Abstract
SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.
Abstract
In this chapter, we examine the nature of correlations in Euclidean
spaces, focusing on the two-dimensional space R
2
and the three-dimensional space
R
3
. We begin by exploring linear correlations in R
2
, where we analyze calculation
techniques and association measures to quantify the relationship between two continuous variables. Next, we delve into multiple correlations in R
3
, examining how
several variables can be related simultaneously and how their strength and direction
can be jointly measured. Subsequently, we address non-linear correlations in R
2
,
expanding the focus beyond traditional linear relationships. We explore advanced
methods and techniques for detecting and measuring non-linear correlations, allowing us to capture complex and non-linear patterns in the data. Furthermore,
examples of practical applications are discussed where the presence of non-linear
correlations is crucial for analysis and decision-making.
Keywords:
R2space, R 3 space, linear correlation on R 2 , multiple correlation on R 3 , non-linear correlation on R 2 , Pearson’s correlation factor, Spearman’s correlation factor.
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Authors:Bentham Science Books