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101.
Jakub Przybyło 《Random Structures and Algorithms》2015,47(4):776-791
Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1,2,…,k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by . The definition of this parameter, which makes sense for graphs containing no isolated edges, immediately implies that , where Δ is the maximum degree of G. On the other hand, it was conjectured by Flandrin et al. that for all those graphs, except for C5. We prove this bound to be asymptotically correct by showing that . The main idea of our argument relays on a random assignment of the colours, where the choice for every edge is biased by so called attractors, randomly assigned to the vertices. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 776–791, 2015 相似文献
102.
A basic problem in the theory of simple games and other fields is to study whether a simple game (Boolean function) is weighted
(linearly separable). A second related problem consists in studying whether a weighted game has a minimum integer realization.
In this paper we simultaneously analyze both problems by using linear programming.
For less than 9 voters, we find that there are 154 weighted games without minimum integer realization, but all of them have minimum normalized realization. Isbell in 1958 was the first to find a weighted game without a minimum normalized
realization, he needed to consider 12 voters to construct a game with such a property. The main result of this work proves
the existence of weighted games with this property with less than 12 voters.
This research was partially supported by Grant MTM 2006-06064 of “Ministerio de Ciencia y Tecnología y el Fondo Europeo de
Desarrollo Regional” and SGRC 2005-00651 of “Generalitat de Catalunya”, and by the Spanish “Ministerio de Ciencia y Tecnología”
programmes ALINEX (TIN2005-05446 and TIN2006-11345). 相似文献
103.
104.
Let G=(V,E) be a connected graph. A dominating set S of G is a weakly connected dominating set of G if the subgraph (V,E∩(S×V)) of G with vertex set V that consists of all edges of G incident with at least one vertex of S is connected. The minimum cardinality of a weakly connected dominating set of G is the weakly connected domination number, denoted . A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γt(G) of G. In this paper, we show that . Properties of connected graphs that achieve equality in these bounds are presented. We characterize bipartite graphs as well as the family of graphs of large girth that achieve equality in the lower bound, and we characterize the trees achieving equality in the upper bound. The number of edges in a maximum matching of G is called the matching number of G, denoted α′(G). We also establish that , and show that for every tree T. 相似文献
105.
A connected graph G=(V,E) is called a quasi-tree graph if there exists a vertex v_0∈V(G) such that G-v_0 is a tree.In this paper,we determine all quasi-tree graphs of order n with the second largest signless Laplacian eigenvalue greater than or equal to n-3.As an application,we determine all quasi-tree graphs of order n with the sum of the two largest signless Laplacian eigenvalues greater than to 2 n-5/4. 相似文献
106.
107.
In this article, we take the point of view that the light scalar meson a0(980) is a conventional qqstate, and calculate the coupling constants ga0ηπ0 and ga0ηπ0 with the light-cone QCD sum rules. The central value of the coupling constant ga0ηπ0 is consistent with that extracted from the radiative decay φ(1020) → a0(980)γ→ηπ0γ. The central value and lower bound of the decay width Γa0→ηπ0 =127+8448 MeV are compatible with the experimental data of the total decay width Γa0(980) = (50-100) MeV from the Particle Data Group with a very model dependent estimation (the decay width can be much larger), while the upper bound is too large. We give a possible explanation for the discrepancy between the theoretical calculation and experimental data. 相似文献
108.
Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ2(G)n+k-1. Let v1,…,vk be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C1,…,Ck with viV(Ci) for all 1ik.Then G has k vertex-disjoint cycles such that
- (i) for all 1ik.
- (ii) , and
- (iii) At least k-1 of the k cycles are triangles.
Keywords: Degree sum condition; Independent vertices; Vertex-disjoint cycles 相似文献
109.
Josef Bukac 《分析论及其应用》2008,24(4):330-335
Minimization of the weighted nonlinear sum of squares of differences may be converted to the minimization of sum of squares. The Gauss-Newton method is recalled and the length of the step of the steepest descent method is determined by substituting the steepest descent direction in the Gauss-Newton formula. The existence of minimum is shown. 相似文献
110.
Graeme Kemkes Cristiane M. Sato Nicholas Wormald 《Random Structures and Algorithms》2013,43(3):354-376
We determine an asymptotic formula for the number of labelled 2‐connected (simple) graphs on n vertices and m edges, provided that m ‐ n →∞ and m = O(nlog n) as n →∞. This is the entire range of m not covered by previous results. The proof involves determining properties of the core and kernel of random graphs with minimum degree at least 2. The case of 2‐edge‐connectedness is treated similarly. We also obtain formulae for the number of 2‐connected graphs with given degree sequence for most (“typical”) sequences. Our main result solves a problem of Wright from 1983. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013 相似文献