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1.
Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial
differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences.
By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via
a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast.
Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized
matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant
matrix.
By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the
block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method.
A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse
GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are
preserved.
AMS subject classification (2000) 43A30, 65T99, 20B25 相似文献
2.
Jan E. Åman Ingemar Bengtsson Narit Pidokrajt 《General Relativity and Gravitation》2006,38(8):1305-1315
The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Supported by VR. 相似文献
3.
4.
Òscar Rubio-Pons Boris Minaev Oleksandr Loboda Hans Ågren 《Theoretical chemistry accounts》2005,113(1):15-27
The phosphorescence spectrum of p-dichlorobenzene has been calculated using multiconfiguration self-consistent-field wave functions and the quadratic response technique. Attention has been paid to the intensity distribution of the singlet–triplet (3B1u1Ag) transition through a number of vibronic subbands. The second order spin–orbit coupling (SOC) contribution to the spin splitting of the 3B1u (3*) state is found to be almost negligible, and the calculations therefore provide a good estimate for the zero-field splitting (ZFS) parameters based only on the electron spin–spin coupling expectation values. Nuclear quadrupole resonance constants for the different Cl isotopes are also calculated to accomplish the ZFS assignment. The electric dipole activity of the spin sublevels in the triplet–singlet transitions to the ground-state vibrational levels is estimated by calculations of derivatives using distorted geometries which are shifted from the equilibrium position along different vibrational modes. A vibrational analysis of the phosphorescence spectrum, based on the SOC-induced mixing of the singlet and triplet states calculated along different vibrational modes, provides reasonable agreement with experimental data.Acknowledgment O. R.-P. would like to thank the European MOLPROP network for support. The authors thank Alexander Baev for fruitful discussions. This work was supported by the Swedish Royal Academy of Science (KVA). 相似文献
5.
Åse Støg»rd 《Chemical physics letters》1975,36(3):357-360
Ab initio as well as semi-empirical SCF MO calculations are presented for ClCN and ONCl. The relative intensities for Cl Kβ emission in the two molecules were calculated. The calculated spectra from the ab initio wavefunctions are in excellent agreement with experiments. 相似文献
6.
As bio‐inspired chemical model of the oxygen‐evolving complex (OEC) in photosystem II, a new tyrosine‐modified corrole ligand 3 and its high‐valent copper and manganese complexes 3a and 3b were synthesized and characterized. The copper complexes 1a and 2a of corrole 1 and 2 were also prepared for comparison. The emission property indicates that the emission of ligands 2 and 3 is located at 670 nm, but no emission is observed for their metal complexes due to its suppression by the metal center. The electrochemical study shows that 3a might dimerize at the first two reversible oxidations, a behavior which was not observed in the case of 1a and 2a . The corrolato manganese(IV) complex 3b shows one reversible reduction and one quasireversible oxidation at ?0.17 and 0.77 V vs. Ag/Ag+, respectively. 相似文献
7.
High-temperature equilibrium calculations are used to study potential interferences in the determination of aluminium by flameless a.a.s. The conditions for the formation of interfering aluminium compounds like AlO(g), Al2O(g), Al2O3(s), AlOH(g), AlH(g), AlHO2(g), AlS(g), AlN(g), AlN(s) and AlCl(g) have been calculated. The influence of kinetic parameters on the equilibrium calculations for the reactions involving carbon—oxygen and carbon—sulphur has been established by varying the input amount of carbon. The results indicate that even in the nanomole range the presence of elements like H, O, N, Cl and S may cause severe interferences during the atomization step (2300–2900 K) 相似文献
8.
Ideal conditions for the determination of phosphorus by graphite-furnace atomic absorption spectrometry are investigated by the use of high-temperature equilibrium calculations. All reasonable reaction products resulting from the reaction between P, C, O, H, N, Ca and Ar are considered. The calculations show that phosphorus forms the volatile monoxide and dioxide molecules below 1800 K (Po2? 10-13 atm.). At higher temperatures the relative amount of atomic phosphorus is mainly controlled by the equilibrium between monatomic and diatomic phosphorus. The significance of the theoretical ' study was investigated experimentally. The relative amounts of P2 and PO were monitored by molecular absorption using vaporization under isothermal conditions; the interfering effects of Ca, N2, H2, and O2 on the atomic absorption signal for phosphorus were also studied. The sensitivity was greatly dependent on graphite tube conditions as well as the heating rate of the furnace. For CaHPO4 the sensitivity for phosphorus was 4.5 × lO-8 g. If samples were introduced into a preheated tube, this value was improved to 2 × 10-9 g. 相似文献
9.
The extracellular β-xylosidase (EC 3.2.1.37) excreted by the thermophilic eubacteriumRhodothermus marinus when grown on xylan has been investigated. The enzyme has been partially purified by ultrafiltration and gel filtration, and some of its characteristics are presented.Rhodothermus marinus grew on xylan with μmax= 0.4 h? and the α-xylosidase activity was 50 nkat/mL after 24 h in a batch fermentation. The α-xylosidase activity had a half-life of more than 1 h at 90°C and of 14 h at 85 °C. At 80°C, 80% of the initial activity remained after 24 h. The initial activity increased with increasing temperature, showing maximal activity at 90°C. The β-xylosidase had a pH-optimum of 6 and was stable in the range between pH 5 and 9. At pH 10 and 11, 82 and 66%, respectively, of the initial activity remained after 24 h when incubated at 65°C. The molecular weight was estimated to be 169,000 dalton by gelfiltration. 相似文献
10.
Simplified method for the Re-Os dating of molybdenite using acid digestion and isotope dilution ICP-MS 总被引:1,自引:0,他引:1
An analytical method was developed for Os-Re dating of molybdenite. The method is based on determination of Os and Re concentrations in molybdenite by isotope dilution inductively-coupled plasma mass spectrometry (ID-ICP-MS). Sample digestion and sample/spike equilibration were achieved by a two-stage autoclave-based procedure using a mixture of nitric and sulphuric acids. Os was separated from the sample digest by modified single-stage distillation of osmium tetraoxide (OsO4) using elevated temperature and on-line addition of hydrogen peroxide. OsO4(g) was trapped in a mixture of 0.05% thiourea in 0.05 M sodium hydroxide. An anion-exchange column was used to separate Re from excess Mo in the solution remaining after distillation. Os and Re isotope ratio measurements were performed by single-collector, double focusing inductively-coupled plasma mass spectrometry (ICP-MS) with on-line mass-bias correction. Typical instrumental precision was in the range 0.02-0.2% relative standard deviation (R.S.D.) depending on the analyte concentrations. Notorious Os memory effects in the ICP-MS introduction system were eliminated using 5% ammonia solution, both as matrix for final dilution of the trap mixture as well as for washing between the samples. The reproducibility of the entire analytical procedure was accessed by replicate dating of two molybdenite standards and three molybdenite separates, and was found to be in the range 0.87-1.52% R.S.D. Though accuracy of the method is limited by difficulties in evaluating exact concentration of Os in spike solution, ages obtained in the course of these work agrees well with previously published data. 相似文献