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Matthias Kriesell 《Graphs and Combinatorics》2002,18(1):133-146
Let k≤n be positive integers. A finite, simple, undirected graph is called k-critically n-connected, or, briefly, an (n,k)-graph, if it is noncomplete and n-connected and the removal of any set X of at most k vertices results in a graph which is not (n−|X|+1)-connected. We present some new results on the number of vertices of an (n,k)-graph, depending on new estimations of the transversal number of a uniform hypergraph with a large independent edge set.
Received: April 14, 2000 Final version received: May 8, 2001 相似文献
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In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure
of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered
under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some
of these along with some other recent advances on graph minors are surveyed.
Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number
16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists
Supported in part by the Research Grant P1–0297 and by the CRC program
On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia 相似文献
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The Randi? index R(G) of a (chemical) graph G is also called connectivity index. Hansen and Mélot [Variable neighborhood search for extremal graphs 6: analyzing bounds for the connectivity index, J. Chem. Inf. Comput. Sci. 43 (2003) 1-14] in their paper, characterized the chemical trees of given order and number of pendent vertices which have the minimum and maximum Randi? index, respectively. In this note, we point out the mistakes in the proofs of their results Theorems 8 and 10, while we still believe that the two theorems are true, and then we give their corrected proofs. 相似文献
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The article reviews in brief, thede novo group additivity approach and, at length, the different topological approaches to obtain predictive and internally consistent
correlations between various properties and structural features of molecules. The stress has mainly been on the molecular
connectivity method. A new rational scheme for nomenclature of connectivity indices of different orders and types is introduced.
The concept of the perturbation connectivity parameter developed by us recently has been applied to obtain correlations for
molar refraction, boiling point, molar volume, heat of atomisation, heat of combustion, heat of vaporisation, magnetic susceptibility
and critical constants of alkanes, alcohols and alkylbenzenes. A comparative study of various approaches reveals that the
present perturbation topological approach has an edge over other similar methods. 相似文献
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Our two original approaches, the first based on the topological (connectivity) index 3χv and the second based on the model of overlapping spheres (OS), were applied for the estimation of stability constants of copper(II) complexes (CuL) with ethylenediamines (N = 14) and diethylenetriamines (N = 8), and mixed complexes (CuLA) of amino acids and diethylenetriamines (N = 18). The stability constants of the ethylenediamine complexes were predicted “indirectly” from calibration models developed on diethylenetriamines and vice versa, and also by a more direct method using the leave-one-out procedure of cross validation (cv). By averaging all the estimates, stability constants were reproduced with a rms error of 0.56 and 0.43 log K units for diethylenetriamines and ethylenediamines, respectively. 相似文献
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