Complexities of Computation: A Survey Report

Abstract

Abstract-Computation of real numbers has been a challenging task for many years. Because of its unique nature of infinity, it is considered as a very good area of research. This paper tries to convey the nature of the real numbers and the difficulty to compute them i.e. to approximate the value and some respective development processes related to the real numbers. While making a general calculation the approximation can go on and on, this still doesn't give the exact value. Computer system's memory is finite. Goal is to approximate the real numbers but the problem arises where to stop and which basis they are subjected for approximation on.

A comparison of EPI sampling, probability sampling, and compact segment sampling methods for micro and small enterprises

“…In compact SSM (cSSM), the segments are smaller than those in tSSM and all eligible respondents in the segment are included in the final study sample. The World Bank Microenterprise Surveys for the Informal Sector in southern and eastern Africa and in Nepal used cSSM (Jain 2010; Gelb et al 2009). The field team first identified clusters of informal sector activity, divided these clusters into segments, randomly selected segments from all possible segments, and then conducted door-to-door surveys with all the households in the selected segments.…”

“…The field team first identified clusters of informal sector activity, divided these clusters into segments, randomly selected segments from all possible segments, and then conducted door-to-door surveys with all the households in the selected segments. Because the segments in cSSM are relatively small in area, a potential pitfall occurs when the segment does not contain the minimum acceptable sample size of a specific target population (e.g., larger businesses), and a larger segment had to be redrawn (as occurred in Jain, 2010). …”

“…For instance, up to 20% of the sample in the World Bank Enterprise Survey in Nepal (Jain 2010) were revisits. ESM, in contrast to PSM and SSM, does not perform revisits.…”

Facet Model of Moving Targets for ISAR Imaging and Radar Back-Scattering Simulation

“…x SR =ŷ SR £ẑ SR (6) wheren is the unitary vector that is orthogonal to the triangle and indicates the active face of the facet. It must be noted that when the incident wave is orthogonal to the triangle, μ = 0, the vectorŷ SR cannot be calculated with (5) because vectorsẑ SR and ¡¡!…”

“…Nevertheless, this information can be useless if the target motion produces blurred images. Motion compensation algorithms [4][5][6][7][8] or time-frequency techniques [9][10][11][12][13][14][15] are useful techniques to solve this problem.…”