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A. D. Biggs D. Rusin I. W. A. Browne A. G. de Bruyn N. J. Jackson L. V. E. Koopmans J. P. McKean S. T. Myers R. D. Blandford K.-H. Chae C. D. Fassnacht M. A. Norbury T. J. Pearson P. M. Phillips A. C. S. Readhead P. N. Wilkinson 《Monthly notices of the Royal Astronomical Society》2003,338(4):1084-1088
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Suppose that ¯(x1),...,¯Z(xn). are observations of vector-valued random function ¯(x). In the isotropic situation, the sample variogram γ*(h) for a given lag h is $$\bar \gamma ^ * (h) = \frac{1}{{2N(h)}}\mathop \sum \limits_{s(h)} (\overline Z (x_1 ) - \overline Z (x_1 )) \overline {(Z} (x_1 ) - \overline Z (x_1 ))^T $$ where s(h) is a set of paired points with distance h and N(h) is the number of pairs in s(h).. For a selection of lags h1, h2, .... hk such that N (h1) > O. we obtain a ktuple of (semi) positive definite matrices $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ . We want to determine an orthonormal matrix B which simultaneously diagonalizes the $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ or nearly diagonalizes them in the sense that the sum of squares of offdiagonal elements is small compared to the sum of squares of diagonal elements. If such a B exists, we linearly transform $\overline Z (x)$ by $\overline Y (x) = B\overline Z (x)$ . Then, the resulting vector function $\overline Y (x)$ has less spatial correlation among its components than $\overline Z (x)$ does. The components of $\overline Y (x)$ with little contribution to the variogram structure may be dropped, and small crossvariograms fitted by straightlines. Variogram models obtained by this scheme preserve the negative definiteness property of variograms (in the matrix-valued function sense). A simplified analysis and computation in cokriging can be carried out. The principles of this scheme arc presented in this paper. 相似文献
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This paper investigates the role of housing age in constraining residential mobility, measured as the percent of households that have moved into their homes in the past 15 months. The leading explanation for why mobility rates differ so much among regions of the United States has been the overall level of growth. The present analysis shows that the growth effect operates through both the newness of population (migration) and the newness of housing available for occupancy by all local residents. The posited explanation for this housing age effect is that progressively older units contain increasingly settled occupants, yielding fewer opportunities for in-movers in areas with older housing. It is empirically demonstrated that households in older housing have lower likelihood of recent mobility even after controlling for age, tenure, migration status, and state location of residence. The analysis reveals the temporal interdependency of mobility, migration, person age, and housing age. 相似文献
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Myers developed a matrix form of the cokriging equations, but one that entails the solution of a large system of linear equations.
Large systems are troublesome because of memory requirements and a general increase in the matrix condition number. We transform
Myers’s system into a set of smaller systems, whose solution gives the classical kriging results, and provides simultaneously
a nested set of lower dimensional cokriging results. In the course of developing the new formulation we make an interesting
link to the Cauchy-Schwarz condition for the invertibility of a system, and another to a simple situation of coregionalization.
In addition, we proceed from these new equations to a linear approximation to the cokriging results in the event that the
crossvariograms are small, allowing one to take advantage of a recent results of Xie and others which proceeds by diagonalizing
the variogram matrix function over the lag classes. 相似文献
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The structures of sodium silicate and aluminosilicate glasses quenched from melts at high pressure (6-10 GPa) with varying degrees of polymerization (fractions of nonbridging oxygen) were explored using solid-state NMR [17O and 27Al triple-quantum magic-angle spinning (3QMAS) NMR]. The bond connectivity in melts among four and highly coordinated network polyhedra, such as [4]Al, [5,6]Al, [4]Si, and [5,6]Si, at high pressure is shown to be significantly different from that at ambient pressure. In particular, in the silicate and aluminosilicate melts, the proportion of nonbridging oxygen (NBO) generally decreases with increasing pressure, leading to the formation of new oxygen clusters that include 5- and 6-coordinated Si and Al in addition to 4-coordinated Al and Si, such as [4]Si-O-[5,6]Si, [4]Si-O-[5,6]Al and Na-O-[5,6]Si. While the fractions of [5,6]Al increase with pressure, the magnitude of this increase diminishes with increasing degrees of ambient-pressure polymerization under isobaric conditions. Incorporating the above structural information into models of melt properties reproduces the anomalous pressure-dependence of O2− diffusivity and viscosity often observed in silicate melts. 相似文献
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Solubility mechanisms of water in depolymerized silicate melts quenched from high temperature (1000°-1300°C) at high pressure (0.8-2.0 GPa) have been examined in peralkaline melts in the system Na2O-SiO2-H2O with Raman and NMR spectroscopy. The Na/Si ratio of the melts ranged from 0.25 to 1. Water contents were varied from ∼3 mol% and ∼40 mol% (based on O = 1). Solution of water results in melt depolymerization where the rate of depolymerization with water content, ∂(NBO/Si)/∂XH2O, decreases with increasing total water content. At low water contents, the influence of H2O on the melt structure resembles that of adding alkali oxide. In water-rich melts, alkali oxides are more efficient melt depolymerizers than water. In highly polymerized melts, Si-OH bonds are formed by water reacting with bridging oxygen in Q4-species to form Q3 and Q2 species. In less polymerized melts, Si-OH bonds are formed when bridging oxygen in Q3-species react with water to form Q2-species. In addition, the presence of Na-OH complexes is inferred. Their importance appears to increase with Na/Si. This apparent increase in importance of Na-OH complexes with increasing Na/Si (which causes increasing degree of depolymerization of the anhydrous silicate melt) suggests that water is a less efficient depolymerizer of silicate melts, the more depolymerized the melt. This conclusion is consistent with recently published 1H and 29Si MAS NMR and 1H-29Si cross polarization NMR data. 相似文献
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