A New Data Processing Inequality and Its Applications in Distributed Source and Channel Coding

In the distributed coding of correlated sources, the problem of characterizing the joint probability distribution of a pair of random variables satisfying an n-letter Markov chain arises. The exact solution of this problem is intractable. In this paper, we seek a single-letter necessary condition for this n-letter Markov chain. To this end, we propose a new data processing inequality on a new measure of correlation by means of spectrum analysis. Based on this new data processing inequality, we provide a single-letter necessary condition for the required joint probability distribution. We apply our results to two specific examples involving the distributed coding of correlated sources: multi-terminal rate-distortion region and multiple access channel with correlated sources, and propose new necessary conditions for these two problems.Comment: 45 pages, 3 figures, submitted to IEEE Trans. Information Theor

Studies of hypersonic viscous flows over a blunt body at low Reynolds number

Viscous hypersonic shock layer over blunt bodies at low Reynolds numbe

Recent trends in particle size analysis techniques

Recent advances and developments in the particle-sizing technologies are briefly reviewed in accordance with three operating principles including particle size and shape descriptions. Significant trends of the particle size analysing equipment recently developed show that compact electronic circuitry and rapid data processing systems were mainly adopted in the instrument design. Some newly developed techniques characterizing the particulate system were also introduced

Small-amplitude perturbations of shape for a nearly spherical bubble in an inviscid straining flow (steady shapes and oscillatory motion)

The method of domain perturbations is used to study the problem of a nearly spherical bubble in an inviscid, axisymmetric straining flow. Steady-state shapes and axisymmetric oscillatory motions are considered. The steady-state solutions suggest the existence of a limit point at a critical Weber number, beyond which no solution exists on the steady-state solution branch which includes the spherical equilibrium state in the absence of flow (e.g. the critical value of 1.73 is estimated from the third-order solution). In addition, the first-order steady-state shape exhibits a maximum radius at θ = 1/6π which clearly indicates the barrel-like shape that was found earlier via numerical finite-deformation theories for higher Weber numbers. The oscillatory motion of a nearly spherical bubble is considered in two different ways. First, a small perturbation to a spherical base state is studied with the ad hoc assumption that the steady-state shape is spherical for the complete Weber-number range of interest. This analysis shows that the frequency of oscillation decreases as Weber number increases, and that a spherical bubble shape is unstable if Weber number is larger than 4.62. Secondly, the correct steady-state shape up to O(W) is included to obtain a rigorous asymptotic formula for the frequency change at small Weber number. This asymptotic analysis also shows that the frequency decreases as Weber number increases; for example, in the case of the principal mode (n = 2), ω^2 = ω_0^0(1−0.31W), where ω_0 is the oscillation frequency of a bubble in a quiescent fluid