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31.
Let G=(V,E) be a graph and S⊆V. The set S is a secure set if ∀X⊆S,|N[X]∩S|≥|N[X]−S|, and S is a global secure set if S is a secure set and a dominating set. The cardinality of a minimum global secure set of G is the global security number of G, denoted γs(G). The sets studied in this paper are different from secure dominating sets studied in Cockayne et al. (2003) [3], Grobler and Mynhardt (2009) [8], or Klostermeyer and Mynhardt (2008) [13], which are also denoted by γs.In this paper, we provide results on the global security numbers of paths, cycles and their Cartesian products. 相似文献
32.
Lajos Soukup 《Discrete Mathematics》2011,311(15):1585
The use of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary submodels. We also present a new proof of Nash-Williams’s theorem on cycle decomposition of graphs, and finally we improve a decomposition theorem of Laviolette concerning bond-faithful decompositions of graphs. 相似文献
33.
双阈值二元神经网络极限环的存在惟一性 总被引:3,自引:0,他引:3
研究具负反馈的双阈值二元神经网络模型的动力学性质。在一定的初始函数空间内,对设定的阈值范围证明了模型存在惟一稳定极限环。 相似文献
34.
Green fluorescent protein (GFP) is used as a biological marker. It is a protein in the jellyfish, Aequorea victorea, which is found in the cold Pacific Northwest. Mature GFP, i.e. fully fluorescent GFP, is most efficiently formed at temperatures well below 37 °C. The GFPuv (F99S/M153T/V163A) and S147P-GFP mutants mature more efficiently at room temperature than wild-type GFP, and therefore result in increased fluorescence at room temperature. Computational methods have been used to examine whether the low-energy precyclized forms of these improved GFP-mutants are preorganized so that they can more efficiently form the chromophore than the wild-type and S65T-GFP. All mutations examined (S147P, F99S, M153T, V163A and F99S/M153T/V163A) more efficiently preorganize the immature precyclized forms of GFP for chromophore formation than immature wild-type GFP. It has been proposed that Arg96 is involved in chromophore formation. Our calculations suggest that the M153T and V163A mutations in GFPuv maybe partially responsible for the increased maturation efficiency observed in GFPuv because they improve the Arg96–Tyr66 interaction. The same is true for the S147P mutation in S147P-GFP. 相似文献
35.
In this paper, we almost completely solve the Hamilton–Waterloo problem with -factors and -factors where the number of vertices is a multiple of . 相似文献
36.
Bojan Mohar 《Discrete Mathematics》2010,310(20):2595-2599
A “folklore conjecture, probably due to Tutte” (as described in [P.D. Seymour, Sums of circuits, in: Graph Theory and Related Topics (Proc. Conf., Univ. Waterloo, 1977), Academic Press, 1979, pp. 341-355]) asserts that every bridgeless cubic graph can be embedded on a surface of its own genus in such a way that the face boundaries are cycles of the graph. Sporadic counterexamples to this conjecture have been known since the late 1970s. In this paper we consider closed 2-cell embeddings of graphs and show that certain (cubic) graphs (of any fixed genus) have closed 2-cell embedding only in surfaces whose genus is very large (proportional to the order of these graphs), thus providing a plethora of strong counterexamples to the above conjecture. The main result yielding such counterexamples may be of independent interest. 相似文献
37.
Dirk Meierling 《Discrete Mathematics》2010,310(4):850-860
A digraph without loops, multiple arcs and directed cycles of length two is called a local tournament if the set of in-neighbors as well as the set of out-neighbors of every vertex induces a tournament. A digraph is 2-connected if the removal of an arbitrary vertex results in a strongly connected digraph.In 2004 and 2005, Li and Shu investigated the structure of strongly connected, but not 2-connected tournaments. Using their structural results they were able to give sufficient conditions for a strongly connected tournament T to have complementary cycles or a k-cycle factor, i.e. a set of k vertex disjoint cycles that span the vertex set of T.Inspired by the articles of Li and Shu we develop in this paper the structure necessary for a strongly connected local tournament to be not cycle complementary. Using this structure, we are able to generalize and transfer various results of Li and Shu to the class of local tournaments. 相似文献
38.
The Bermond-Thomassen conjecture states that, for any positive integer r, a digraph of minimum out-degree at least 2r−1 contains at least r vertex-disjoint directed cycles. Thomassen proved that it is true when r=2, and very recently the conjecture was proved for the case where r=3. It is still open for larger values of r, even when restricted to (regular) tournaments. In this paper, we present two proofs of this conjecture for tournaments with minimum in-degree at least 2r−1. In particular, this shows that the conjecture is true for (almost) regular tournaments. In the first proof, we prove auxiliary results about union of sets contained in another union of sets, that might be of independent interest. The second one uses a more graph-theoretical approach, by studying the properties of a maximum set of vertex-disjoint directed triangles. 相似文献
39.
Cycle embedding in star graphs with conditional edge faults 总被引:1,自引:0,他引:1
Ming-Chien Yang 《Applied mathematics and computation》2010,215(10):3541-3867
Among the various interconnection networks, the star graph has been an attractive one. In this paper, we consider the cycle embedding problem in star graphs with conditional edge faults. We show that there exist cycles of all even lengths from 6 to n! in an n-dimensional star graph with ?2n-7 edge faults in which each vertex is incident with at least two healthy edges for n?4. 相似文献
40.
Given a graph , let be the set of all cycle lengths contained in and let . Let and let be the greatest common divisor of and all the positive pairwise differences of elements in . We prove that if a Hamiltonian graph of order has at least edges, where is an integer such that , then or is exceptional, by which we mean for some . We also discuss cases where is not exceptional, for example when is prime. Moreover, we show that , which if is bipartite implies that , where is the number of edges in . 相似文献