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31.
On Best Approximations from RS-sets in Complex Banach Spaces 总被引:2,自引:0,他引:2
ChongLI 《数学学报(英文版)》2005,21(1):31-38
The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established, 相似文献
32.
Omer Ozturk Steven N. MacEachern 《Annals of the Institute of Statistical Mathematics》2004,56(4):701-720
We develop a method of randomizing units to treatments that relies on subjective judgement or on possible coarse modeling
to produce restrictions on the randomization. The procedure thus fits within the general framework of ranked set sampling.
However, instead of selecting a single unit from each set for full measurement, all units within a set are used. The units
within a set are assigned to different treatments. Such an assignment translates the positive dependence among units within
a set into a reduction in variation of contrasting features of the treatments.
A test for treatment versus control comparison, with controlled familywise error rate, is developed along with the associated
confidence intervals. The new procedure is shown to be superior to corresponding procedures based on completely randomized
or ranked set sample designs. The superiority appears both in asymptotic relative efficiency and in power for finite sample
sizes. Importantly, this test does not rely on perfect rankings; rather, the information in the data on the quality of rankings
is exploited to maintain the level of the test when rankings are imperfect. The asymptotic relative efficiency of the test
is not affected by estimation of the quality of rankings, and the finite sample performance is only mildly affected. 相似文献
33.
Hubert Grudziński 《Reports on Mathematical Physics》2004,53(2):317-328
The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P2g∧I1A3∑1≤i≤j≤3P2g(i, j)A3 acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here Pg2 denotes the projection operator onto a 2-particle antisymmetric function g2, while A3 denotes the 3-particle antisymmetrizing operator. 相似文献
34.
In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $. 相似文献
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38.
Based on the Fourier transform method, a simple closed-form expression for the on-axis power spectrum of ultrashort Gaussian pulsed beams in diffraction at a circular aperture is derived, which permits us to study spectral changes both analytically and numerically. It is shown that for diffracted pulsed beams there exist spectral red and blue shifts, spectral narrowing, and spectral switches in the near field. The aperture diffraction plays an important role in spectral switching, but both the truncation parameter and bandwidth (or equally, Fourier transform limited pulse duration) affect the behavior of spectral switches. 相似文献
39.
We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L
2-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SUq(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L
2-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India. 相似文献
40.