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23.
Mathieu Liedloff 《Information Processing Letters》2008,107(5):154-157
Finding a dominating set of minimum cardinality is an NP-hard graph problem, even when the graph is bipartite. In this paper we are interested in solving the problem on graphs having a large independent set. Given a graph G with an independent set of size z, we show that the problem can be solved in time O∗(2n−z), where n is the number of vertices of G. As a consequence, our algorithm is able to solve the dominating set problem on bipartite graphs in time O∗(2n/2). Another implication is an algorithm for general graphs whose running time is O(n1.7088). 相似文献
24.
In this paper we consider the p-ary transitive reduction (TR
p
) problem where p>0 is an integer; for p=2 this problem arises in inferring a sparsest possible (biological) signal transduction network consistent with a set of
experimental observations with a goal to minimize false positive inferences even if risking false negatives. Special cases
of TR
p
have been investigated before in different contexts; the best previous results are as follows:
In this paper, our contributions are as follows:
R. Albert’s research was partly supported by a Sloan Research Fellowship in Science and Technology.
B. DasGupta’s research was partly supported by NSF grants DBI-0543365, IIS-0612044 and IIS-0346973.
E. Sontag’s research was partly supported by NSF grants EIA 0205116 and DMS-0504557. 相似文献
(1) | The minimum equivalent digraph problem, that correspond to a special case of TR1 with no critical edges, is known to be MAX-SNP-hard, admits a polynomial time algorithm with an approximation ratio of 1.617+ε for any constant ε>0 (Chiu and Liu in Sci. Sin. 4:1396–1400, 1965) and can be solved in linear time for directed acyclic graphs (Aho et al. in SIAM J. Comput. 1(2):131–137, 1972). |
(2) | A 2-approximation algorithm exists for TR1 (Frederickson and JàJà in SIAM J. Comput. 10(2):270–283, 1981; Khuller et al. in 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 937–938, 1999). |
• | We observe that TR p , for any integer p>0, can be solved in linear time for directed acyclic graphs using the ideas in Aho et al. (SIAM J. Comput. 1(2):131–137, 1972). |
• | We provide a 1.78-approximation for TR1 that improves the 2-approximation mentioned in (2) above. |
• | We provide a 2+o(1)-approximation for TR p on general graphs for any fixed prime p>1. |
25.
For a simple graph G, let . In this paper, we prove that if NCD(G)≥|V(G)|, then either G is Hamiltonian-connected, or G belongs to a well-characterized class of graphs. The former results by Dirac, Ore and Faudree et al. are extended. 相似文献
26.
随机图点覆盖1度顶点核化算法分析 总被引:1,自引:0,他引:1
将随机图引入参数计算领域,利用随机图统计和概率分布等特性,从全局和整体上研究参数化点覆盖问题1度点核化过程中问题的核及度分布演变的内在机制和变化规律,并得出关于随机图1度点核化强度与顶点平均度关系及随机图点覆盖问题的决策与度分布关系的两个重要推论.最后分别从MIPS和BIND提取数据进行1度核化实验和分析.初步结果表明,对随机图点覆盖问题的分析方法不仅具有理论上的意义,而且随着问题随机度的大小而对问题有不同程度的把握能力. 相似文献
27.
This paper investigates the controllability of multi-agent systems based on agreement protocols. First, for a group of single-integrator
agents, the controllability is studied in a unified framework for both networks with leader-following structure and networks
with undirected graph. Some new necessary/sufficient conditions for the controllability of networks of single-integrator agents
are established. Second, we prove that, under the same topology and same prescribed leaders, a network of high-order dynamic
agents is completely controllable if and only if so is a network of single-integrator agents. Third, how the selection of
leaders and the coupling weights of graphs affect the controllability is analyzed. Finally, some numerical simulations are
presented to demonstrate the effectiveness of the theoretical results. 相似文献
28.
In this paper, we provide a necessary infrastructure to define an abstract state exploration in the HOL theorem prover. Our infrastructure is based on a deep embedding of the Multiway Decision Graphs (MDGs) theory in HOL. MDGs generalize Reduced Ordered Binary Decision Diagrams (ROBDDs) to represent and manipulate a subset of first-order logic formulae. The MDGs embedding is based on the logical formulation of an MDG as Directed Formulae (DF). Then, the MDGs operations are defined and the correctness pro... 相似文献
29.
Graph drawing and visualization represent structural information as diagrams of abstract graphs and networks. An important subset of graphs is directed acyclic graphs (DAGs). This paper presents a new E-Spring algorithm, extended from the popular spring embedder model, which eliminates node overlaps in clustered DAGs. In this framework, nodes are modeled as non-uniform charged particles with weights, and a final drawing is derived by adjusting the positions of the nodes according to a combination of spring forces and repulsive forces derived from electrostatic forces between the nodes. The drawing process needs to reach a stable state when the average distances of separation between nodes are near optimal. We introduce a stopping condition for such a stable state, which reduces equilibrium distances between nodes and therefore results in a significantly reduced area for DAG visualization. It imposes an upper bound on the repulsive forces between nodes based on graph geometry. The algorithm employs node interleaving to eliminate any residual node overlaps. These new techniques have been validated by visualizing eBay buyer–seller relationships and has resulted in overall area reductions in the range of 45–79%. 相似文献
30.
Graph matching is a fundamental problem that arises frequently in the areas of distributed control, computer vision, and facility allocation. In this paper, we consider the optimal graph matching problem for weighted graphs, which is computationally challenging due the combinatorial nature of the set of permutations. Contrary to optimization-based relaxations to this problem, in this paper we develop a novel relaxation by constructing dynamical systems on the manifold of orthogonal matrices. In particular, since permutation matrices are orthogonal matrices with nonnegative elements, we define two gradient flows in the space of orthogonal matrices. The first minimizes the cost of weighted graph matching over orthogonal matrices, whereas the second minimizes the distance of an orthogonal matrix from the finite set of all permutations. The combination of the two dynamical systems converges to a permutation matrix, which provides a suboptimal solution to the weighted graph matching problem. Finally, our approach is shown to be promising by illustrating it on nontrivial problems. 相似文献