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991.
This paper deals with the inverse problem of the calculus of variations for systems of second-order ordinary differential equations. The case of the problem which Douglas, in his classification of pairs of such equations, called the separated case is generalized to arbitrary dimension. After identifying the conditions which should specify such a case for n equations in a coordinate-free way, two proofs of its variationality are presented. The first one follows the line of approach introduced by some of the authors in previous work, and is close in spirit, though being coordinate independent, to the Riquier analysis applied by Douglas for n = 2. The second proof is more direct and leads to the discovery that belonging to the separated case has an intrinsic meaning for the given second-order differential equations: the system is separable in the sense that it can be decoupled into n pairs of first-order equations. 相似文献
992.
Given a continuous P0-function F : Rn Rn, we describe a method of constructing trajectories associated with the P0-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P0-function lead to P0-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P0-equations when the underlying function is P0. To generate the trajectories, we perturb the given P0-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem. 相似文献
993.
Dimitri P. Bertsekas 《Computational Optimization and Applications》1999,12(1-3):41-51
Given a single feasible solution
and a single infeasible solution
of a mathematical program, we provide an upper bound to the optimal dual value. We assume that
satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a point to a convex set specified by inequalities. 相似文献
994.
We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html. 相似文献
995.
Gianni Di Pillo Stefano Lucidi Laura Palagi 《Computational Optimization and Applications》1999,12(1-3):157-188
In this paper we describe a Newton-type algorithm model for solving smooth constrained optimization problems with nonlinear objective function, general linear constraints and bounded variables. The algorithm model is based on the definition of a continuously differentiable exact merit function that follows an exact penalty approach for the box constraints and an exact augmented Lagrangian approach for the general linear constraints. Under very mild assumptions and without requiring the strict complementarity assumption, the algorithm model produces a sequence of pairs
converging quadratically to a pair
where
satisfies the first order necessary conditions and
is a KKT multipliers vector associated to the linear constraints. As regards the behaviour of the sequence x
k alone, it is guaranteed that it converges at least superlinearly. At each iteration, the algorithm requires only the solution of a linear system that can be performed by means of conjugate gradient methods. Numerical experiments and comparison are reported. 相似文献
996.
Shigehiko Kuratsubo 《Proceedings of the American Mathematical Society》1999,127(10):2987-2994
We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.
997.
Mingchu Gao 《数学学报(英文版)》1999,15(4):535-548
In this paper, we first give a sufficient and necessary condition for
to generate an exponentially bounded
-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem ((ACP2) for short) in some sense. Then we use these results and those in [1] to discuss the C-(exponential) wellposedness of a kind of (ACP2) with application backgrounds, and develop the results in [2].
This project is supported by the NNSF of China, and the Youth Science and Technique Foundation of Shanxi Province, China 相似文献
998.
恒定电场边值问题中点源的处理 总被引:1,自引:0,他引:1
讨论了不同情况下恒定电场中点源函数的表达式;用两种方法对点源作不同的处理;通过一个实的求解验证和说明了本文的方法。 相似文献
999.
Poisson跳的拟线性倒向随机微分方程x(t) ∫tf(s,x(s),,x(s)) y(s)]dMs =ξ,t∈[0,1],这里M = (W,Q)T,其中W为Wiener过程,Q为补偿Poisson过程.利用区间延拓和 Bihari 不等式证明了在某种弱于Lipschitz条件下方程存在唯一适应解,并给出了解的估计,从而将文章[1]的结论推广到带 Poission 跳的情形.另外,本文还讨论了以下形式的边值问题:dx(t) = f(t,x(t),y(t))dt y(t)dMt,Ax(0) Bx(1) =ξ*,t∈[0,1],并证明了在Lipschitz条件下适应解的存在唯一性. 相似文献
1000.