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51.
52.
Marston Conder Aleksander Malnič Dragan Marušič Primž Potočnik 《Journal of Algebraic Combinatorics》2006,23(3):255-294
A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This
list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer
algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several
previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its
girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms,
its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite
families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of
the list are identified with these. The special case of those graphs having K1,3 as a normal quotient is investigated in detail.
Supported in part by N.Z. Marsden Fund (grant no. UOA 124) and N.Z. Centres of Research Excellence Fund (grant no. UOA 201)
Supported in part by “Ministrstvo za šolstvo, znanost in šport Slovenije”, research program no. 101-506.
Supported in part by research projects no. Z1-4186-0101 and no. Z1-3124-0101. The fourth author would like to thank the University
of Auckland for hospitality during his visit there in 2003. 相似文献
53.
The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods.In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.This is a written account of an invited lecture delivered by the second author on occasion of the 12. Symposium on Operations Research, Passau, 9.–11. 9. 1987. 相似文献
54.
A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity. 相似文献
55.
We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice. 相似文献
56.
Topological indices are graph invariants used in computational chemistry to encode molecules. A frequent problem when performing structure-activity studies is that topological indices are inter-correlated. We consider a simple topological index and show asymptotic independence for a random tree model. This continues previous work on the correlation among topological indices. These findings suggest that a size-dependence in a certain class of distance-based topological indices can be eliminated.AMS subject classification: 05C80, 60E10, 92E10 相似文献
57.
W. Grüner R. Giegerich D. Strothmann C. Reidys J. Weber I. L. Hofacker P. F. Stadler P. Schuster 《Monatshefte für Chemie / Chemical Monthly》1996,127(4):355-374
Summary Global relations between RNA sequences and secondary structures are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of allGC andAU sequences with chain lengths up to 30. The computed structural data are evaluated through exhaustive enumeration and used as an exact reference for testing analytical results derived from mathematical models and sampling based on statistical methods. Several new concepts of RNA sequence to secondary structure mappings are investigated, among them that ofneutral networks (being sets of sequences folding into the same structure). Exhaustive enumeration allows to test several previously suggested relations: the number of (minimum free energy) secondary structures as a function of the chain length as well as the frequency distribution of structures at constant chain length (commonly resulting in generalized forms ofZipf's law).
Analyse der Beziehungen zwischen RNA-Sequenzen und Sekundärstrukturen durch vollständige Faltung, 1. Mitt. Faltung, Neutrale Netzwerke
Zusammenfassung Die globalen Benziehungen zwischen RNA-Sequenzen und Sekundärstrukturen werden als Abbildungen aus einem Raum aller Sequenzen in einen Raum aller Strukturen aufgefaßt. Diese Abbildungen werden durch Falten aller binären Sequenzen desGC-undAU-Alphabets mit Kettenlängen bis zun=30 untersucht. Die berechneten Strukturdaten werden durch vollständiges Abzählen ausgewertet und als eine exakte Referenz zum Überprüfen analytischer Resultate aus mathematischen Modellen sowie zum Testen statistisch erhobener Proben verwendet. Einige neuartige Konzepte zur Beschreibung der Beziehungen zwischen Sequenzen und Strukturen werden eingehend untersucht, unter ihnen der Begriff derneutralen Netzwerke. Ein neutrales Netzwerk besteht aus allen Sequenzen, die eine bestimmte Struktur ausbilden. Vollständiges Abzählen ermöglicht beispielsweise die Bestimmung aller Strukturen minimaler freier Energie in Abhängigkeit von der Kettenlänge ebenso wie die Bestimmung der Häufigkeitsverteilungen der Strukturen bei konstanten Kettenlängen. Die letzteren folgen einer verallgemeinerten FormZipfschen Gesetzes.相似文献
58.
《Operations Research Letters》2022,50(6):655-659
In finite graphs, greedy algorithms are used to find minimum spanning trees (MinST) and maximum spanning trees (MaxST). In infinite graphs, we illustrate a general class of problems where a greedy approach discovers a MaxST while a MinST may be unreachable. Our algorithm is a natural extension of Prim's to infinite graphs with summable and strictly positive edge weights, producing a sequence of finite trees that converge to a MaxST. 相似文献
59.
《Discrete Mathematics》2022,345(3):112721
This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates. 相似文献
60.
András Telcs 《Journal of Theoretical Probability》1995,8(1):77-96
This paper continues the study of exponentsd(x), d
(x), d
R
(x) andd
(x) for graphG; and the nearest neighbor random walk {X
n
}
nN
onG, if the starting pointX
0=x is fixed. These exponents are responsible for the geometric, resistance, diffusion and spectral properties of the graph. The main concern of this paper is the relation of these exponents to the spectral density of the transition matrix. A series of new exponentse, e
,e
R
,e
are introduced by allowingx to vary along the vertices. The results suggest that the geometric and resistance properties of the graph are responsible for the diffusion speed on the graph. 相似文献