| The simplest nontrivial monotone functions are \staircases." The problem arises: what is the best approximation of some monotone function f(x) by a staircase with M jumps? In particular: what if f(x) is itself a staircase with N, N > M, steps? This paper considers algorithms for solving, and theorems relating to, this problem. All of the algorithms we propose are space-optimal up to a constan...

A laser ultrasonic system is a non-contact inspection device with a long stand-off distance and it is applicable to hard-to-access locations such as in a nuclear power plant. In this paper, multiple surface waves generated by line-shaped multiple pulse laser beams are adopted to precisely detect a surface-breaking crack with its depth information. When a surface crack is positioned at the cente...

We have derived the set of reference scaling parameters yielding collapse of isentropic acoustic and thermoacoustic (or heat-release-induced) waves across different pure compressible fluids with an assigned equation of state. The resulting reference pressure and velocity are consistent with classic acoustic scaling. The reference temperature and heat release rate need to be expressed in terms o...

The main issue in any image zooming techniques is to preserve the structure of the zoomed image. The zoomed image may suffer from the discontinuities in the soft regions and edges; it may contain artifacts, such as image blurring and blocky, and staircase effects. This paper presents a novel image zooming technique using Partial Differential Equations (PDEs). It combines a non-linear Fourth-ord...

in this study, absorption of high frequency radio waves in the ionospheric plasma have beeninvestigated. the wave equation was obtained in terms of ionospheric parameters. the numerical values ofthe absorption have been calculated for 4 mhz, 4.5 mhz and 5 mhz waves. the necessary parameters forcalculation have been obtained using an international reference ionosphere (iri) model. the altitudina...

We report on the optimization of staircase grating profiles for the case of absorbing grating materials. Using a simple numerical algorithm, we determined the grating parameters, maximizing the first-order diffraction efficiency for different numbers of staircase steps. The results show that there is a significant difference between the staircase profiles for nonnegligible and negligible absorp...

AIM Psychophysical strategies designed for clinical visual field testing produce rapid estimates of threshold with relatively few stimulus presentations and so represent a trade-off between test quality and efficiency. The aim of this study was to determine the measurement error of a staircase algorithm similar to full threshold with standard automated perimetry (SAP) and frequency doubling per...

Using a simple transfer matrix approach we have derived very long series expansions for the perimeter generating function of punctured staircase polygons (staircase polygons with a single internal staircase hole). We find that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We perform an analysis of the properties of the differ...

We consider staircase codes and study their performance using an analysis of the decoding information flow. We derive bounds on the information transfer functions for long binary linear codes serving as component codes for staircase ensembles and compute them for several BCH codes and bounded distance decoding. The resulting expressions are used to obtain upper bounds on the iterative threshold...