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961.
针对经典的图着色问题,在蚁群算法的基础上结合量子计算提出一种求解图着色问题的量子蚁群算法. 将量子比特和量子逻辑门引入到蚁群算法中,较好地避免了蚁群算法搜索易陷入局部极小的缺陷,并显著加快了算法的运算速度. 通过图着色实例的大量仿真实验,表明算法对图着色问题的求解是可行的、有效的,且具有通用性. 相似文献
962.
963.
We show that arising out of noncommutative geometry is a natural family of edge Laplacians on the edges of a graph. The family includes a canonical edge Laplacian associated to the graph, extending the usual graph Laplacian on vertices, and we find its spectrum. We show that for a connected graph its eigenvalues are strictly positive aside from one mandatory zero mode, and include all the vertex degrees. Our edge Laplacian is not the graph Laplacian on the line graph but rather it arises as the noncommutative Laplace-Beltrami operator on differential 1-forms, where we use the language of differential algebras to functorially interpret a graph as providing a ‘finite manifold structure’ on the set of vertices. We equip any graph with a canonical ‘Euclidean metric’ and a canonical bimodule connection, and in the case of a Cayley graph we construct a metric compatible connection for the Euclidean metric. We make use of results on bimodule connections on inner calculi on algebras, which we prove, including a general relation between zero curvature and the braid relations. 相似文献
964.
965.
In this work we show that among all n-vertex graphs with edge or vertex connectivity k, the graph G=Kk(K1+Kn−k−1), the join of Kk, the complete graph on k vertices, with the disjoint union of K1 and Kn−k−1, is the unique graph with maximum sum of squares of vertex degrees. This graph is also the unique n-vertex graph with edge or vertex connectivity k whose hyper-Wiener index is minimum. 相似文献
966.
There are numerous means for measuring the closeness to planarity of a graph such as crossing number, splitting number, and
a variety of thickness parameters. We focus on the classical concept of the thickness of a graph, and we add to earlier work
in [4]. In particular, we offer new 9-critical thickness-two graphs on 17, 25, and 33 vertices, all of which provide counterexamples
to a conjecture on independence ratio of Albertson; we investigate three classes of graphs, namely singly and doubly outerplanar
graphs, and cloned planar graphs. We give a sharp upper bound for the largest chromatic number of the cloned planar graphs,
and we give upper and lower bounds for the largest chromatic number of the former two classes. 相似文献
967.
Gregg Musiker 《Journal of Algebraic Combinatorics》2009,30(2):255-276
Let q be a power of a prime, and E be an elliptic curve defined over
. Such curves have a classical group structure, and one can form an infinite tower of groups by considering E over field extensions
for all k≥1. The critical group of a graph may be defined as the cokernel of L(G), the Laplacian matrix of G. In this paper, we compare elliptic curve groups with the critical groups of a certain family of graphs. This collection
of critical groups also decomposes into towers of subgroups, and we highlight additional comparisons by using the Frobenius
map of E over
.
This work was partially supported by the NSF, grant DMS-0500557 during the author’s graduate school at the University of California,
San Diego, and partially supported by an NSF Postdoctoral Fellowship. 相似文献
968.
若干笛卡尔积图的邻点可区别E-全染色 总被引:4,自引:2,他引:2
图G(V,E)的k是一个正整数,f是V(G)∪E(G)到{1,2,…,k}的一个映射,如果u,v∈V(G),则f(u)≠f(v),f(u)≠f(uv),f(v)≠f(uv),C(u)≠C(v),称f是图G的邻点可区别E-全染色,称最小的数k为图G的邻点可区别E-全色数.得到了Pm×Pn,Pm×Cn,Cm×Cn的邻点可区别E-全色数,其中C(u)={f(u)}∪{f(uv)uv∈E(G)}. 相似文献
969.
By traversing square lattices, the cardinality of the set of congruence classes induced by the graph endomorphisms of undirected paths is determined. Enhancing this idea, formulas for the cardinality of the set of endomorphisms and the set of congruence classes of undirected cycles are developed. 相似文献
970.
For integers , n≥k and r≥s, let m(n,r,s,k) be the largest (in order) k-connected component with at most s colours one can find in any r-colouring of the edges of the complete graph Kn on n vertices. Bollobás asked for the determination of m(n,r,s,k).Here, bounds are obtained in the cases s=1,2 and k=o(n), which extend results of Liu, Morris and Prince. Our techniques use Szemerédi’s Regularity Lemma for many colours.We shall also study a similar question for bipartite graphs. 相似文献