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151.
We prove an existence theorem of Lagrange multipliers for an abstract control problem in Banach spaces. This theorem may be applied to obtain optimality conditions for control problems governed by partial differential equations in the presence of pointwise state constraints. 相似文献
152.
Wiesł Nizioł 《Compositio Mathematica》2001,129(2):123-147
We define and study a candidate for 'arithmetic' cohomology theory with values in crystalline p-adic smooth sheaves. We show that it injects into arithmetic étale cohomology and prove a duality result. 相似文献
153.
L.Venkateswara Reddy R.N. Mukherjee 《Journal of Mathematical Analysis and Applications》1999,240(2):37
In this paper, a generalized ratio invexity concept has been applied for single objective fractional programming problems. A concept which has been invoked seems to be more general than the one used earlier by Khan and Hanson in such contexts. Further, duality results for fractional programs have also been obtained. 相似文献
154.
In this paper, we intend to establish relations between the way efficiency is measured in the literature on efficiency analysis and the notion of distance in topology. To this effect, we are interested particularly in the Hölder norm concept, providing a duality result based upon the profit function. Along this line, we prove that the Luenberger shortage function and the directional distance function of Chambers, Chung, and Färe appear as special cases of some l
p distance (also called Hölder distance), under the assumption that the production set is convex. Under a weaker assumption (convexity of the input correspondence), we derive a duality result based on the cost function, providing several examples in which the functional form of the production set is specified. 相似文献
155.
本利用次微分建立了多目标规划的一个新的对偶问题,并给出其弱、强和逆对偶性,得到了一个新的次梯度的定义,并用其建立了一个新的对偶问题。 相似文献
156.
We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained. 相似文献
157.
In this work, we implemented and compared two different methods to impose the rigid‐body motion constraint on a solid particle moving inside a fluid. We consider a fictitious domain method to easily manage the particle motion. As the solid as well as the fluid inertia are neglected, the particle can be discretized through its boundary only. The rigid‐body motion is imposed via Lagrange multipliers on the boundary. In the first method, such constraints are imposed in discrete points on the boundary (collocation), whereas in the second the constraint is imposed in a weak way on elements dividing the particle surface. Two test problems, that is, a spherical and an ellipsoidal particle in a sheared Newtonian fluid, are chosen to compare the methods. In both cases, the analysis is carried out in 2D as well as in 3D. The results show that for the collocation method an optimal number of collocation points exist leading to the smallest error. However, small variations in the optimal value can generate large deviations. In the weak implementation, the error is only mildly affected by the number of elements used to discretize the particle boundary and by the Lagrange multiplier's interpolation space. A further analysis is carried out to study the effect of an approximated integration of weak constraints. A comparison between the two methods showed that the same accuracy can be achieved by using less constraints if the weak discretization is used. Finally, the rigid‐body motion imposed via weak constraints leads to better conditioned linear systems. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
158.
159.
J. Hoffman 《国际流体数值方法杂志》2009,59(11):1241-1258
General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient cD for the flow past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate cD to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 105 mesh points, which makes the simulations possible using a standard PC. The mesh is adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is cD. Both the stopping criterion and the mesh‐refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals times derivatives of the solution of a dual problem, linearized at the approximate solution, and with data coupling to the output of interest. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
160.