Functions and Analysis

1904 Submissions

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

Unitary Quantum Groups vs Quantum Reflection Groups

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 $H_N^{[\infty]}=$, coming via crossed product methods. Also, we conjecture the existence of a ``contravariant duality'' between the liberations of $H_N$ and of $U_N$, as a solution to the lack of a covariant duality between these liberations.
Category: Functions and Analysis

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

What Was Division by Zero?; Division by Zero Calculus and New World

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

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

Integral Seno Por Coseno Que Tiene Como Solución un Determinado Número de Fibonacci

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

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

Surprising Integral Definition of the Number e

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

Some Hereditary Properties of the E-J Generalized Cesàro Matrices

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

Ramanujan Value of Ln(x) When X Tends to Zero

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

D\"aumler's Horn Torus Model and\\ Division by Zero \\ - Absolute Function Theory -\\ New World

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