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111.
Annals of Combinatorics - We define operators on semistandard shifted tableaux and use Stembridge’s local characterization for regular graphs to prove they define a crystal structure. This... 相似文献
112.
The g(44) grating is an electroholographic transmission grating in which the applied field is perpendicular to both the grating vector and the wave vector of the incident beam. It is argued that in this configuration the incident beam traverses through a periodically rotating index ellipsoid. It is shown that in the g(44) configuration the Bragg condition is fulfilled for a specific value of the applied field and for a diffracting beam polarization that is perpendicular to that of the incident beam. Consequently, the g(44) grating can be used as an electrically controlled filter. Tunability of 7 nm is demonstrated in a 2mm thick grating. 相似文献
113.
We have recently proposed a protocol for retrieving multidimensional magnetic resonance spectra and images within a single scan, based on a spatial encoding of the spin interactions. The spatial selectivity of this encoding process also opens up new possibilities for compensating magnetic field inhomogeneities; not by demanding extreme uniformities from the B(0) fields, but by compensating for their effects at an excitation and/or refocusing level. This potential is hereby discussed and demonstrated in connection with the single-scan acquisition of high-definition multidimensional images. It is shown that in combination with time-dependent gradient and radiofrequency manipulations, the new compensation approach can be used to counteract substantial field inhomogenities at either global or local levels over relatively long periods of time. The new compensation scheme could find uses in areas where heterogeneities in magnetic fields present serious obstacles, including rapid studies in regions near tissue/air interfaces. The principles of the B(0) compensation method are reviewed for one- and higher-dimensional cases, and experimentally demonstrated on a series of 1D and 2D single-scan MRI experiments on simple phantoms. 相似文献
114.
Let X be a normed space that satisfies the Johnson–Lindenstrauss lemma (J–L lemma, in short) in the sense that for any integer
n and any x
1,…,x
n
∈X, there exists a linear mapping L:X→F, where F⊆X is a linear subspace of dimension O(log n), such that ‖x
i
−x
j
‖≤‖L(x
i
)−L(x
j
)‖≤O(1)⋅‖x
i
−x
j
‖ for all i,j∈{1,…,n}. We show that this implies that X is almost Euclidean in the following sense: Every n-dimensional subspace of X embeds into Hilbert space with distortion
22O(log*n)2^{2^{O(\log^{*}n)}}
. On the other hand, we show that there exists a normed space Y which satisfies the J–L lemma, but for every n, there exists an n-dimensional subspace E
n
⊆Y whose Euclidean distortion is at least 2Ω(α(n)), where α is the inverse Ackermann function. 相似文献
115.
We show that the cyclic lamplighter group C 2 ? C n embeds into Hilbert space with distortion $\mathrm{O}(\sqrt{\log n})We show that the cyclic lamplighter group C
2
≀
C
n
embeds into Hilbert space with distortion
O(?{logn})\mathrm{O}(\sqrt{\log n})
. This matches the lower bound proved by Lee et al. (Geom. Funct. Anal., 2009), answering a question posed in that paper. Thus, the Euclidean distortion of C
2
≀
C
n
is
\varTheta(?{logn})\varTheta(\sqrt{\log n})
. Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Euclidean
embedding of a finite group can always be chosen to be equivariant, as shown by Aharoni et al. (Isr. J. Math. 52(3):251–265,
1985) and by Gromov (see de Cornulier et. al. in Geom. Funct. Anal., 2009), such representation-theoretic considerations suggest a general tool for obtaining upper and lower bounds on Euclidean embeddings
of finite groups. 相似文献
116.
Let (X,d
X
) be an n-point metric space. We show that there exists a distribution over non-contractive embeddings into trees f: X → T such that for every x ∈ X, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs,
including fault-tolerant versions of k-median and facility location. 相似文献
117.
Let (X,d,μ) be a metric measure space. For ∅≠R⊆(0,∞) consider the Hardy-Littlewood maximal operator
118.
A novel method for benzylic hydroxylation is introduced based on the use of photo-excited nitrobenzene. Applying this method 17β-acetoxy-3-methoxy-estra-1,3,5(10)-triene (I) is efficiently converted to 17β-acetoxy-9α-hydroxy-3-methoxy-estra-1,3,5(10)-triene (IIIa). 相似文献
119.
We show that any embedding of the level k diamond graph of
Newman and Rabinovich [NR] into Lp, 1 < p 2, requires distortion at
least
. An immediate corollary is that there exist arbitrarily
large n-point sets
such that any D-embedding of X into
requires
. This gives a simple proof of a recent result of Brinkman
and Charikar [BrC] which settles the long standing question of whether
there is an L1 analogue of the Johnson-Lindenstrauss dimension reduction
lemma [JL]. 相似文献
120.
Shiri Artstein Keith M. Ball Franck Barthe Assaf Naor 《Journal of the American Mathematical Society》2004,17(4):975-982
It is shown that if are independent and identically distributed square-integrable random variables, then the entropy of the normalized sum
is an increasing function of .
is an increasing function of .
The result also has a version for non-identically distributed random variables or random vectors.