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71.
李师正 《应用数学学报(英文版)》2000,16(4):362-365
1. IntroductionLet X be the n-dimensional Euclidean space Rad. Denote the transpose of the columnvector y by yT. Suppose that R7 and nit R= are the n-dimensional vector sets with nonnegative and positive components, whose elements are denoted by y 3 0 and y > 0, respectively.Write R for the nonnegative real number set.Consider a nondiffereatiable convex programming problem:We assume that f(x), gi(x),..', g.(x) are finite reaLvalued continuous, convex functions on X, but not necessarily d… 相似文献
72.
73.
Martin Gugat 《Mathematical Programming》1999,85(3):643-653
The growth of the multipliers, when the parameter approaches such a critical parameter, is characterized by a parametric constraint
qualification which is introduced here. It is equivalent to a bound on the growth of the multipliers.
Received May 8, 1995 / Revised version received February 12, 1998
Published online February 25, 1999 相似文献
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We optimise a distribution of two isotropic materials α
I and β
I (α < β) occupying the given body in R
d
. The optimality is described by an integral functional (cost) depending on temperatures u
1, . . . , u
m
of the body obtained for different source terms f
1, . . . ,f
m
with homogeneous Dirichlet boundary conditions. The relaxation of this optimal design problem with multiple state equations
is needed, introducing the notion of composite materials as fine mixtures of different phases, mathematically described by
the homogenisation theory. The necessary conditions of optimality are derived via the Gateaux derivative of the cost functional.
Unfortunately, there could exist points in which necessary conditions of optimality do not give any information on the optimal
design. In the case m < d we show that there exists an optimal design which is a rank-m sequential laminate with matrix material α
I almost everywhere on Ω. Contrary to the optimality criteria method, which is commonly used for the numerical solution of optimal design problems
(although it does not rely on a firm theory of convergence), this result enables us to effectively use classical gradient
methods for minimising the cost functional.
相似文献
77.
78.
In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising. 相似文献
79.
In the design of a system, the comparison of possible solutions using simulation is generally performed with fixed environmental conditions. In practice, however, unexpected changes can occur for example in the part mix of a manufacturing facility or in the customer demand. Such changes, which are considered as modifications in environmental factors, can impact the system response. As a consequence, a solution A that is better than B for a given environment, can yield poorer performance than B for another environment. Therefore, we are interested in robust simulation studies, which aim at taking into account several possible environments. In methods based on Taguchi’s principles, no distinction is made between these environments in the robustness computation. In the suggested heuristic approach, we focus on problems where a particular environment is expected when the system will be in operation (the others being unexpected environments). This particular environment will be considered in the study as a “base environmental scenario”. The robustness of a solution of the design problem is computed as an approximate measure of what will be saved or lost if the environment becomes the unexpected. Reference curves are suggested to allow these solutions to be empirically compared in accordance with the decision-maker’s requirements. A simplified example is provided. The results are different from those obtained using a signal to noise ratio, which is typically used in Taguchian approaches. 相似文献
80.