[5] **viXra:2001.0419 [pdf]**
*submitted on 2020-01-20 11:42:21*

**Authors:** Francisco Moga Moscoso, Marina Moga Lozano

**Comments:** 5 Pages. email for contact: mmoga@uma.es. Book and copyright: Desdedondetodocomienza

A possible demonstrations of the riemann hypothesis based on every infinite complex solution of zeta function of Riemann ζ(s) with it is conjugated root, can also be used to be the solution of a quadratic equation of real coefficients which admits it as zeros, using the root theorem of Viete.

**Category:** General Mathematics

[4] **viXra:2001.0374 [pdf]**
*submitted on 2020-01-19 12:35:05*

**Authors:** Leszek Mazurek

**Comments:** 49 Pages. Text in Polish, English version soon

Since the beginning of time, the ban on dividing by zero has been a serious problem for all thinking people, who have found this restriction hard to accept. Moreover, intuitively it seems very artificial and unjustified. In this work, I have made the effort to analyze this problem very carefully, to try and finally understand where it comes from, why it is a problem, a limitation, and what should be done to solve it. By a very detailed analysis of multiplication and division, I have found out that these operations are the same. Combined with the selection operation they are transformations that perform the change of a pair of numbers into another pair of numbers. After the analysis, I’ve found out that a ratio of two numbers, that can represent such a transformation, is the most natural form of a number. I’m proposing a new understanding of fractions and explaining why 1/2 should not be equal to 2/4. I presented an explanation to the problem of why division by zero is not possible in real numbers’ domain and how easy it can be understood in the domain of rational numbers. The results that I have obtained not only solve this problem but also shed a whole new light on understanding the numbers and operations of numbers. My work fixes one of the foundations of mathematics, it is difficult to predict all consequences which this change can bring, to everything, what was created based on this wrong foundation.

**Category:** General Mathematics

[3] **viXra:2001.0054 [pdf]**
*submitted on 2020-01-04 13:06:37*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

We give a formula involving Pi.

**Category:** General Mathematics

[2] **viXra:2001.0053 [pdf]**
*submitted on 2020-01-04 13:08:05*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

We give some elementary integrals.

**Category:** General Mathematics

[1] **viXra:2001.0036 [pdf]**
*submitted on 2020-01-02 23:38:03*

**Authors:** Shiyou Lian

**Comments:** 26 Pages.

This paper introduces the measure of approximate-degree and the concept of approximate-degree function between numerical values, thus developing a new interpolation method —— approximation-degree-based interpolation, i.e., AD interpolation. One-dimensional AD interpolation is done directly by using correlative interpolation formulas; n(n>1)-dimensional AD interpolation is firstly separated into n parallel one-dimensional AD interpolation computations to do respectively, and then got results are synthesized by Sum-Times-Difference formula into a value as the result value of the n-dimensional interpolation. If the parallel processing is used, the efficiency of n-dimensional AD interpolation is almost the same as that of the one-dimensional AD interpolation. Thus it starts a feasible and convenient approach and provides an effective method for high-dimensional interpolations. Furthermore, if AD interpolation is introduced into machine learning, a new instance-based learning method is expected to be realized.

**Category:** General Mathematics