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[en] We developed a linear theory of backward stimulated Brillouin scatter (BSBS) of a spatially and temporally random laser beam relevant for laser fusion. Our analysis reveals a new collective regime of BSBS (CBSBS). Its intensity threshold is controlled by diffraction, once cTc exceeds a laser speckle length, with Tc the laser coherence time. The BSBS spatial gain rate is approximately the sum of that due to CBSBS, and a part which is independent of diffraction and varies linearly with Tc. The CBSBS spatial gain rate may be reduced significantly by the temporal bandwidth of KrF-based laser systems compared to the bandwidth currently available to temporally smoothed glass-based laser systems
[en] Calculation of low-lying excitation spectra and electromagnetic responses of doubly closed shell nuclei within Random Phase Approximation theory using four phenomenological effective interactions was made. Particular attention has been paid to observe the sensitivity of the quantities studied to different interactions. Then self-consistent RPA calculations were made to test the validity of the finite range D1 Gogny interaction. For all the nuclei investigated was found that this interaction inverts the energies of all the magnetic states forming isospin doublets. Then an improvement of discrete RPA was illustrated that treats the continuum particle space correctly using an expansion on Sturmian functions basis.
[en] This paper considers the problem of determining a confidence interval for the difference between two treatments in a simplified sequential paired clinical trial, which is analogous to setting an interval for the drift of a random walk subject to a parabolic stopping boundary. Three bootstrap methods of construction are applied: Efron's accelerated bias-covered, the DiCiccio-Romano, and the bootstrap-t. The results are compared with a theoretical approximate interval due to Siegmund. Difficulties inherent in the use of these bootstrap methods in a complex situations are illustrated. The DiCiccio-Romano method is shown to be the easiest to apply and to work well. 13 refs
[en] By coupling a doorway state to a sea of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically different from the standard description of doorway states in the shell model. We derive the Pastur equation in the limit of large matrix dimension and show that the results agree with those of matrix diagonalization in large spaces. The complexity of the Pastur equation does not allow for an analytical approach that would approximately describe the doorway state. Our numerical results display unexpected features: The coupling of the doorway state with states of opposite energy leads to strong mutual attraction
[en] We demonstrate that the cross sections for photoionization of the outer shells are noticeably modified at the photon energies close to the thresholds of ionization of the inner shells due to correlations with the latter. The correlations may lead to increase or to decrease of the cross sections just above the ionization thresholds.
[en] D'Espagnat and others have shown that different preparation procedures that mix systems prepared in unequivalent states and objectively different, are nevertheless assigned the same state. This unpalatable result follows from the usual interpretative rules of quantum mechanics. It is shown here that this result is incompatible with the strengthened interpretative rules (requiring randomness of the measurement outcome sequence) recently proposed. Thus, the randomness requirement restores reasonableness
[en] We investigate small deviation probabilities of the cumulative sum of independent positive random variables, the common distribution of which decreases at zero not faster than exponential function.
[en] Some of known inequalities for the uniform distance between distributions of sequential sums of independent identically distributed random variables are considered. In the case where the distribution F has 0 as the q-quantile, an upper bound for the absolute constant in the inequality is given.
[en] In order to formulate and examine the central limit theorem for a binary tree numerically, a method for generating random binary trees is presented. We first propose the correspondence between binary trees and a certain type of binary sequences (which we call Dyck sequences). Then, the method for generating random Dyck sequences is shown. Also, we propose the method of branch ordering of a binary tree by means of only the corresponding Dyck sequence. We confirm that the method is in good consistency with the topological analysis of binary trees known as the Horton-Strahler analysis. Two types of central limit theorem are numerically confirmed, and the obtained results are expressed in simple forms. Furthermore, the proposed method is available for a wide range of the topological analysis of binary trees.