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851.
George B. Kleindorfer Gray A. Kochenberger Edward T. Reutzel 《Operations Research Letters》1981,1(1):31-33
Routing and scheduling problems have received considerable attention in the literature in terms of model building and algorithm development. On these fronts, progress has been substantial. However, one often neglected (yet critical) aspect concerning the use of these models and algorithms is their data requirements. In particular, the distance matrix yielding the shortest distance between each pair of sites (nodes) represents a major portion of the data required by all such problems. Yet, such data are seldom available with the degree of accuracy desired and often are not available at all.This paper describes an efficient method for obtaining this distance matrix that is based on the underlying road structure for the geographic region in question. Thus, the distances obtained reflect ‘actual’ distances. Finally, the paper presents some brief computational experience and discusses an implementation concerning the routing of environmental inspectors in the state of Pennsylvania. 相似文献
852.
To investigate the influences of time scheme, pressure treatment and initial conditions in incompressible fluid dynamics, a Stokes problem is solved numerically on a slab geometry within the framework of spectral approximation in space. Four algorithms are examined: splitting schemes, influence matrix method, penalty formulation and pseudo-spectral space-time technique. It is shown that splitting schemes are less accurate than the other processes. Furthermore, the initial field should respect a compatibility condition to avoid singularities at the initial time. If it is not possible to build such a compatible field, the numerical procedure has to present good damping properties at the first steps of the time integration. 相似文献
853.
A common approach in studying the linear complementarity problem is via the geometry of the complementary cones. In the case
of nondegeneracy, the concept of a ‘proper facet’ and a ‘reflecting facet’ have proven useful. This paper extends these concepts
to the degenerate case. Under degeneracy, a facet may turn out to be neither proper nor reflecting, but, a third type which
we designate as ‘absorbing’. Previous results in this area can be easily extended using these more general definitions. 相似文献
854.
Dynamical systems and variational inequalities 总被引:1,自引:0,他引:1
The variational inequality problem has been utilized to formulate and study a plethora of competitive equilibrium problems in different disciplines, ranging from oligopolistic market equilibrium problems to traffic network equilibrium problems. In this paper we consider for a given variational inequality a naturally related ordinary differential equation. The ordinary differential equations that arise are nonstandard because of discontinuities that appear in the dynamics. These discontinuities are due to the constraints associated with the feasible region of the variational inequality problem. The goals of the paper are two-fold. The first goal is to demonstrate that although non-standard, many of the important quantitative and qualitative properties of ordinary differential equations that hold under the standard conditions, such as Lipschitz continuity type conditions, apply here as well. This is important from the point of view of modeling, since it suggests (at least under some appropriate conditions) that these ordinary differential equations may serve as dynamical models. The second goal is to prove convergence for a class of numerical schemes designed to approximate solutions to a given variational inequality. This is done by exploiting the equivalence between the stationary points of the associated ordinary differential equation and the solutions of the variational inequality problem. It can be expected that the techniques described in this paper will be useful for more elaborate dynamical models, such as stochastic models, and that the connection between such dynamical models and the solutions to the variational inequalities will provide a deeper understanding of equilibrium problems. 相似文献
855.
于秀源 《高校应用数学学报(A辑)》1992,7(4):502-508
利用不定方程理论及中国剩余定理,我们设计了一类陷门背包公开钥密码系统,它们具有更好的安全性. 相似文献
856.
In this paper the linear relaxation of the weightedr-covering problem (r-LCP) is considered. The dual problem (c-LMP) is the linear relaxation of the well-knownc-matching problem and hence can be solved in polynomial time. However, we describe a simple, but nonpolynomial algorithm in
which ther-LCP is decomposed into a sequence of 1-LCP’s and its optimal solution is obtained by adding the optimal solutions of these
1-LCP’s. An 1-LCP can be solved in polynomial time by solving its dual as a max-flow problem on a bipartite graph. An accelerated
algorithm based on this decomposition scheme to solve ar-LCP is also developed and its average case behaviour is studied. 相似文献
857.
Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality 总被引:2,自引:0,他引:2
The multiconstraint 0–1 knapsack problem is encountered when one has to decide how to use a knapsack with multiple resource
constraints. Even though the single constraint version of this problem has received a lot of attention, the multiconstraint
knapsack problem has been seldom addressed.
This paper deals with developing an effective solution procedure for the multiconstraint knapsack problem. Various relaxation
of the problem are suggested and theoretical relations between these relaxations are pointed out. Detailed computational experiments
are carried out to compare bounds produced by these relaxations. New algorithms for obtaining surrogate bounds are developed
and tested. Rules for reducing problem size are suggested and shown to be effective through computational tests. Different
separation, branching and bounding rules are compared using an experimental branch and bound code. An efficient branch and
bound procedure is developed, tested and compared with two previously developed optimal algorithms. Solution times with the
new procedure are found to be considerably lower. This procedure can also be used as a heuristic for large problems by early
termination of the search tree. This scheme was tested and found to be very effective. 相似文献
858.
Stephen J. Grotzinger 《Mathematical Programming》1985,31(3):339-347
The construct of anL
1-Support is extended to the environment of a lower semicontinuous function over a solid, finite union of polytopes by utilizing
the convex envelope of the function. The existence of and a characterization for theL
1-Support of the convex envelope are established. The characterization is solely dependent upon the original function’s characteristics
and thus the need to calculate the functional form of the convex envelope explicity is eliminated. 相似文献
859.
The acyclic subgraph problem can be formulated as follows. Given a digraph with arc weights, find a set of arcs containing no directed cycle and having maximum total weight. We investigate this problem from a polyhedral point of view and determine several classes of facets for the associated acyclic subgraph polytope. We also show that the separation problem for the facet defining dicycle inequalities can be solved in polynomial time. This implies that the acyclic subgraph problem can be solved in polynomial time for weakly acyclic digraphs. This generalizes a result of Lucchesi for planar digraphs. 相似文献
860.
Dorota Dabrowska. 《Mathematics of Computation》2005,74(249):279-290
The paper deals with recovering band- and energy-limited signals from a finite set of perturbed inner products involving the prolate spheroidal wavefunctions. The measurement noise (bounded by ) and jitter meant as perturbation of the ends of the integration interval (bounded by ) are considered. The upper and lower bounds on the radius of information are established. We show how the error of the best algorithms depends on and . We prove that jitter causes error of order , where is a bandwidth, which is similar to the error caused by jitter in the case of recovering signals from samples.