[8] **viXra:1903.0488 [pdf]**
*submitted on 2019-03-27 21:04:39*

**Authors:** Saburou Saitoh

**Comments:** 18 Pages. In this paper, we will introduce the division by zero calculus in complex analysis for one variable at the first stage in order to see the elementary properties.

In this paper, we will introduce the division by zero calculus in complex analysis for one variable at the first stage in order to see the elementary properties.

**Category:** Functions and Analysis

[7] **viXra:1903.0432 [pdf]**
*submitted on 2019-03-24 23:28:16*

**Authors:** Saburou Saitoh

**Comments:** 10 Pages. In this paper, we will show a very interesting interpretation of singular integrals by the division by zero calculus. This may be considered as the basic relation of ZERO and INFINITY through integrals. Furthermore, we will see a similar nature of singula

What are the singular integrals? Singular integral equations are presently encountered
in a wide range of mathematical models,
for instance in acoustics, fluid dynamics, elasticity
and fracture mechanics.
Together with these models, a variety of methods
and applications for these integral equations has been developed.
In this paper, we will give the interpretation for the Hadamard finite part of singular integrals by means of the division by zero calculus.

**Category:** Functions and Analysis

[6] **viXra:1903.0421 [pdf]**
*submitted on 2019-03-23 11:17:49*

**Authors:** Federico Espil

**Comments:** 9 Pages.

The problem of integration technique over integrands of the form f(t)/t^n, can be solved by differentiation(n times) by using Leibniz's rule to get rid of t^n, that leads to integrate back (n times) to end the game which it's harder than the original problem.This work focuses on the derivation of the formula (Espil's theorem) which is a perfect tool to avoid that hard task. It allows to change the difficult n iterated integrals into a more outstanding easier problem which consists of n -1 derivatives.The Espil's theorem is a generalization of the Dirichlet integral.

**Category:** Functions and Analysis

[5] **viXra:1903.0409 [pdf]**
*submitted on 2019-03-22 11:29:29*

**Authors:** Teo Banica

**Comments:** 12 Pages.

We investigate the liberation question for the compact Lie groups, by using various ``soft'' and ``hard'' methods, based respectively on joint generation with a free quantum group, and joint generation with a free torus. The soft methods extend the ``easy'' methods, notably by covering groups like $SO_N,SU_N$, and the hard methods partly extend the soft methods, notably by covering the real and complex tori themselves.

**Category:** Functions and Analysis

[4] **viXra:1903.0371 [pdf]**
*submitted on 2019-03-20 23:56:47*

**Authors:** Saburou Saitoh

**Comments:** 9 Pages. In this paper, we will introduce the division by zero calculus in multiply dimensions in order to show some wide and new open problems as we see from the one dimensional case.

In this paper, we will introduce the division by zero calculus in multiply dimensions in order to show some wide and new open problems as we see from the one dimensional case.

**Category:** Functions and Analysis

[3] **viXra:1903.0326 [pdf]**
*submitted on 2019-03-17 07:33:40*

**Authors:** Federico Espil

**Comments:** 6 Pages.

The problem of fraction decomposition it's easy to solve by using the cover up method, when there are no repeated linear factors in the denominator .
Nevertheless it could turn into a hard work if these factors are raised to a high power, where the cover up method doesn't work. This technique shows how to calculate these coefficients without solving large systems of equations with a clever rearrangement of the numerator.

**Category:** Functions and Analysis

[2] **viXra:1903.0315 [pdf]**
*submitted on 2019-03-18 05:25:09*

**Authors:** Fayowole David Ayadi

**Comments:** 3 Pages.

The laws of Physics and some other related courses are generally written as differential equations. Therefore, all of science
and engineering use differential equations to some extent. A good knowledge of differential equations will be an integral
part of your study in science and/or engineering classes. You can think of mathematics as the language of science, and
differential equations are one of the most important parts of this language as far as science and engineering are concerned.

**Category:** Functions and Analysis

[1] **viXra:1903.0231 [pdf]**
*submitted on 2019-03-12 22:17:08*

**Authors:** Federico Espil

**Comments:** 5 Pages.

Shortly from the Espil's theorem, we can derive the generalized Dirichlet
integral for any natural value when the hole integrand is raised to the n-th power.

**Category:** Functions and Analysis