting iterative methods for Toeplitz systems are proposed by means of recently developed matrix splittings based on discrete sine and cosine transforms due to Kailath and Olshevsky [Displacement structure approach to discrete-trigonometric transform-based preconditioners of G. Strang type and of T. Chan type, SIAM J. Matrix Anal. Appl. 26 (2005), pp. 706–734]. Theoretical analysis shows that new splitting iterative methods converge to the unique solution of a symmetric Toeplitz linear system. Moreover, an upper bound of the contraction factor of our new splitting iterations is derived. Numerical examples are reported to illustrate the effectiveness of new splitting iterative methods. 相似文献
997.
《国际计算机数学杂志》2012,89(9):1397-1411
In this paper an origin-shifted algorithm for matrix eigenvalues based on Frobenius-like form of matrix and the quasi-Routh array for polynomial stability is given. First, using Householder's transformations, a general matrix A is reduced to upper Hessenberg form. Secondly, with scaling strategy, the origin-shifted Hessenberg matrices are reduced to the Frobenius-like forms. Thirdly, using quasi-Routh array, the Frobenius-like matrices are determined whether they are stable. Finally, we get the approximate eigenvalues of A with the largest real-part. All the eigenvalues of A are obtained with matrix deflation. The algorithm is numerically stable. In the algorithm, we describe the errors of eigenvalues using two quantities, shifted-accuracy and satisfactory-threshold. The results of numerical tests compared with QR algorithm show that the origin-shifted algorithm is fiducial and efficient for all the eigenvalues of general matrix or for all the roots of polynomial. 相似文献
998.
《国际计算机数学杂志》2012,89(9):1413-1429
With the aid of computerized symbolic computation, we obtain new types of general solution of a first-order nonlinear ordinary differential equation with six degrees of freedom and devise a new generalized method and its algorithm, which can be used to construct more new exact solutions of general nonlinear differential equations. The (2+1)-dimensional K–D equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain non-travelling wave solutions and travelling wave solutions. 相似文献
999.
《国际计算机数学杂志》2012,89(4):840-848
A novel approach to simulate cellular neural networks (CNN) is presented in this paper. The approach, time-multiplexing simulation, is prompted by the need to simulate hardware models and test hardware implementations of CNN. For practical applications, due to hardware limitations, it is impossible to have a one-to-one mapping between the CNN hardware processors and all the pixels of the image. This simulator provides a solution by processing the input image block by block, with the number of pixels in a block being the same as the number of CNN processors in the hardware. The algorithm for implementing this simulator is presented along with popular numerical integration algorithms. Some simulation results and comparisons are also presented. 相似文献
1000.
《国际计算机数学杂志》2012,89(12):2567-2574
In this paper, the computation of dominant generalized eigenvalue problem using the new Monte Carlo method are presented. We also compare the numerical results and the CPU-time of two different methods for evaluating dominant generalized eigenvalue. The first method is the QR method. The second method is the extended Monte Carlo method which is called the resolvent Monte Carlo algorithm. Finally, using these methods the numerical results for the general symmetric dense/sparse matrices are performed. 相似文献