Mercedes Orús-Lacort

Universitat Autònoma de Bsrcelona - UAB

« La puissance d’une civilisation épouse toujours la puissance de la religion qui la légitime. Quand la religion se trouve dans une phase ascendante, la civilisation l’est également ; quand elle se trouve dans une phase descendante, la civilisation déchoit ; quand la religion meurt, la civilisation trépasse avec elle. (...) La civilisation judéo- c...

La puissance d'une civilisation épouse toujours la puissance de la religion qui la légitime. Quand la religion se trouve dans une phase ascendante, la civilisation l'est également ; quand elle se trouve dans une phase descendante, la civilisation déchoit ; quand la religion meurt, la civilisation trépasse avec elle. (…) La civilisation judéo-chréti...

Here we analyze three well-known conjectures: (i) the existence of infinitely many twin primes, (ii) Goldbach's strong conjecture, and (iii) Polignac's conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of Goldbach's strong conjecture, one must consider also the existence o...

In this paper we analyze the premise that Fermat numbers Fn = 2^(2^n) + 1 are not prime numbers for n ≥ 5. In particular, using Édouard Lucas' result, we initially show for n = 5 how one can write 2^(2^5) + 1 as something similar to a linear combination of certain powers of 2, such that one can write F5 as a product of two prime factors, written as...

Here we analyze three well-known conjectures: (i) the existence of infinitely-many twin primes, (ii) Goldbach's strong conjecture, and (iii) Polignac's conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of the Goldbach's strong conjecture, one must consider also the existen...

Philosophical conclusions derived of the validity of this three conjectures, not included in the main article proving the three conjectures, because I think that it is not appropriated to mix a pure Mathematical proof with philosophical derived conclusions.

In this paper we perform a detailed analysis of Riemann’s hypothesis, dealing with the zeros of the analytically-extended zeta function. We use the functional equation ζ(s) = 2^s π^(s−1) sin(πs/2)Γ(1 − s)ζ(1 − s) for complex numbers s such that 0 < Re(s) < 1 and the reduction to the absurd method where we use an analytical study based on a complex...

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In this paper we perform a detailed analysis of Riemann's hypothesis, dealing with the zeros of the analytically-extended zeta function. We use the functional equation ζ(s) = 2^s π^(s−1)sin(πs/2)Γ(1 − s)ζ(1 − s) for complex numbers s such that 0 < Re(s) < 1, as well as reduction to the absurd in combination with a deep numerical analysis, to show t...

This document discusses the ergonomic problems with currently available software products, and what in general is necessary to make an application pleasant to work with. The application of these principles to a new open-architecture user interface system, Views, is then described.

In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can deduce a formula for the general term of the Collatz sequence for any odd natural number n after seve...

Certificate of acceptance for the manuscript (mathematics-1742201 by MDPI) in Mathematics (ISSN 2227-7390) on 05 June 2022

In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can deduce a formula for the general term of the Collatz sequence for any odd natural number n after seve...

This paper explains how to obtain the number Φ, using a square with side length equal to a, the right triangle with sides a/2 and a, and a circle with radius equal to the hypotenuse of this right triangle. In particular, from a square whose side length is equal to a, we will show how to obtain a segment b in such a way that the value of a/b is the...

In this article, we will analyze how to obtain pertinent Information in the form of Qualitative Data graphically represented from unstructured Big Textual data. Unstructured data refers to information that either does not have a pre-defined data model or is not organized in a pre-defined manner (80-90% of all information). Obviously, it is not usef...

This paper explains how to obtain the number Φ, using a square with side length equal to a, the right triangle with sides a/2 and a, and a circle with radius equal to the hypotenuse of this right triangle. In particular, from a square whose side length is equal to a, we will show how to obtain a segment b in such a way that the value of a/b is the...

This paper explains how to obtain the number Φ, using a square with side length equal to a, the right triangle with sides a/2 and a, and a circle with radius equal to the hypotenuse of this right triangle. In particular, from a square whose side length is equal to a, we will show how to obtain a segment b in such a way that the value of a/b is the...

This document aims to show a medicinal herb, which began to be used in April (2020) in Africa, against the SARS-CoV-2 virus. This herb is called Artemisia Annua or also Sweet Wormwood. We talk about: - What is this medicinal herb?. We will show some references and its main properties. - Which africans countries began to use it?. We will show the fi...

In this paper we analyze the possibility of the existence of infinite twin primes numbers, or on the contrary, if we can guarantee that there is a finite number of them. Using the formula 4((n − 1)! + 1) ≡ −n (mod n(n + 2)), satisfied if and only if (n, n + 2) are twin primes, and Wilson Theorem, we analyze what conditions the twin primes meet, and...

