[8] **viXra:1904.0414 [pdf]**
*submitted on 2019-04-21 10:18:41*

**Authors:** Teo Banica

**Comments:** 26 Pages.

We study the intermediate liberation problem for the real and complex unitary and reflection groups, namely $O_N,U_N,H_N,K_N$. For any of these groups $G_N$, the problem is that of understanding the structure of the intermediate quantum groups $G_N\subset G_N^\times\subset G_N^+$, in terms of the recently introduced notions of ``soft'' and ``hard'' liberation. We solve here some of these questions, our key ingredient being the generation formula $H_N^{[\infty]}=

**Category:** Functions and Analysis

[7] **viXra:1904.0408 [pdf]**
*submitted on 2019-04-22 00:32:30*

**Authors:** Saburou Saitoh

**Comments:** 73 Pages. Please kindly give me suggestions and comments to the paper.

In this survey paper, we will introduce the importance of the division by zero and its great impact to elementary mathematics and mathematical sciences for some general people. For this purpose, we will give its global viewpoint in a self-contained manner by using the related references.

**Category:** Functions and Analysis

[6] **viXra:1904.0380 [pdf]**
*submitted on 2019-04-19 20:00:44*

**Authors:** Pedro Hugo García Peláez

**Comments:** 2 Pages.

Integral seno por coseno que tiene como solución un determinado número de Fibonacci.
La fórmula sirve tanto para hallar integrales de línea de funciones tipo x*y sobre trayectorias curvas si queremos que tenga como solución un número de Fibonacci. Como para integrales de campos vectoriales como un campo de fuerzas en trayectorias curvas.

**Category:** Functions and Analysis

[5] **viXra:1904.0379 [pdf]**
*submitted on 2019-04-19 20:19:55*

**Authors:** Pedro Hugo García Peláez

**Comments:** 2 Pages.

Integral sine by cosine that has a certain Fibonacci number as a solution.
The formula is useful both for finding line integrals of functions type x * y on curved trajectories if we want a Fibonacci number as a solution. As for integrals of vector fields as a force field in curved trajectories.

**Category:** Functions and Analysis

[4] **viXra:1904.0360 [pdf]**
*submitted on 2019-04-18 13:19:38*

**Authors:** Jesús Álvarez Lobo

**Comments:** 2 Pages. MSC2010: 58C05

A new definition of the number e is presented by the integral of a function that involves
an infinite product of nested radicals whose indexes form the sequence 1, 2, 3, ...
____________________________________________________________________

**Category:** Functions and Analysis

[3] **viXra:1904.0259 [pdf]**
*submitted on 2019-04-13 08:45:34*

**Authors:** H. C. Rhaly Jr.

**Comments:** 3 Pages.

A countable subcollection of the Endl-Jakimovski generalized Ces\`{a}ro matrices of positive order is seen to inherit posinormality, coposinormality, and hyponormality from the Ces\`{a}ro matrix of the same order.

**Category:** Functions and Analysis

[2] **viXra:1904.0138 [pdf]**
*submitted on 2019-04-06 08:36:03*

**Authors:** Jesús Sánchez

**Comments:** 3 Pages.

As we know, the natural logarithm at zero diverges, towards minus infinity:
lim┬(x→0)〖Ln(x)〗=-∞
But, as happens with other functions or series that diverge at some points, it has a Ramanujan or Cauchy principal value (a finite value) associated to that point. In this case, it will be calculated to be:
lim┬(x→0)〖Ln(x)〗=-γ
Being γ the Euler-Mascheroni constant 0.577215... It will be shown that Ln(0) tends to the negative of the sum of the harmonic series (that of course, diverges). But the harmonic series has a Cauchy principal value that is γ, the Euler-Mascheroni constant. So the finite associated value to Ln(0) will be calculated as - γ .

**Category:** Functions and Analysis

[1] **viXra:1904.0052 [pdf]**
*submitted on 2019-04-03 20:31:13*

**Authors:** Saburou Saitoh

**Comments:** 12 Pages. In Section 1, we will introduce the horn torus model by V.V. Puha and in Section 1.1, by modifying the Puha mapping, we introduce D\"aumler's horn torus model. In Section 1.2 we introduce division by zero and division by zero calculus with up-to-date

In this paper, we will introduce a beautiful horn torus model by Puha and D\"aumler for the Riemann sphere in complex analysis attaching the zero point and the point at infinity. Surprisingly enough, we can introduce analytical structure of conformal to the model. Here, some basic opinions on the D\"aumler's horn torus model will be stated as the basic ones in mathematics.

**Category:** Functions and Analysis