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71.
Michael D. Barrus 《Discrete Mathematics》2010,310(20):2600-2612
A card of a graph G is a subgraph formed by deleting one vertex. The Reconstruction Conjecture states that each graph with at least three vertices is determined by its multiset of cards. A dacard specifies the degree of the deleted vertex along with the card. The degree-associated reconstruction number drn(G) is the minimum number of dacards that determine G. We show that drn(G)=2 for almost all graphs and determine when drn(G)=1. For k-regular n-vertex graphs, drn(G)≤min{k+2,n−k+1}. For vertex-transitive graphs (not complete or edgeless), we show that drn(G)≥3, give a sufficient condition for equality, and construct examples with large drn. Our most difficult result is that drn(G)=2 for all caterpillars except stars and one 6-vertex example. We conjecture that drn(G)≤2 for all but finitely many trees. 相似文献
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Collaborative knowledge creation is important for firms to gain new competitive advantages, but knowledge outgoing spillover harms their existing competitive advantages, which puts them into a dilemma when investing R&D resources. This study formalizes and investigates this dilemma using the Stackelberg leader–follower framework. Through our analyses, we find that, (1) current knowledge creation efforts and prior knowledge are substitutable in collaborative knowledge creation, and through controlling the ratio of current knowledge creation efforts to prior knowledge invested, the leader and the follower can gain benefits from collaboration and restrict knowledge outgoing spillover simultaneously; (2) because the leader invests resources first and faces moral hazards, it has the incentives to participate in collaborative knowledge creation only when its benefits from collaborative knowledge creation fruits and knowledge incoming spillover are bigger than those of the follower, and the more moral hazards it confronts, the more it demands; (3) the leader and the follower invest resources at ratios consistent with the benefits and costs the resources bring to them if they can determine the amount, or the collaboration is unstable. 相似文献
74.
Oxygen and carbon isotopic compositions of tree ring cellulose (δ13Ccell and δ18Ocell) were measured for pines growing at four sites in east Germany. Three sites differed markedly in soil water availability within a short distance and the fourth site served as a reference. The choice of the sites was guided by the desire to detect effects of air pollution on the long-term trend of isotopic compositions and to examine the influence of soil water availability on the relationship between the carbon and oxygen isotope ratios. Locations in east Germany are particularly well suited for the study of pollution effects because there was a steady increase in environmental contamination until the German Reunification in 1990, followed by a sharp decline due to the implementation of stricter environmental standards. The long-term trend of δ13Ccell showed an extraordinary increase in the period 1945–1990 and a rapid decrease after 1990, whereas δ18Ocell remained nearly constant. The increase of δ13Ccell is explained by secondary fractionation caused by phytotoxicity of SO2. Two effects are mainly responsible for the secondary fractionation under SO2 exposure: increase of dark respiration, and changes in photosynthate allocation and partitioning. Both effects do not influence δ18Ocell. Furthermore, a significant positive correlation between the year-to-year variations of carbon and oxygen isotope ratios (δ13Cresid and δ18Oresid) has been found for all sites. The slopes of the relationship between δ13Cresid and δ18Oresid differ insignificantly. It is concluded that this relationship is not influenced by soil water availability but by climatic variables. 相似文献
76.
Xu introduced a family of root-tree-diagram nilpotent Lie algebras of differential operators, in connection with evolution partial differential equations. We generalized his notion to more general oriented tree diagrams. These algebras are natural analogues of the maximal nilpotent Lie subalgebras of finite-dimensional simple Lie algebras. In this article, we use Hodge Laplacian to study the cohomology of these Lie algebras. The “total rank conjecture” and “b 2-conjecture” for the algebras are proved. Moreover, we find the generating functions of the Betti numbers by means of Young tableaux for the Lie algebras associated with certain tree diagrams of single branch point. By these functions and Euler–Poincaré principle, we obtain analogues of the denominator identity for finite-dimensional simple Lie algebras. The result is a natural generalization of the Bott's classical result in the case of special linear Lie algebras. 相似文献
77.
Tracy L. Weston 《Research in Mathematics Education》2013,15(3):286-302
This study examined trainee teachers' mathematical knowledge in teaching (MKiT) over their final year in a US Initial Teacher Education (ITE) programme. This paper reports on an exploratory methodological approach taken to use the Knowledge Quartet to quantify MKiT through the development of a new protocol to code trainees' teaching of mathematics lessons. This approach extends Rowland's et al. work on the Knowledge Quartet (KQ). Justification for using the KQ to quantify MKiT, and the potential benefits such an attempt might provide those involved with ITE, are discussed. It is suggested that quantified MKiT data based on the Knowledge Quartet can be used to consider MKiT development in novice teachers in order to inform ITE programmes and form new theoretical loops between theory and practice in teacher education. 相似文献
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