Functions and Analysis

2107 Submissions

[2] viXra:2107.0119 [pdf] submitted on 2021-07-19 21:40:19

A Unique Step Function and Stitching Piecewise Defined Functions

Authors: William Blickos
Comments: 12 Pages. thoughtfarm@live.com

This paper discusses a unique complex logarithmic function that can be used as an alternative to piecewise defined step functions such as the Heaviside function. It describes how to create second tier logical functions such as multi-steps, boxcars, and valleys, and it provides a method to stitch the components of piecewise functions into a single function.
Category: Functions and Analysis

[1] viXra:2107.0053 [pdf] submitted on 2021-07-08 01:32:16

On the Elementary Function y=|x| and Division by Zero Calculus

Authors: Hiroshi Okumura, Saburou Saitoh, Keitarou Uchida
Comments: 7 Pages.

In this paper, we will consider the elementary function $y=|x|$ from the viewpoint of the basic relations of the normal solutions (Uchida's hyper exponential functions) of ordinary differential equations and the division by zero calculus. In particular, $y^\prime(0) =0$ in our sense and this function will show the fundamental identity with the natural sense $$ \frac{0}{0} =0 $$ with the sense $$ \frac{1}{0} =0 $$ that may be considered as $0$ as the inversion of $0$ through the Uchida's hyper exponential function.
Category: Functions and Analysis