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991.
Yusuf Z. Umul 《Optics & Laser Technology》2010,42(8):1323-1327
The paraxial wave equation is a reduced form of the Helmholtz equation. Its solutions can be directly obtained from the solutions of the Helmholtz equation by using the method of complex point source. We applied the same logic to quantum mechanics, because the Schrödinger equation is parabolic in nature as the paraxial wave equation. We defined a differential equation, which is analogous to the Helmholtz equation for quantum mechanics and derived the solutions of the Schrödinger equation by taking into account the solutions of this equation with the method of complex point source. The method is applied to the problem of diffraction of matter waves by a shutter. 相似文献
992.
993.
994.
Dedicated to Professor Gerry Ladas on his sixtieth birthday in acknowledgement of his leading role of difference equations. We extend the notions of dichotomy and trichotomy to nonlinear ordinary difference equations. This is accomplished by using two completely different approaches. In the first approach we use a notion, independent of the nature of our difference equation, called tracking. In the second approach we introduce a discrete analogue of dichotomy and trichotomy in variation. 相似文献
995.
996.
《Journal of computational and graphical statistics》2013,22(2):399-421
Wavelet-based denoising techniques are well suited to estimate spatially inhomogeneous signals. Waveshrink (Donoho and Johnstone) assumes independent Gaussian errors and equispaced sampling of the signal. Various articles have relaxed some of these assumptions, but a systematic generalization to distributions such as Poisson, binomial, or Bernoulli is missing. We consider a unifying l1-penalized likelihood approach to regularize the maximum likelihood estimation by adding an l1 penalty of the wavelet coefficients. Our approach works for all types of wavelets and for a range of noise distributions. We develop both an algorithm to solve the estimation problem and rules to select the smoothing parameter automatically. In particular, using results from Poisson processes, we give an explicit formula for the universal smoothing parameter to denoise Poisson measurements. Simulations show that the procedure is an improvement over other methods. An astronomy example is given. 相似文献
997.
In this paper,we consider the(L,1) state-dependent reflecting random walk(RW) on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for(positive) recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the(L,1)-random walk. 相似文献
998.
999.
Ayman I. Madbouly Amin Y. Noaman Abdul Hamid M. Ragab Ahmed M. Khedra Ayman G. Fayoumi 《Applied Acoustics》2016
In this paper, a new classroom acoustics assessment model (CAAM) based on analytic hierarchy process (AHP) for enhancing speech intelligibility and learning quality is proposed. The model is based on five main criteria that affect the learning process and related to classrooms acoustical properties. These include classroom specifications, noise sources inside and outside the classroom, teaching style, and vocal effort. The priority and weights of these major criteria along with their alternatives are identified using the views of students, staff, education consultants, and expertise by using a developed questionnaire, and the AHP methodology. This model can be considered as a helpful framework enabling universities decision makers to take effective decisions on classroom acoustics treatment issues. It also provides colleges’ higher authorities the suitable guidelines that help for determining necessary requirements that help to raise the quality and efficiency of the educational environment; in order to reach an excellent learning environment; and hence increasing students learning outcomes. 相似文献
1000.
Let , be independent and identically distributed random variables with values in . We transform (‘prune’) the sequence , of discrete random samples into a sequence , of contiguous random sets by replacing with if . We consider the asymptotic behaviour of as . Applications include path growth in digital search trees and the number of tables in Pitmanʼs Chinese restaurant process if the latter is conditioned on its limit value. 相似文献