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41.
A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. 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 matching number is the maximum cardinality of a matching of G, while the total domination number of G is the minimum cardinality of a total dominating set of G. In this paper, we investigate the relationships between the matching and total domination number of a graph. We observe that the total domination number of every claw-free graph with minimum degree at least three is bounded above by its matching number, and we show that every k-regular graph with k?3 has total domination number at most its matching number. In general, we show that no minimum degree is sufficient to guarantee that the matching number and total domination number are comparable. 相似文献
42.
43.
Total Domination in Graphs with Given Girth 总被引:1,自引:0,他引:1
A set S of vertices in a graph G without isolated vertices 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 γ
t
(G) of G. In this paper, we establish an upper bound on the total domination number of a graph with minimum degree at least two in
terms of its order and girth. We prove that if G is a graph of order n with minimum degree at least two and girth g, then γ
t
(G) ≤ n/2 + n/g, and this bound is sharp. Our proof is an interplay between graph theory and transversals in hypergraphs.
Michael A. Henning: Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal. 相似文献
44.
Reaction of 2,3-diaminopyridine with one equivalent of a functionalised vicinal diketone, in ethanol, yields a series of ligands based upon the pyrido[2,3-b]pyrazine core. The ligands were characterised by 1H, 13C–{1H} NMR, MS and UV–Vis spectroscopy. Reaction of the ligands with one equivalent of {ReBr(CO)5} gave a series of Re-Ln complexes based upon the general formula fac-{ReBr(CO)3(L)} (where L = pyrido[2,3-b]pyrazine-derived ligands, L1–L6). Solution IR studies confirmed the retention of the facially capped, tri-carbonyl coordination geometry at rhenium, and 1H NMR studies confirmed coordination of the ligand to Re(I). EI HR MS data were obtained for each complex confirming the proposed formulation and stoichiometry. Single crystal X-ray structures were obtained for three of the complexes (Re-L1, Re-L2, Re-L6), with each demonstrating that the ligands coordinate to Re(I) in a bidentate manner, via a four-membered chelate ring, which was unsymmetrical in the former two cases. The electronic absorption spectra of the complexes showed absorption into the visible region ca. 375–500 nm, (the complexes are orange-red in appearance). Following irradiation at 350–450 nm, the complexes display a solid-state broad emission peaking between 600–700 nm. The complexes were not sufficiently luminescent in solution to allow further investigation into the origin of this emission band, although with reference to related 1,8-naphthyridine complexes of Re(I) it is likely to incorporate significant 3MLCT character. 相似文献
45.
Many Primary Four students (fourth graders) in Singapore have difficulties initiating or persevering in the problem-solving process even though the curriculum has focused on problem solving since 1992. This study served to examine the role of metacognition in self-regulated problem solving. The study, a quasi-experimental pretest–posttest design involving a convenience sample of 63 students from two intact mixed-ability Primary Four classes, examined the impact of using a metacognitive scheme that focuses on the understanding and planning stages of Pòlya’s four-stage approach on students’ mathematical problem-solving behavior, performance and attitudes. The findings revealed that the metacognitive-based scheme had a positive impact on students’ understanding of the problem posed, solution planning, confidence in and personal control of problem-solving behavior and emotions. It had also helped them to initiate and persevere in the problem-solving process to achieve a higher level of problem-solving success. Limitations and instructional implications are discussed. 相似文献
46.
The open neighborhood N(v) of a vertex v in a graph G is the set of vertices adjacent to v in G. A graph is twin-free (or open identifiable) if every two distinct vertices have distinct open neighborhoods. A separating open code in G is a set C of vertices such that \({N(u) \cap C \neq N(v) \cap C}\) for all distinct vertices u and v in G. An open dominating set, or total dominating set, in G is a set C of vertices such that \({N(u) \cap C \ne N(v) \cap C}\) for all vertices v in G. An identifying open code of G is a set C that is both a separating open code and an open dominating set. A graph has an identifying open code if and only if it is twin-free. If G is twin-free, we denote by \({\gamma^{\rm IOC}(G)}\) the minimum cardinality of an identifying open code in G. A hypergraph H is identifiable if every two edges in H are distinct. A distinguishing-transversal T in an identifiable hypergraph H is a subset T of vertices in H that has a nonempty intersection with every edge of H (that is, T is a transversal in H) such that T distinguishes the edges, that is, \({e \cap T \neq f \cap T}\) for every two distinct edges e and f in H. The distinguishing-transversal number \({\tau_D(H)}\) of H is the minimum size of a distinguishing-transversal in H. We show that if H is a 3-uniform identifiable hypergraph of order n and size m with maximum degree at most 3, then \({20\tau_D(H) \leq 12n + 3m}\) . Using this result, we then show that if G is a twin-free cubic graph on n vertices, then \({\gamma^{\rm IOC}(G) \leq 3n/4}\) . This bound is achieved, for example, by the hypercube. 相似文献
47.
Min Yeo K Ji Gao C Ahn KH Su Lee I 《Chemical communications (Cambridge, England)》2008,(38):4622-4624
The incorporation of superparamagnetic iron oxide nanoparticles with sulfur-oxidized diarylethene molecules resulted in a novel multifunctional nanosystem, in which the fluorescent performance and flocculation and dispersion are reversibly switched by light irradiation and external magnetic field, respectively. 相似文献
48.
Akerke Shakirbay Jeong Sik Choi Dong Chul Kim Hyo Soon Shin Dong Hun Yeo Joon Hyung Lee 《Magnetic resonance in chemistry : MRC》2022,60(9):877-883
In this paper, we evaluated the particle dispersion degree of alumina slurry containing a dispersant by solvent nuclear magnetic resonance (NMR) relaxation and compared it with conventional dispersion evaluation methods such as viscosity, particle size, and sedimentation height measurements. The dispersion of slurry was evaluated via numerical analysis of the transverse relaxation time (T2). The effect of the changes in different parameters of the experiment in terms of milling time, solid loading, and dispersant amount was investigated by NMR relaxation as well as conventional methods. The results of NMR relaxation measurements revealed that T2 correlates well with other dispersion evaluation methods; thus, it is an efficient technique to evaluate the dispersion of alumina slurry, specifically, when studying the effect of the change in milling time and dispersion amount. 相似文献
49.
50.
Experiments were carried out to measure the base pressure distribution of a flow field induced by a potential vortex with its axis normal to a stationary disk. The center base pressure coefficient of the vortex, C0(0), was found to be proportional to Reynolds number from Re = 2.0 × 103 to Re > 2.5 × 104, where Re is based on the disk radius and azimuthal velocity at the disk edge. This behavior of C0(0) is at variance with the experimental results of Phillips (Phys. Fluids, 27, 2215, 1984) and Khoo (M. Eng. Thesis, Natl. Univ. Singapore, 1984), which showed vastly different trends depending on Re. Plausible reasons are suggested for the apparent discrepancies observed. Finally, the extent of the effusing core at the center, r1 (taken to be the radial position where departure from the outer potential flow took place), was found to be proportional to Re−1/2 for all Re values considered. 相似文献