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71.
For many orbital measures μ, on SU(n), we show that either μk ∈ L2 or μk is singular to L1. The least k for which μk ∈ L2 is determined and is shown to be the minimum k for which the k-fold product of the conjugacy class supporting the measure has positive measure. It would be interesting to know if all orbital
measures satisfy this dichotomy. 相似文献
72.
Solid-phase production of carbon nanotubes 总被引:4,自引:0,他引:4
W.K. Hsu Y.Q. Zhu S. Trasobares H. Terrones M. Terrones N. Grobert H. Takikawa J.P. Hare H.W. Kroto D.R.M. Walton 《Applied Physics A: Materials Science & Processing》1999,68(4):493-495
4 C3) are heated to 1000–1100 °C for 2–4 hr in an argon flow. Carbon nanotubes are formed when metal powders, e.g. Fe, Co, Y and
Ni, are also present.
Received: 2 February 1999 / Accepted: 3 February 1999 相似文献
73.
For many orbital measures μ, on SU(n), we show that either μk ∈ L2 or μk is singular to L1. The least k for which μk ∈ L2 is determined and is shown to be the minimum k for which the k-fold product of the conjugacy class supporting the measure has positive measure. It would be interesting to know if all orbital
measures satisfy this dichotomy. 相似文献
74.
75.
76.
In this paper we present a derivative-free optimization algorithm for finite minimax problems. The algorithm calculates an approximate gradient for each of the active functions of the finite max function and uses these to generate an approximate subdifferential. The negative projection of 0 onto this set is used as a descent direction in an Armijo-like line search. We also present a robust version of the algorithm, which uses the ‘almost active’ functions of the finite max function in the calculation of the approximate subdifferential. Convergence results are presented for both algorithms, showing that either f(x k )→?∞ or every cluster point is a Clarke stationary point. Theoretical and numerical results are presented for three specific approximate gradients: the simplex gradient, the centered simplex gradient and the Gupal estimate of the gradient of the Steklov averaged function. A performance comparison is made between the regular and robust algorithms, the three approximate gradients, and a regular and robust stopping condition. 相似文献
77.
Optimization Letters - Originally developed in 1954, positive bases and positive spanning sets have been found to be a valuable concept in derivative-free optimization (DFO). The quality of a... 相似文献
78.
A set of integers S is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant. 相似文献
79.
We consider the challenge of numerically comparing optimization algorithms that employ random-restarts under the assumption that only limited test data is available. We develop a bootstrapping technique to estimate the incumbent solution of the optimization problem over time as a stochastic process. The asymptotic properties of the estimator are examined and the approach is validated by an out-of-sample test. Finally, three methods for comparing the performance of different algorithms based on the estimator are proposed and demonstrated with data from a real-world optimization problem. 相似文献
80.
We prove that if ${\mu _{a}\,{=}\,m_{K}*\delta _{a}*m_{K}}$ is the K-bi-invariant measure supported on the double coset ${KaK\subseteq SU(n)}$ , for K = SO(n), then ${\mu _{a}^{k}}$ is absolutely continuous with respect to the Haar measure on SU(n) for all a not in the normalizer of K if and only if k ≥ n. The measure, μ a , supported on the minimal dimension double coset has the property that ${\mu _{a}^{n-1}}$ is singular to the Haar measure. 相似文献