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71.
J. I. Ramos 《国际流体数值方法杂志》1991,12(9):881-894
Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies. 相似文献
72.
In this paper we outline a new particle-mesh method for rapidly rotating shallow water flows based on a set of regularized equations of motion. The time-stepping method uses an operator splitting of the equations into an Eulerian gravity wave part and a Lagrangian advection part. An essential ingredient is the advection of absolute vorticity by means of translated radial basis functions. We show that this implies exact conservation of enstrophy. The method is tested on two model problems based on the qualitative features of the solutions obtained (i.e., dispersion or smoothness of potential vorticity contours) as well as on the increase in mean divergence level. 相似文献
73.
In contrast to stochastic differential equation models used for the calculation of the term structure of interest rates, we
develop an approach based on linear dynamical systems under non-stochastic uncertainty with perturbations. The uncertainty
is described in terms of known feasible sets of varying parameters. Observations are used in order to estimate these parameters
by minimizing the maximum of the absolute value of measurement errors, which leads to a linear or nonlinear semi-infinite
programming problem. A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems
is suggested. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the
framework of an interior point approach. A special deleting rule permits one to use only a part of the constraints of the
discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convexC
1-functions are studied. On the basis of the solutions of the semi-infinite programming problems a technical trading system
for future contracts of the German DAX is suggested and developed.
Supported by the Stiftung Rheinland/Pfalz für Innovation, No. 8312-386261/307. 相似文献
74.
Willem Hundsdorfer. 《Mathematics of Computation》1998,67(221):183-190
In this note some stability results are derived for the Douglas splitting method. The relevance of the theoretical results is tested for an advection-reaction equation.
75.
Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having
the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered
for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
76.
Liqun Qi 《Operations Research Letters》1997,20(5):223-228
We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent. 相似文献
77.
We use boundary value methods to compute consistent initial values for fully implicit nonlinear differential-algebraic equations.
The obtained algorithm uses variable order formulae and a deferred correction technique to evaluate the error. A rigorous
theory is stated for nonlinear index 1, 2 and 3 DAEs of Hessenberg form. Numerical tests on classical index 1, 2 and 3 DAE
problems are reported.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
78.
Inexact Newton methods for the nonlinear complementarity problem 总被引:2,自引:0,他引:2
Jong-Shi Pang 《Mathematical Programming》1986,36(1):54-71
An exact Newton method for solving a nonlinear complementarity problem consists of solving a sequence of linear complementarity
subproblems. For problems of large size, solving the subproblems exactly can be very expensive. In this paper we study inexact
Newton methods for solving the nonlinear, complementarity problem. In such an inexact method, the subproblems are solved only
up to a certain degree of accuracy. The necessary accuracies that are needed to preserve the nice features of the exact Newton
method are established and analyzed. We also discuss some extensions as well as an application.
This research was based on work supported by the National Science Foundation under grant ECS-8407240. 相似文献
79.
We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177-182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579-584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155-158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141-159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement. 相似文献
80.
The paper deals with the global minimization of a differentiable cost function mapping a ball of a finite dimensional Euclidean space into an interval of real numbers. It is established that a suitable random perturbation of the gradient method with a fixed parameter generates a bounded minimizing sequence and leads to a global minimum: the perturbation avoids convergence to local minima. The stated results suggest an algorithm for the numerical approximation of global minima: experiments are performed for the problem of fitting a sum of exponentials to discrete data and to a nonlinear system involving about 5000 variables. The effect of the random perturbation is examined by comparison with the purely deterministic gradient method. 相似文献