scholarly journals First-order statistical properties of ultrasonic speckles back-scattered from a kind of weak scattering interface

2003 ◽  
Vol 52 (6) ◽  
pp. 1438
Author(s):  
Zhu Hong-Mao ◽  
Wu Yan-Yang ◽  
Huang Zhong-Wen ◽  
Wang Yin-Guan ◽  
Zhu Cheng
Keyword(s):  
Statistical Properties ◽  
First Order ◽  
Weak Scattering

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (03) ◽  
pp. 648-668
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind. Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

scholarly journals Symmetry of the Optical Phonons in LuVO4: A Raman Study

Crystals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 341 ◽  
Author(s):  
Peter Rafailov ◽  
Dimitre Dimitrov ◽  
Yen-Fu Chen ◽  
Chi-Shen Lee ◽  
Jenh-Yih Juang
Keyword(s):  
Vibrational Spectrum ◽  
Special Focus ◽  
Phonon Modes ◽  
Theory Analysis ◽  
Rotational Angle ◽  
First Order ◽  
Weak Scattering ◽  
Complete Assignment ◽  
Raman Study

A thorough analysis of the first-order vibrational spectrum of LuVO4 is presented by using polarized micro-Raman spectroscopy with special focus on the phonon modes with the weakest intensity and occasional controversial assignment. Group-theory analysis is carried out to demonstrate the determination of numbers and symmetries of the Raman active modes. Crystal- and correlation-field splitting effects in the vibrational spectrum of LuVO4 are discussed. Under conditions adjusted to minimize the birefringence effects we recorded, in each main scattering configuration, a series of Raman spectra in different sample orientations achieved by rotating the sample around the incident laser beam. The dependence of the Raman intensity on the rotational angle allowed us to identify the correct symmetry of the phonons with exceptionally weak scattering cross-section. A complete assignment of all twelve first-order Raman active phonons of LuVO4 is thus obtained.

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (3) ◽  
pp. 648-668 ◽  
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind.Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

scholarly journals Some first-order and higher-order statistical properties of polarization speckle (Erratum)

2021 ◽  
Author(s):  
Shengzhu Xiao ◽  
Jianlin Nie ◽  
Steen G. Hanson ◽  
Mitsuo Takeda ◽  
Wei Wang
Keyword(s):  
Higher Order ◽  
Statistical Properties ◽  
First Order
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