[8] **viXra:1912.0537 [pdf]**
*submitted on 2019-12-31 15:38:36*

**Authors:** Theophilus Agama

**Comments:** 12 Pages.

In this paper we introduce the concept of surgery. This concept ensures that almost all discontinuous functions can be made to be continuous without redeﬁning their support. Inspite of this, it preserves the properties of the original function. Consequently we are able to get a handle on the number of points of discontinuities on a ﬁnite interval by having an information on the norm of the repaired function and vice-versa.

**Category:** Functions and Analysis

[7] **viXra:1912.0347 [pdf]**
*submitted on 2019-12-18 13:17:20*

**Authors:** Martin Nicholson

**Comments:** 8 Pages.

$q$-analogs of sum equals integral relations $\sum_{n\in\mathbb{Z}}f(n)=\int_{-\infty}^\infty f(x)dx$ for sinc functions and binomial coefficients are studied. Such analogs are already known in the context of $q$-hypergeometric series. This paper deals with multibasic `fractional' generalizations that are not $q$-hypergeometric functions.

**Category:** Functions and Analysis

[6] **viXra:1912.0340 [pdf]**
*replaced on 2020-01-07 08:13:17*

**Authors:** Andrej Liptaj

**Comments:** 15 Pages.

In this text explicit forms of several higher precision order kernel functions (to be used in the differentiation-by-integration procedure) are given for several derivative orders. Also, a system of linear equations is formulated which allows to construct kernels with arbitrary precision for arbitrary derivative order. A computer study is realized and it is shown that numerical differentiation based on higher precision order kernels performs much better (w.r.t. errors) than the same procedure based on usual Legendre-polynomial kernels. Presented results may have implications for numerical implementations of the differentiation-by-integration method.

**Category:** Functions and Analysis

[5] **viXra:1912.0327 [pdf]**
*replaced on 2019-12-26 06:33:43*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 345 Pages. In ascending order of time of first versions.

My papers about Euler and Navier-Stokes Equations,
from 2015-May-11 to 2019-December-15.

**Category:** Functions and Analysis

[4] **viXra:1912.0300 [pdf]**
*submitted on 2019-12-16 18:37:53*

**Authors:** Saburou Saitoh

**Comments:** 12 Pages. I am writing a book on the division by zero calculus; these series may be considered as the materials for the book.

Based on the preprint survey paper (What Was Division by Zero?; Division by Zero Calculus and New World, viXra:1904.0408 submitted on 2019-04-22 00:32:30) we will give a viewpoint of the division by zero calculus from the origins of mathematics that are the essences of mathematics. The contents in this paper seem to be serious for our mathematics and for our world history with the materials in the preprint.
So, the author hopes that the related mathematicians, mathematical scientists and others check and consider the topics from various viewpoints.

**Category:** Functions and Analysis

[3] **viXra:1912.0182 [pdf]**
*submitted on 2019-12-09 09:59:19*

**Authors:** Viola Maria Grazia

**Comments:** 1 Page.

I talk about functions in particular I speak when the serie diverges and so when a function tends to infinity.

**Category:** Functions and Analysis

[2] **viXra:1912.0123 [pdf]**
*submitted on 2019-12-06 17:40:20*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

The definition of the decidable fan theorem is evaluated as not tautologous, hence refuting it and derived conjectures such as “uniform continuity theorem with continuous moduli”. These results form a non tautologous fragment of the universal logic VŁ4.

**Category:** Functions and Analysis

[1] **viXra:1912.0030 [pdf]**
*submitted on 2019-12-02 11:50:41*

**Authors:** Jonathan W. Tooker

**Comments:** 22 Pages. 1 color figure

In a recent paper, the author demonstrated the existence of real numbers in the neighborhood of infinity. It was shown that the Riemann zeta function has non-trivial zeros in the neighborhood of infinity but none of those zeros lie within the critical strip. While the Riemann hypothesis only asks about non-trivial zeros off the critical line, it is also an open question of interest whether or not there are any zeros off the critical line yet still within the critical strip. In this paper, we show that the Riemann zeta function does have non-trivial zeros of this variety. The method used to prove the main theorem is only the ordinary analysis of holomorphic functions. After giving a brief review of numbers in the neighborhood of infinity, we use Robinson's non-standard analysis and Eulerian infinitesimal analysis to examine the behavior of zeta on an infinitesimal neighborhood of the north pole of the Riemann sphere. After developing the most relevant features via infinitesimal analysis, we will proceed to prove the main result via standard analysis on the Cartesian complex plane without reference to infinitesimals.

**Category:** Functions and Analysis