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81.
After investigating all conceivable properties of decidable objects and maps in left exact categories with well-behaved finite sums (‘lextensive categories’), we give a characterization in such categories of decidable morphisms which are (finite) coverings (in an appropriate sense). Finally, we give two applications of this result, to separable algebras and to local homeomorphisms. In both cases it explains categorically the advantage of two well-known notions — strongly separable algebras and local homeomorphisms with path lifting property, respectively. 相似文献
82.
非光滑半无限多目标规划弱非控解的充分性 总被引:4,自引:0,他引:4
张庆祥 《高校应用数学学报(A辑)》1996,(4):461-466
本文利用锥次微分的概念,在一点处定义了η-(A,N)凸函数、η-(A,N)伪凸函数和η-(A,N)严格伪凸函数,在相当弱的假设下,在η-(A,N)意义下,给出了非光滑η-(A,N)凸半无限多目标规划弱非控解的一些充分条件。 相似文献
83.
Robert Fourer 《Mathematical Programming》1983,25(3):251-292
This and a companion paper consider how current implementations of the simplex method may be adapted to better solve linear
programs that have a staged, or ‘staircase’, structure. The preceding paper considered ‘inversion’ routines that factorize
the basis and solve linear systems. The present paper examines ‘pricing’ routines that compute reduced costs for nonbasic
variables and that select a variable to enter the basis at each iteration. Both papers describe extensive (although preliminary)
computer experiments, and can point to some quite promising results. For pricing in particular, staircase computation strategies
appear to offer modest but consistent savings; staircase selection strategies, properly chosen, may offer substantial savings
in number of iterations, time per iteration, or both. 相似文献
84.
J. E. Spingarn 《Mathematical Programming》1982,22(1):82-92
Optimality conditions for families of nonlinear programming problems inR
n
are studied from a generic point of view. The objective function and some of the constraints are assumed to depend on a parameter, while others are held fixed. Techniques of differential topology are used to show that under suitable conditions, certain strong second-order conditions are necessary for optimality except possibly for parameter values lying in a negligible set.Research sponsored, in part, by the Air Force Office of Scientific Research, under grants number 77-3204 and 79-0120. 相似文献
85.
Israel Zang 《Mathematical Programming》1978,15(1):36-52
The gradient path of a real valued differentiable function is given by the solution of a system of differential equations. For a quadratic function the above equations are linear, resulting in a closed form solution. A quasi-Newton type algorithm for minimizing ann-dimensional differentiable function is presented. Each stage of the algorithm consists of a search along an arc corresponding to some local quadratic approximation of the function being minimized. The algorithm uses a matrix approximating the Hessian in order to represent the arc. This matrix is updated each stage and is stored in its Cholesky product form. This simplifies the representation of the arc and the updating process. Quadratic termination properties of the algorithm are discussed as well as its global convergence for a general continuously differentiable function. Numerical experiments indicating the efficiency of the algorithm are presented. 相似文献
86.
The concept of multitasking mathematical programs is discussed, and an application of multitasking to the multiple-cost-row linear programming problem is considered. Based on this, an algorithm for solving the Linear Complementarity Problem (LCP) in parallel is presented. A variety of computational results are presented using this multitasking approach on the CRAY X-MP/48. These results were obtained for randomly generated LCP's where thenxn dense matrixM has no special properties (hence, the problem is NP-hard). based on these results, an average time performance ofO(n
4) is observed. 相似文献
87.
A finite algorithm is presented in this study for solving Bilinear programs. This is accomplished by developing a suitable cutting plane which deletes at least a face of a polyhedral set. At an extreme point, a polar cut using negative edge extensions is used. At other points, disjunctive cuts are adopted. Computational experience on test problems in the literature is provided.This paper is based upon work supported by the National Science Foundation under Grant No. ENG-77-23683. 相似文献
88.
This paper reports on an experimental study of the distribution of the length of simplex paths for the Optimal Assignment
Problem. We study the distribution of the pivot counts for a version of the simplex method that with essentially equal probabilities
introduces any variable with negative reduced cost into the basis.
In this situation the distribution of the pivot counts turns out to be normally distributed and independent of the actual
cost coefficients, provided these are sufficiently spread out. Further, the mean and standard deviation grow only moderately
with the size of the problem, namely asd
1.8, andd
1.5 respectively for ad×d problem, implying in particular that the pivot counts concentrate around the mean with growingd.
The usual simplex method on the other hand gives a growth ofd
1.6. Hence a large part of the favourable polynomial growth experienced on practical problems may be attributed to the fact that
the simplex paths are rather short on the average, at least for assignment problems. 相似文献
89.
Gur Huberman 《Mathematical Programming》1983,26(1):100-108
Applied mathematical programming problems are often approximations of larger, more detailed problems. One criterion to evaluate
an approximating program is the magnitude of the difference between the optimal objective values of the original and the approximating
program. The approximation we consider is variable aggregation in a convex program. Bounds are derived on the difference between
the two optimal objective values. Previous results of Geoffrion and Zipkin are obtained by specializing our results to linear
programming. Also, we apply our bounds to a convex transportation problem.
Thanks are due to Ron Dembo, Paul Zipkin and the referees for valuable comments. This research was supported by NSF Grant
ENG-76-15599. 相似文献
90.
J. -C. Pomerol 《Mathematical Programming》1984,30(2):238-241
We show that the limiting infisup theorem of Blair, Duffin and Jeroslow (1982) is a consequence of the classical bifunctional
duality. By doing so we generalize their results and prove another limiting infisup theorem for convex quasi-concave functions. 相似文献