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81.
Robert Willenbring 《Discrete Applied Mathematics》2009,157(7):1607-1614
We construct a permutation representation for RNA secondary structure. We also introduce some basic combinatorial statistics for RNA secondary structure and relate them to permutation statistics when appropriate. These statistics allow us to quantify some structural phenomena in RNA secondary structure. 相似文献
82.
Konrad J. Swanepoel 《Discrete and Computational Geometry》2009,41(1):1-27
We show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d≥4 and n sufficiently large depending on d. As a corollary, we determine the exact maximum number of unit distances for all even d≥6 and the exact maximum number of diameters for all d≥4 and all n sufficiently large depending on d.
This material is based upon work supported by the South African National Research Foundation. 相似文献
83.
Adam N. Letchford Saeideh D. Nasiri Dirk Oliver Theis 《European Journal of Operational Research》2013
The Steiner Traveling Salesman Problem (STSP) is a variant of the TSP that is particularly suitable when routing on real-life road networks. The standard integer programming formulations of both the TSP and STSP have an exponential number of constraints. On the other hand, several compact formulations of the TSP, i.e., formulations of polynomial size, are known. In this paper, we adapt some of them to the STSP, and compare them both theoretically and computationally. It turns out that, just by putting the best of the formulations into the CPLEX branch-and-bound solver, one can solve instances with over 200 nodes. We also briefly discuss the adaptation of our formulations to some related problems. 相似文献
84.
The object of the article is to characterize epigroups which are locally completely regular. Some subclasses of such epigroups are also described. 相似文献
85.
Elena Barcucci Alberto Del Lungo Elisa Pergola 《Journal of Difference Equations and Applications》2013,19(4-5):435-490
In this Paper, we illustrate a method (called the ECO method) for enumerating some classes of combinatorial objects. The basic idea of this method is the following: by means of an operator that performs a "local expansion" on the objects, we give some recursive constructions of these classes. We use these constructions to deduce some new funtional equations verified by classes' generating functions. By solving the functional equations, we enumerate the combinatorial objects according to various parameters. We show some applications of the method referring to some classical combinatorial objects, such as: trees, paths, polyminoes and permutations 相似文献
86.
《Journal of computational and graphical statistics》2013,22(1):236-258
Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data. 相似文献
87.
88.
Large part of combinatorial optimization research has been devoted to the study of exact methods leading to a number of very
diversified solution approaches. Some of those older frameworks can now be revisited in a metaheuristic perspective, as they
are quite general frameworks for dealing with optimization problems. In this work, we propose to investigate the possibility
of reinterpreting decompositions, with special emphasis on the related Benders and Lagrangean relaxation techniques. We show
how these techniques, whose heuristic effectiveness is already testified by a wide literature, can be framed as a “master
process that guides and modifies the operations of subordinate heuristics”, i.e., as metaheuristics. Obvious advantages arise
from these approaches, first of all the runtime evolution of both upper and lower bounds to the optimal solution cost, thus
yielding both a high-quality heuristic solution and a runtime quality certificate of that same solution. 相似文献
89.
Greedy algorithms for combinatorial optimization problems are typically direct and efficient, but hard to prove optimality.
The paper presents a special class of transportation problems where a supplier sends goods to a set of customers, returning
to the source after each delivery. We show that these problems with different objective functions share a common structural
property, and therefore a simple but powerful generic greedy algorithm yields optimal solutions for all of them. 相似文献
90.
We formulate the fixed-charge multiple knapsack problem (FCMKP) as an extension of the multiple knapsack problem (MKP). The Lagrangian relaxation problem is easily solved, and together with a greedy heuristic we obtain a pair of upper and lower bounds quickly. We make use of these bounds in the pegging test to reduce the problem size. We also present a branch-and-bound (B&B) algorithm to solve FCMKP to optimality. This algorithm exploits the Lagrangian upper bound as well as the pegging result for pruning, and at each terminal subproblem solve MKP exactly by invoking MULKNAP code developed by Pisinger [Pisinger, D., 1999. An exact algorithm for large multiple knapsack problems. European Journal of Operational Research 114, 528–541]. As a result, we are able to solve almost all test problems with up to 32,000 items and 50 knapsacks within a few seconds on an ordinary computing environment, although the algorithm remains some weakness for small instances with relatively many knapsacks. 相似文献