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51.
Joe Warren Scott Schaefer Anil N. Hirani Mathieu Desbrun 《Advances in Computational Mathematics》2007,27(3):319-338
In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates
over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located
on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation
in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric
coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review
the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how
these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide
a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally,
we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they
can be used to perform freeform deformations.
相似文献
52.
The structure, growth and stoichiometry of heteroepitaxial Pr2O3 films on Si(1 1 1) were characterized by a combined RHEED, XRD, XPS and UPS study in view of future applications as a surface science model catalyst system. RHEED and XRD confirm the growth of a (0 0 0 1) oriented hexagonal Pr2O3 phase on Si(1 1 1), matching the surface symmetry by aligning the oxide in-plane direction along the Si azimuth. After an initial nucleation stage RHEED growth oscillation studies point to a Frank-van der Merwe growth mode up to a thickness of approximately 12 nm. XPS and UPS prove that the initial growth of the Pr2O3 layer on Si up to ∼1 nm thickness is characterized by an interface reaction with Si. Nevertheless stoichiometric Pr2O3 films of high crystalline quality form on top of these Pr-silicate containing interlayers. 相似文献
53.
54.
Matthew L. Leininger C. David Sherrill Wesley D. Allen Henry F. Schaefer 《Journal of computational chemistry》2001,22(13):1574-1589
Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (CI) computations. The combination of a generalized Davidson method, a periodic two‐vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large‐scale CI matrices by eliminating the need to ever store more than three expansion vectors ( b i) and associated matrix‐vector products ( σ i), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal‐storage, single‐vector method of Olsen is found to be a reasonable alternative for obtaining energies of well‐behaved systems to within μEh accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10?10 Eh) for very large CI problems. Several approximations to the diagonal elements of the CI Hamiltonian matrix are found to allow simple on‐the‐fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant‐based wave function, and to preserve the convergence characteristics of the diagonalization procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1574–1589, 2001 相似文献
55.
Per JensenSteven S. Wesolowski Nicole R. BrinkmannNancy A. Richardson Yukio YamaguchiHenry F. Schaefer III P.R. Bunker 《Journal of Molecular Spectroscopy》2002,211(2):254-261
The potential energy surface and dipole moment surfaces of the ã4A2 electronic state of CH2+ are calculated ab initio using an augmented correlation-consistent polarized valence quadruple-ζ (aug-cc-pVQZ) basis set, with the incorporation of dynamical correlation using the coupled cluster method with single and double excitations and perturbatively connected triple excitations [CCSD(T)]. We use these surfaces in the MORBID program system to calculate rotation and rotation-vibration term values for ã-state CH2+, CD+2, and CHD+ and to simulate the rotation and rotation-vibration absorption spectrum of CH2+ in the ã4A2 electronic state. Our work is motivated by studies of CH2+ that use the Coulomb explosion imaging technique and by the goal of predicting spectra that may be obtained from discharge sources. Although the ã state is the lowest-lying excited state above the X?/Ã ground state pair, it turns out to be relatively high-lying, and we determine that Te(ã)=30447.5 cm−1. The equilibrium bond angle for ã-state CH2+ is only 77.1°; as a result the asymmetric top κ value is close to 0, and the molecule is equally far from the oblate and prolate symmetric top limits in this electronic state. 相似文献
56.
In the present record a model for the gas-phase reactions during the chemical vapor deposition (CVD) processes of group 13-15 materials is presented, based on the results of extensive quantum-chemical modeling. Thermodynamic criteria have been introduced to evaluate the importance of a range of association reactions. For the organometallic and hydride derivatives, association processes are found to be favorable both thermodynamically and kinetically. Formation of high mass association products takes place under CVD conditions, including laser-assisted CVD. Structural and thermodynamic properties of the most important ring and cluster intermediates have been predicted. The stoichiometry-controlled synthesis of the 13-15 ternary alloys and nanoparticles using cluster compounds as single-source precursors is predicted to be viable. The association pathway described may be generalized to the CVD reactions of many binary materials (12-16, 13-16, 13-15, 14-15, 14-16). 相似文献
57.
Water-oil interfacial area in porous media was determined in laboratory experiments using sand columns consisting of either 2 (water and oil) or 3 (water, oil, and air) fluid phases. Surfactant sorption at the water-oil interface was directly measured for a wide range of water, oil, and air saturations undergoing gravity drainage. Differing values of the water-oil interfacial tension were also examined. The Gibbs adsorption equation was then used to obtain values for the water-oil interfacial area. Both 2- and 3-phase water-oil experiments showed a linear increase in interfacial area with decreasing water saturation. Results also showed that interfacial areas were not affected by changes in interfacial tension. The interfacial areas in the 3-phase experiments were less than half the calculated values of the corresponding 2-phase experiments, which contradicts predictions from a conventional pore level analysis of 3-phase flow. Copyright 2000 Academic Press. 相似文献
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60.
In this paper we report the development of new apparatus for the containment and study of dense alkali metal vapors, and the use of the apparatus to study the infrared spectra of potassium vapor. The apparatus is the first to employ aerodynamic confinement of a dense alkali vapor. We have recorded absorption spectra, thermal emission spectra, and laser-induced emission spectra of dense potassium vapor. These techniques all reveal a spectral feature near 1.1 μm which we believe originates in 3Σ+g→3Σ+u transitions of the K2 molecule. 相似文献