In one day we have received this achievement, and reads follow increasing. Thank you very much to all the colleagues holding us. https://www.researchgate.net/publication/339799952_How_to_extract_knowledge_of_Qualit ative_Data_from_Big_Textual_Data

Topology concepts

Introducció a la Matemàtica Financera

In this chapter, we will analyze how to obtain pertinent Information in the form of Qualitative Data graphically represented from unstructured Big Tex-tual data. Unstructured data refers to information that either does not have a pre-defined data model or is not organized in a pre-defined manner (80-90% of all information). Obviously, it is not use...

Topología en R^n

Topología básica en R

Basic Topology in R

Delta de Dirac

Equacions Diferencies Finites i Equacions Diferencials

Estadística aplicada a Disseny d'experiments i Segmentació de Mercats

Sistemas lineales e invariantes LTI

Estadística aplicada a Posicionament de productes i Comportament del consumidor

Funcions diverses variables Optimització

Programació lineal

Usually, I don’t pay many attention to my achievements, but this one I have thought it was important, because, you made it possible. Thank you very much to all the colleagues holding me on RG. I am very grateful to all you.

Thank you very much to all the colleagues holding me on RG. I am very grateful to all you. I will be always holding you too.

In this paper we show a demonstration which allow us to prove how the Fermat numbers 2^2^n + 1 are not prime numbers for n ≥ 5. In particular, usingÉdouardusing´usingÉdouard Lucas result, we show that for n ≥ 5, 2^2^n + 1 can be written as (k1 · 2^(n+2) + 1) · k2 for k1 and k2 positive integer numbers.

In structured indexes, classification systems, thesauri, conceptual structures or semantic networks, relationships are too often vague. For instance, in terminology, the relationships between concepts are often reduced to the distinction established by standard between hierarchical relationships (genus-species relationships and part/whole relations...

Examples Statement Logic Formalization

Examples Statement Logic Validation using Natural Deduction

Examples Statement Logic Validation using Resolution Method

Examples Statement Logic Validation using Truth Tables

Examples Predicate Logic Formalization

Examples Predicate Logic Validation using Natural Deduction

Examples Predicate Logic Validation using Resolution Method

Z Transform

Laplace Transform

Fourier Series

Power Series

Exponencial de una matriz

Calculo de numero mayor de 4 cifras que al dividir entre 15 el resto es 2 y al dividir entre 24 el resto es 5

Minimo numero entre 200 y 500 con resto 3 al dividirlo por otros numeros

Ultimas 3 cifras del resultado de elevar 1299 a 1299

Solucion positiva para una Ecuacion Diofántica

Confidence Interval for one mean

Hypothesis test for one proportion

ANOVA Example

Como calcular las raices de ecuación usando las formulas de Cardano Vieta

Raiz cuadrada de una matriz no diagonal

Confidence Interval for one proportion

Hypothesis test for 2 proportions

Hypothesis tests for one mean

Hypothesis test for 2 mean

Examples of Hypothesis test for two means

Hypothesis test for 2 variances

Chi Square test

Chi Square Example

ANOVA Test for more than 2 samples

Regression Line

Linear Regression Examples

Intervalo de confianza para la media parte 2

Intervalo de confianza para una proporción

Contraste de hipótesis para 2 medias parte 1

Contraste de hipótesis para 2 medias parte 2

Contraste de hipótesis para una proporción parte 1

Contraste de hipótesis para una varianza

Contraste de hipotesis para una media parte 1

Contraste de hipotesis para una media parte 2

Contraste de hipótesis para una proporción parte 2

Contraste de hipótesis para 2 medias parte 4

Contraste de hipótesis para 2 proporciones parte 1

Intervalo de confianza para la media parte 1

Contraste de hipótesis para 2 medias parte 3

Contraste de hipótesis para 2 proporciones parte 2

Contraste de varianzas parte 1

Contraste de varianzas parte 2

ANOVA parte 1

ANOVA parte 2

Contraste Chi Cuadrado parte 2

Contraste Chi Cuadrado parte 1

Contraste Chi Cuadrado parte 3

Regresión lineal simple recta de regresión parte 1

Regresión lineal simple recta de regresión parte 2

Regresión lineal simple recta de regresión parte 3

Estadistica Aplicada Modelo de Regresión lineal multiple

Estadistica aplicada Analisis de Componentes Principales

Estadística Aplicada Análisis de Conglomerados o Análisis de Cluster

Regresión lineal simple recta de regresión parte 4

Estadística Aplicada Análisis de Correspondencias Simple o Múltiple parte 1