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1.
A two-dimensional framework (G,p) is
a graph G = (V,E) together with a map p: V → ℝ2. We view (G,p) as a straight line realization of G in ℝ2. Two realizations of G are equivalent if the corresponding edges in the two frameworks have the same length.
A pair of vertices {u,v} is globally linked in G if %and for all equivalent frameworks (G,q), the distance between the points
corresponding to u and v is the same
in all pairs of equivalent generic realizations of G. The graph G is globally rigid
if all of its pairs of vertices are globally linked. We extend the characterization of globally rigid graphs given by the
first two authors [13] by characterizing globally linked pairs in M-connected graphs, an important family of rigid graphs.
As a byproduct we simplify the proof of a result of Connelly [6] which is a key step in the characterization of globally rigid
graphs. We also determine the number of distinct realizations of an M-connected graph, each of which is equivalent to a given
generic realization. Bounds on this number for minimally rigid graphs were obtained by Borcea and Streinu in [3]. 相似文献
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3.
Let G = (V,E) be a graph or digraph and r : V → Z+. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν1,…,νr(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003 相似文献
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6.
Leavitt AJ Wyrwas RB Wallace WT Serrano DS Arredondo MG Leslie LM Khan FA Whetten RL 《The journal of physical chemistry. A》2005,109(28):6218-6222
Carbon-cluster anions, CN-, are very reactive toward SO2 (sticking probability of 0.012 +/- 0.005 for C27- at 25 degrees C), in contrast to their inertness toward other common atmospheric gases and pollutants. In flow reactor experiments at ambient temperature and near atmospheric pressure, primary adsorption of SO2 by the carbon cluster anions, N = 4-60, yields CNSO2- or CN-1S-. The inferred elimination of neutral CO2 is also detected as meta-stable decay in collision-induced dissociation. At higher temperatures, the reaction of SO2 with nascent carbon clusters yields CN-1SO- as well as undetected CO. The size-dependent initial reactivity reflects the previously established structural transitions (i.e., from chain to cyclic to cage structures). Such carbon clusters are formed in sooting flames and may act as nuclei for the formation of primary soot particles and serve as models for the local structural features of active soot particle sites for black-carbon soot. The facile generation of reactive carbon-sulfide and -sulfinate units may therefore have implications for understanding the health and environmental effects attributed to the coincidence of soot and SO2. 相似文献
7.
Spikmans V Lane SJ Leavens B Manz A Smith NW 《Rapid communications in mass spectrometry : RCM》2002,16(14):1377-1388
A system is presented that demonstrates the principle of on-line and on-chip post-column derivatisation reactions in micro-high-performance liquid chromatography (micro-HPLC) hyphenated to electrospray time-of-flight mass spectrometry (ESI-TOFMS). In this micro-HPLC-chip-MS set-up, the analytes are separated using gradient micro-HPLC and subsequently derivatised on-chip and detected. One of the major limitations of MS detection is its dependency on the degree of ionisation, which is widely variable and compound-specific. Optimising and controlling the degree of ionisation in a simple manner would allow MS detection to be truly generic. One way of achieving this is by pre-ionisation of analytes using simple derivatisation procedures that are both rapid and quantitative. Performing this in situ on the system described here overcomes issues of sample handling and efficiency losses when time-consuming "bench chemistry" is necessary prior to analysis. The power of the system is demonstrated by the separation of primary and secondary amines, which are subsequently derivatised with a positively charged phosphonium complex and detected in an enhanced manner. Typically, molecular cations (M(+)) are detected showing that the ionisation process is dominated by the phosphonium species, leading to more constant ionisation for a variety of compounds. In addition, stable isotopically labelled ((12)C/(13)C)-phosphonium reagent is used for the reactions, allowing for inherent signal/noise (S/N) improvement and automated data processing using cluster analysis. A similar reaction scheme is used for the derivatisation of ketones and aldehydes, also demonstrating dramatic increases in sensitivity, especially with increasing temperature. Minimal loss in chromatographic fidelity in terms of retention times is observed by the introduction of the micromixer chip into the system. Optimal flow rates in micro-HPLC and ESI-MS are compatible with flow rates for the chip as well as a multitude of in-line optical detectors including UV and fluorescence. In addition, the micromixer chip can be positioned pre-column if preferred. The system is robust, easily fully automated and applicable to a wide variety of reactions. The system has a major advantage in its simple robust connection to the "normal scale" outside world. 相似文献
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9.
In the structure Ba12F19Cl5 [hexagonal space group P6 2m] the two chlorides on the sites Cl(1) and Cl(2) can partially be replaced by bromide ions. Single crystals of the type Ba12F19ClδBr5–δ with a chloride to bromide ratio up to 2 : 3 could be obtained by cooling a flux of 75 mol% BaF2 and 25 mol% BaX2 with X = Cl, Br. The crystal quality decreases with increasing bromide concentration. Structural parameters of five selected single crystals with different chloride/bromide ratio were studied by single crystal X-ray diffraction methods. The refined total Cl?/Br? population ratio in the crystals is close to the one of the flux. The lattice parameters and interatomic distances change in various ways, when the smaller chloride ion is replaced by the bigger bromide ion. The refinements show a statistical disorder on the halide sites with preferential bromide substitution on site Cl(1). 相似文献
10.
57Fe electric and magnetic hyperfine parameters were calculated for a series of 10 iron model complexes, covering a wide range of oxidation and spin states. Employing the B3LYP hybrid method, results from nonrelativistic density functional theory (DFT) and quasi-relativistic DFT within the zero-order regular approximation (ZORA) were compared. Electron densities at the iron nuclei were calculated and correlated with experimental isomer shifts. It was shown that the fit parameters do not depend on a specific training set of iron complexes and are, therefore, more universal than might be expected. The nonrelativistic and quasi-relativistic electron densities gave fit parameters of similar quality; the ZORA densities are only shifted by a factor of 1.32, upward in the direction of the four-component Dirac-Fock value. From a correlation of calculated electric field gradients and experimental quadrupole splittings, the value of the 57Fe nuclear quadrupole moment was redetermined to a value of 0.16 barn, in good agreement with other studies. The ZORA approach gave no additional improvement of the calculated quadrupole splittings in comparison to the nonrelativistic approach. The comparison of the calculated and measured 57Fe isotropic hyperfine coupling constants (hfcc's) revealed that both the ZORA approach and the inclusion of spin-orbit contributions lead to better agreement between theory and experiment in comparison to the nonrelativistic results. For all iron complexes with small spin-orbit contributions (high-spin ferric and ferryl systems), a distinct underestimation of the isotropic hfcc's was found. Scaling factors of 1.81 (nonrelativistic DFT) and 1.69 (ZORA) are suggested. The calculated 57Fe isotropic hfcc's of the remaining model systems (low-spin ferric and high-spin ferrous systems) contain 10-50% second-order contributions and were found to be in reasonable agreement with the experimental results. This is assumed to be the consequence of error cancellation because g-tensor calculations for these systems are of poor quality with the existing DFT approaches. Excellent agreement between theory and experiment was found for the 57Fe anisotropic hfcc's. Finally, all of the obtained fit parameters were used for an application study of the [Fe(H2O)6]3+ ion. The calculated spectroscopic data are in good agreement with the Mossbauer and electron paramagnetic resonance results discussed in detail in a forthcoming paper. 相似文献