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111.
Jerzy Kyparisis 《Mathematical Programming》1985,32(2):242-246
Recently Fujiwara, Han and Mangasarian introduced a new constraint qualification which is a slight tightening of the well-known Mangasarian—Fromovitz constraint qualification. We show that this new qualification is a necessary and sufficient condition for the uniqueness of Kuhn—Tucker multipliers. We also show that it implies the satisfaction of second order necessary optimality conditions at a local minimum. 相似文献
112.
Erik L. Demeulemeester Willy S. Herroelen Salah E. Elmaghraby 《European Journal of Operational Research》1996
We describe two algorithms, based on dynamic programming logic, for optimally solving the discrete time/cost trade-off problem (DTCTP) in deterministic activity-on-arc networks of the CPM type, where the duration of each activity is a discrete, nonincreasing function of the amount of a single nonrenewable resource committed to it. The first algorithm is based on a procedure proposed by Bein, Kamburowski and Stallmann for finding the minimal number of reductions necessary to transform a general network to a series-parallel network. The second algorithm minimizes the estimated number of possibilities that need to be considered during the solution procedure. Both procedures have been programmed in C and tested on a large set of representative networks to give a good indication of their performance, and indicate the circumstances in which either algorithm performs best. 相似文献
113.
114.
Daniel Granot 《Mathematical Programming》1986,34(2):212-222
We introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producersS is not restricted to be the vector sum of the resources held by the members ofS. We provide sufficient conditions for the non-emptiness of the core of the associated generalized linear production game, and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem. Our generalized linear production model is a proper generalization of the linear production model introduced by Owen, and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework. We use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non-empty core. We further employ our model to prove the non-emptiness of the core of two other classes of cooperative games, which were not previously studied in the literature, and we also use our generalized model to provide an alternative proof for the non-emptiness of the core of the class of minimum cost spanning tree games. Thus, it appears that the generalized linear production model is a unifying model which can be used to explain the non-emptiness of the core of cooperative games generated by various, seemingly different, optimization models.This research was partially done while the author was visiting the Graduate School of Business Administration at Tel-Aviv University. The research was partially supported by Natural Sciences and Engineering Research Council Canada Grant A4181 and by SSHRC leave fellowship 451-83-0030.Dedicated to George B. Dantzig. 相似文献
115.
S. -C. Fang 《Mathematical Methods of Operations Research》1992,36(2):149-161
The major interest of this paper is to show that, at least in theory, a pair of primal and dual -optimal solutions to a general linear program in Karmarkar's standard form can be obtained by solving an unconstrained convex program. Hence unconstrained convex optimization methods are suggested to be carefully reviewed for this purpose. 相似文献
116.
This paper considers the set packing problem max{wx: Ax b, x 0 and integral}, whereA is anm × n 0–1 matrix,w is a 1 ×n weight vector of real numbers andb is anm × 1 vector of ones. In equality form, its linear programming relaxation is max{wx: (x, y) P(A)} whereP(A) = {(x, y):Ax +I
m
y =b, x0,y0}. Letx
1 be any feasible solution to the set packing problem that is not optimal and lety
1 =b – Ax
1; then (x
1,y
1) is an integral extreme point ofP(A). We show that there exists a sequence of simplex pivots from (x
1,y
1) to (x*,y*), wherex* is an optimal solution to the set packing problem andy* =b – Ax*, that satisfies the following properties. Each pivot column has positive reduced weight and each pivot element equals plus one. The number of pivots equals the number of components ofx* that are nonbasic in (x
1,y
1).This research was supported by NSF Grants ECS-8005360 and ECS-8307473 to Cornell University. 相似文献
117.
A linear expected-time algorithm for deriving all logical conclusions implied by a set of boolean inequalities 总被引:1,自引:0,他引:1
Consider a setR ofm binary relations on a set ofn boolean variables.R may imply a contradiction, the fixation of some variables at 0 or at 1 and/or the identification of some pairs of variables in direct or complemented form. An O(n) expected-time algorithm is given for the derivation of all such logical conclusions. Computational experiments with problems involving up to 2000 variables are reported on. The proposed algorithm is more than 100 times faster than previous methods whenn 100.On leave from Faculté Universitaire Catholique de Mons, Belgium. Written at CNRS, LAMSADE. Support of CNRS is gratefully acknowledged. 相似文献
118.
Israel Zang 《Mathematical Programming》1980,19(1):61-77
In this paper, we suggest approximations for smoothing out the kinks caused by the presence of max or min operators in many non-smooth optimization problems. We concentrate on the continuous-discrete min—max optimization problem. The new approximations replace the original problem in some neighborhoods of the kink points. These neighborhoods can be made arbitrarily small, thus leaving the original objective function unchanged at almost every point ofR
n
. Furthermore, the maximal possible difference between the optimal values of the approximate problem and the original one, is determined a priori by fixing the value of a single parameter. The approximations introduced preserve properties such as convexity and continuous differentiability provided that each function composing the original problem has the same properties. This enables the use of efficient gradient techniques in the solution process. Some numerical examples are presented. 相似文献
119.
The use of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been growing
at a very fast pace. The level of integration as measured by the number of logic gates in a chip has been steadily rising
due to the rapid progress in processing and interconnect technology. The interconnect delay in VLSI circuits has become a
critical determiner of circuit performance. As a result, circuit layout is starting to play a more important role in today’s
chip designs. Global routing is one of the key sub-problems of circuit layout which involves finding an approximate path for
the wires connecting the elements of the circuit without violating resource constraints. In this paper, several integer programming
(ILP) based global routing models are fully investigated and explored. The resulting ILP problem is relaxed and solved as
a linear programming (LP) problem followed by a rounding heuristic to obtain an integer solution. Experimental results obtained
show that the proposed combined WVEM (wirelength, via, edge capacity) model can optimize several global routing objectives
simultaneously and effectively. In addition, several hierarchical methods are combined with the proposed flat ILP based global
router to reduce the CPU time by about 66% on average for edge capacity model (ECM). 相似文献
120.
In this paper a basic structural problem in Generalized Semi-Infinite Programming is solved. In fact, under natural and generic
assumptions we show that at any (local) minimizer the “Symmetric Reduction Ansatz” holds.
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