Introduction to the Sub-Interval Analysis. Part 2: Sub-Interval Images. Big Data

Abstract

A sub-interval analysis (SI analysis or SI-analysis or S-I analysis or SIA or S-IA) is a new field or direction of applied mathematical research. It deals with properties of entire intervals and their sub-intervals without considering the insides of the sub-intervals. That is each sub-interval can be represented by only three quantities: by the two coordinates and one weight. This can evidently ease and simplify some considerations and calculations. The S-IA can be developed both as a pure mathematical and mainly as an applied research, in particular in the field of economics. For example, reporting periods in accounting and audit can evidently be considered as some sub-intervals. If this entire interval is a one-dimensional smooth schedule, then these sub-intervals can represent a one-dimensional stepped sub-interval image. If this entire interval is a two-dimensional smooth picture, then these sub-intervals can represent a two-dimensional stepped sub-interval image.