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1.
In this paper we prove that all positive eigenvalues of the Laplacian of an arbitrary simple graph have some positive lower bounds. For a fixed integer k 1 we call a graph without isolated vertices k-minimal if its kth greatest Laplacian eigenvalue reaches this lower bound. We describe all 1-minimal and 2-minimal graphs and we prove that for every k 3 the path Pk+1 on k + 1 vertices is the unique k-minimal graph.  相似文献   
2.
We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss–Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss–Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.  相似文献   
3.
Extremal hexagonal chains   总被引:6,自引:0,他引:6  
Some extremal properties of the linear chainL h ofh hexagons are pointed out. In the class of all hexagonal chains withh hexagons,L h has minimumK,Z andx 1 values, as well as maximum W and values;K = number of perfect matchings,Z = number of independent edge sets (Hosoya index),x 1 = largest graph eigenvalue,W = Wiener index, = number of independent vertex sets (Merrifield-Simmons index). The extremality ofL h with respect toZ, andx 1 is demonstrated here for the first time.Dedicated to Frank Harary, teacher, inspirer and friend, pioneer, champion and proprietor of graph theory, on the occasion of his 70th birthday.  相似文献   
4.
Summary. In a recent work it was demonstrated that in linear hexagonal chains the distribution of π-electrons into rings (as computed by means of the Randić–Balaban method) is uniform, irrespective of the nature of the terminal fragments. We now establish that an analogous, yet somewhat more complex, uniformity in the π-electron distribution exists also in double linear hexagonal chains, as well as in some other benzenoid systems.  相似文献   
5.
The resistance distance r ij between two vertices v i and v j of a (connected, molecular) graph G is equal to the resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any two adjacent points is unity. We show how the matrix elements r ij can be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||r ij ||. AcknowledgementsThis research was supported by the Natural Science Foundation of China and Fujian Province, and by the Ministry of Sciences, Technologies and Development of Serbia, within Project no. 1389. The authors thank Douglas J. Klein (Galveston) for useful comments.  相似文献   
6.
Summary. Hydrolytic reactions between various palladium(II) complexes of the type cis-[Pd(L)(H2O)2]2+ in which L is ethylenediamine (en), 1,2-propylenediamine (1,2-pn), isobutylenediamine (ibn), 1,2-diaminocyclohexane (1,2-dach), N-methylethylenediamine (Meen), N,N,N,N-tetramethylethylenediamine (Me4en), S-methyl L-cysteine (MeS-L-HCys), L-methionine (L-HMet), and 2,5-dithiahexane (dth) and dipeptide N-acetylated L-methionylglycine (MeCOMet-Gly) were studied by 1H NMR spectroscopy. The reactions were carried out in the pH range 2.0–2.5 and at 50°C. In all these reactions, palladium(II) complex bound to a methionine residue effects the regioselective cleavage of the amide bond involving the carboxylic group of methionine. We found that the rate of hydrolysis and mechanism of this reaction are strongly dependent from the nature of the chelate ligand L in palladium(II) complexes of the type cis-[Pd(L)(H2O)2]2+.  相似文献   
7.
Summary. The fact that cyclic arrangements of double bonds have a dramatic effect on the behavior of conjugated organic molecules is known since the 19th century. The fact that in monocyclic conjugated systems the size of the cycle and the number of -electrons involved is decisive for their stability (aromaticity) or lack of stability (antiaromaticity) is known since the 1930s. In polycyclic -electron systems several cyclic effects are present simultaneously and their separation became possible only recently. A molecular orbital method has been elaborated, by means of which the energy effects of individual cycles in polycyclic -electron systems can be estimated. This method is briefly outlined and illustrated by pertinent examples. An exhaustive bibliography of the topic considered is given.  相似文献   
8.
Summary The [h]phenylene C6h H2h+4 isomers are enumerated up toh=12. The numbers are compared with old and new data for C n H5 isomers of benzenoids, fluoranthenoids and biphenylenoids.
Anzahl möglicher Isomerer von Phenylenen
Zusammenfassung Die Anzahl der [h]Phenylen-Isomeren C6h H2h+4 wurde bish=12 ausgewertet. Die Zahlen wurden mit alten und neuen Daten für C n H s -Isomere von Benzenoiden, Fluoranthenoiden und Biphenyloiden verglichen.
  相似文献   
9.
An analysis is given of the behavior of an interface above a stepped substrate in the presence of an external pinning potential for the lattice solid-on-solid (SOS) interface model in 2D. Step-free energy including step-step interaction free energy is calculated, for large step separation. It is found it vanishes at temperatures lower thanT w (wetting transition temperature), which is different from the case having only one step on a substrate where, as it is well known, step-free energy vanishes at the wetting transition.  相似文献   
10.
An algebraic Kekulé structure of a benzenoid hydrocarbon is obtained from an ordinary Kekulé structure by inscribing into each hexagon the number of pi-electrons which (according to this Kekulé structure) belong to this hexagon. We show that in the case of catafusenes, there is a one-to-one correspondence between ordinary and algebraic Kekulé structures. On the other hand, in the case of perifusenes, one algebraic Kekulé structure may correspond to several ordinary Kekulé structures.  相似文献   
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