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21.
The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity
R. E. L. Aldred Yoshimi Egawa Jun Fujisawa Katsuhiro Ota Akira Saito 《Journal of Graph Theory》2011,68(1):77-89
In this article, we study the existence of a 2‐factor in a K1, n‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K1, n‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K1, n‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K1, n‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K1, n‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K1, n‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011 相似文献
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The emission spectra of naphthalene (NP)–triethylamine (TEA) systems were measured under steady-state illumination conditions in some protic and aprotic solvent-tetrahydrofuran (THF) mixtures. The fluorescence spectrum of the NP–TEA system in THF could be separated into two component bands (band A at 329 nm (fluorescence of NP) and band B at 468 nm (emission from an intermolecular exciplex)). The intensities of bands A and B decreased with increasing solvent polarity. The intensity of band B also decreased owing to the hydrogen-bonding interaction between TEA and protic solvents, but in this case the intensity of band A increased. The decrease in the intensity of band A with increasing solvent polarity is considered to be caused by the enhanced formation of an ion-pair parallel to the formation of an exciplex with increasing solvent polarity. The decrease in the intensity of band B is considered to be caused by the enhanced formation of ion-pair both parallel to and through the formation of the exciplex. The increase in the intensity of band A and the decrease in that of band B upon the addition of protic solvents is caused by the decrease in the concentration of free TEA. Acetonitrile only has a polar effect and trichloroacetic acid only has a hydrogen-bonding (protonation) effect, while alcohols have both the effects. 相似文献
24.
We examined the utility of a monolithic capillary column in the analysis of pyridylaminated oligosaccharides. Fluorescence detection and mass spectrometry were used to monitor a series of oligosaccharides. Although the total-ion chromatogram appeared similar to that obtained with fluorescence detection, the sensitivity of this technique was limited, especially in the case of smaller oligosaccharides. This limitation was overcome by applying selected ion current monitoring. Further, the capillary column also exhibited good reproducibility. We showed that the retention times obtained by using the monolithic capillary column could be converted into the standard data to enable comparison of the experimental data with the existing data. Furthermore, our studies revealed an important difference in the separation profile, i.e., the monolithic capillary column could resolve smaller oligosaccharides to a greater extent. 相似文献
25.
Yoshimi Yamaguchi Yoshihisa Okamoto Kazuho Harada 《Journal of heterocyclic chemistry》1999,36(4):841-847
The revision of the structure of hydrolytic product from 4-cyano-1-ethoxypyrirnido[1,6-a]benzimidazole (1) and the properties of ethyl (2-benzimidazolyl)cyanoacetimidate (3a) are described. 相似文献
26.
LetK be a connected graph. A spanning subgraphF ofG is called aK-factor if every component ofF is isomorphic toK. On the existence ofK-factors we show the following theorem: LetG andK be connected graphs andp be an integer. Suppose|G| = n|K| and 1 <p < n. Also suppose every induced connected subgraph of orderp|K| has aK-factor. ThenG has aK-factor. 相似文献
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We shall study the relation between the unstable homotopy spectral sequence associated with the cell decomposition of the source space and the one associated with the Postnikov decomposition of the target space. It is proved that the Maunder's result holds for these two types of spectral sequences. This result will be exploited to study the differentials of these spectral sequences and we obtain a generalization of a theorem due to Atiyah-Hirzebruch and Dold. Making use of these spectral sequences with the convergence lemma, some results on the phantom maps and the homotopy groups of map*(Y, X) will be proved. 相似文献
29.
Yoshimi Sueishi Atsushi Miyata Daisuke Yoshioka Masato Kamibayashi Yashige Kotake 《Journal of inclusion phenomena and macrocyclic chemistry》2010,66(3-4):357-364
The effect of CD-inclusion on spin-trapping rates and spin-adduct decay rates for sulfur trioxide radical anion (SO3 ??) was investigated. SO3 ?? radical was produced with UV photolysis of sodium sulfite in basic aqueous solution, and spin-trapped with various spin traps, i.e., PBN (α-phenyl-N-t-butylnitrone), DMPO (5,5-dimethyl pyrroline-1-oxide), and three other phosphoryl DMPO-type spin traps. A modified β-CD, 6-O-α-d-glucosyl-β-cyclodextrin (G-β-CD) having better inclusion properties than β-CD, was employed. Upon adding excess G-β-CD, decay rates of SO3 ?? radical adducts significantly decreased in most spin traps. Half-lives of SO3 ?? radical adducts of phosphoryl spin traps were one to two orders of magnitude longer than that of PBN or DMPO, and the G-β-CD addition further extended the half-life time. The spin traps containing phosphoryl-group all showed higher SO3 ?? trapping rates than those of PBN and DMPO, but two phosphoryl spin traps achieved slower trapping rates by G-β-CD addition. In addition, the structures of CD-inclusion complexes of spin traps were established by means of 1D and 2D NMR measurements. Based on the results, the influences of inclusion on the spin-trapping rate processes and spin-adduct stabilizations were discussed. We conclude that substituents in DMPO-type spin traps may be modified to provide best spin-trapping capabilities in the presence or absence of CD. 相似文献
30.
Naoya Inazumi Yoshimi Sueishi 《Journal of inclusion phenomena and macrocyclic chemistry》2010,68(1-2):93-98
The equilibrium constants for the inclusion complexation of octaethyl-p-tert-butylcalix[8]arene octaacetate (Calix-B8-EA) with methylene blue (MB) were determined spectrophotometrically. Calix-B8-EA, which has a flexible hydrophilic pseudo-cavity formed by polyfunctional esters on the lower rim, is an effective receptor for alkali and alkaline-earth cations, and its ester carbonyl group forms the complex with metal cations. We have examined the ability to include the organic molecule (methylene blue (MB)) into the upper main cavity of Calix-B8-EA formed the complex of alkali metal cations with ester carbonyl groups on the lower rim. It was found that Calix-B8-EA forms a 1:1 inclusion complex of MB with the upper main cavity and, in the presence of excess alkali metal cations, the association constants increase with an increase in the size of the metal cations complexed with the polyfunctional groups on the lower rim. Further, the structure of the inclusion complex of MB with cation-complexed Calix-B8-EA is characterized by 2D ROESY-NMR measurements. Based on the results, we have demonstrated the control of the inclusion ability by changing the portal size of the calixarene cavity. 相似文献