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- W186904752 abstract "A mother, a father, and their daughter were taking a picture. They were 5, 7, and 2 feet tall respectively. The parents stood in a row, and their daughter stood in front of her mother. My son saw this and ran quickly in front of the father before the picture was taken. I asked my son why. He answered that he was exactly 4 feet tall. I figured out his reasoning, and afterwards I have become an astrophysicist. A pattern is a distribution of differences. In the array pattern of the above-said four people, the height differences between adults and between kids are equal, and the height differences between females and between males are equal too. This simple pattern can be generalized into any array of numbers. Assume the differences of numbers in a row are equal to the corresponding differences in any other row. That is, there exist the common differences in all rows. Similarly assume the common differences in all columns. Then the pattern is called a rational structure. Assume the number at the bottom left corner is zero, C(0,0) = 0, and denote the series of numbers in the bottom row by U(i) and the series of numbers in the first column by V(j). I found the formula for the rational array: C = U(i) + V(j). This is called Skew Law. I generalized the rows and columns to be curved, and required that the curves cross each other at a right angle. This was exactly my idea of galaxy patterns. In this paper I show that the patterns are governed by the Riccati equation with constant coefficients; and the curves are governed by a type of algebraic equations. The cubic equation of the type gives a pattern which resembles the sharp bar of galaxy NGC 1073. Are all barred galaxies governed by the cubic and higher degrees of algebraic equations? The question will be resolved in the near future." @default.
- W186904752 created "2016-06-24" @default.
- W186904752 creator A5061554742 @default.
- W186904752 date "2014-02-01" @default.
- W186904752 modified "2023-09-23" @default.
- W186904752 title "Are Galaxies Structured by Riccati Equation? The First Graph of Rational Bar" @default.
- W186904752 hasPublicationYear "2014" @default.
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