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31.
厄米-双曲余弦-高斯光束的瞄准稳定性 总被引:1,自引:0,他引:1
用失调叠加积分的方法 ,对厄米双曲余弦高斯光束的瞄准稳定性作了研究 ,得到了厄米双曲余弦高斯光束失调因子 ηm2 的精确解析公式和近似解析公式 ,并用数值计算了相对横向偏移和相对角向偏移对失调因子ηm2 的影响以及对精确解析公式和近似解析公式的适用范围作了分析和说明。 相似文献
32.
33.
In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem—namely that of expressing the mean residual life in terms of the failure rate—typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure. 相似文献
34.
For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) zi, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics Smax=maxu S(u) and Smin=minu S(u), where u is a unit vector and nS(u) is the sum of squares of u′zi's. In this paper, we also consider another test statistic Srange=Smax−Smin. We provide formulas for the P-values of Smax, Smin, Srange by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given. 相似文献
35.
Quantization consists in studying the L
r
-error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer(4) and Dereich et al.
(3) relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L
r
-quantization error from logarithmic small ball asymptotics and vice versa. 相似文献
36.
Stefan Jaschke Claudia Klüppelberg Alexander Lindner 《Journal of multivariate analysis》2004,88(2):252-273
We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension. 相似文献
37.
In this paper we investigate the
probabilistic linear $(n,\delta)$-widths and $p$-average linear
$n$-widths of the Sobolev space $W^r_2$ equipped with the Gaussian
measure $\mu$ in the $L_{\infty}$-norm, and determine the
asymptotic equalities
\begin{eqnarray*}
\lambda_{n,\delta}(W^r_2,\mu,L_{\infty})
&\asymp&\frac{\sqrt{\ln
(n/\delta)}}{n^{r+(s-1)/2}},\\[3pt]
\lambda^{(a)}_n(W^r_2,\mu,L_{\infty})_p &\asymp&\frac{\sqrt{\ln
n}}{n^{r+(s-1)/2}}, \qquad 0 < p < \infty.
\end{eqnarray*} 相似文献
38.
Wensheng Wang 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(5):619-631
The almost sure sample function behavior of the vector-valued fractional Brownian sheet is investigated. In particular, the global and the local moduli of continuity of the sample functions are studied. These results give precise information about the continuity and the oscillation behavior of the sample functions. 相似文献
39.
高斯光束照射下的圆盘夫琅禾费衍射 总被引:9,自引:3,他引:6
推导了高斯光束照射圆孔或圆盘的衍射场普遍表达式,计算了半波带数接近于零的情况下上述衍射场的数据,进而分析了圆盘衍射场在艾里斑中增加一个暗环的原因。 相似文献
40.
Nicholas J. Curro Charles P. Slichter 《Journal of magnetic resonance (San Diego, Calif. : 1997)》1998,130(2):186-194
Measurement ofT2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT2Gand show thatT2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa2Cu4O8, we find a correction on the order of 10% inT2Gand using the corrected values we find that the isotope ratio63T2G/65T2Gagrees with theory. 相似文献