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41.
To reduce bandwidth in elliptic curve cryptography one can transmit only x-coordinates of points (or x-coordinates together with an extra bit). This is called point compression. For further computation using the points one can
either recover the y-coordinates by taking square roots or one can use point multiplication formulae which use x-coordinates only. We consider how to efficiently use point compression in pairing-based cryptography when the embedding degree
is even. We give a method to compute compressed pairings using x-coordinates only. We also show how to compute the compressed pairings using two x-coordinates and one y-coordinate. Our methods are more efficient than taking square roots when the embedding degree is small. We implemented the
algorithms in the case of embedding degree 2 curves over where (mod 4) and found that our methods can be 10–15% faster than the analogous methods using square roots.
相似文献
42.
Serguei Zernov Victoria Zinde-Walsh John W. Galbraith 《Journal of multivariate analysis》2009,100(3):497-508
Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples. 相似文献
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Because of its numerous applications to physics, there have been many solutions published on the problem of reducing a given irreducible representation (irrep) of the unitary unimodular group SU(3) into irreps of the proper orthogonal subgroup SO(3). Such solutions are generally based on an arbitrary construction of a nonorthogonal basis of the highest weight space for an irrep of SO(3), followed by an equally arbitrary orthonormalization procedure. This paper presents a unique solution of this problem based on the intrinsic structure of the multiplicity function, which is a function M
L(p, q) giving the number of times irrep[L] of SO(3) is contained in irrep[pq0] of SU(3). This structure is implemented uniquely into the reduction problem through the use of the SU(3) pattern calculus.Work performed under the auspices of the U.S. Department of Energy. 相似文献
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Three-center four-electron (3c4e) pi bonding systems analogous to that of the ozone molecule have been studied using modern valence bond theory. Molecules studied herein consist of combinations of first row atoms C, N, and O with the addition of H atoms where appropriate in order to preserve the 3c4e pi system. Breathing orbital valence bond (BOVB) calculations were preformed at the B3LYP/6-31G**-optimized geometries in order to determine structural weights, pi charge distributions, resonance energies, and pi bond energies. It is found that the most weighted VB structure depends on atomic electronegativity and charge distribution, with electronegativity as the dominant factor. By nature, these systems are delocalized, and therefore, resonance energy is the main contributor to pi bond energies. Molecules with a single dominant VB structure have low resonance energies and therefore low pi bond energies. 相似文献
47.
Forgan RS Davidson JE Galbraith SG Henderson DK Parsons S Tasker PA White FJ 《Chemical communications (Cambridge, England)》2008,(34):4049-4051
Attaching dialkylaminomethyl arms to commercial phenolic oxime copper extractants yields reagents which transport base metal salts very efficiently by forming neutral 1 ratio 1 or 1 ratio 2 complexes with zwitterionic forms of the ligands. 相似文献
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