Papers by Mississippi Valenzuela Durán
Revista de Investigación de Física , 2024
Particle physics emerged as a pioneer discipline in "big science"; experiments are being carried ... more Particle physics emerged as a pioneer discipline in "big science"; experiments are being carried out
in accelerators that are increasing in energy and complexity by the collaborations of thousands of
physicists from hundreds of institutes in a few dozen countries. In "big science" a research methodology
has been developed in which statistics is of great importance to interpret the results obtained from these
experiments. Despite the discovery of the Higgs boson in 2012, which contributed to the success of the
Standard Model and the award of the 2013 Nobel Prize in Physics. Based on these motivations, in the
present work certain statistical tests based on the "likelihood" method are shown and are applied in
high energy physics in the discovery of new phenomena, by making use of the construction of confidence
intervals of the model parameters. We focus on properties of methods called statistical "proofs" that
allow systematic uncertainties to be included. Also, we work with explicit formulas for the asymptotic
distributions of the statistical tests. In addition, we will use a representative data set, called the "Asimov"
data set, which provides a method for obtaining the experimental sensitivity of a search or measurement,
as well as the fluctuations in that expectation.
Revista de Investigación de Física , 2024
La evidencia experimental hasta ahora sugiere que sólo existen tres generaciones de quarks y lept... more La evidencia experimental hasta ahora sugiere que sólo existen tres generaciones de quarks y leptones. Antes de que se rompa la simetría electrodébil, las tres familias de quarks y leptones son indistinguibles,
por lo que son invariantes ante transformaciones del grupo S3. Usando la simetría S3 tenemos a nuestra disposición 3 representaciones irreductibles, 2, 1s, 1a, donde podemos acomodar hasta cuatro dobletes de Higgs en un modelo que ocupa todas las representaciones irreductibles del grupo S3. Este modelo con cuatro dobletes de Higgs (4HDM) es de gran interés, gracias a que podemos tomar el cuarto doblete de Higgs como una partícula estable sin interacción con los fermiones por lo que se convierte en candidato a materia oscura, mientras que con los tres restantes las propiedades obtenidas se mantienen. Una condición importante para tener un candidato viable a materia oscura es su estabilidad, es decir, no se desintegra en partículas del modelo estándar. La forma más sencilla de establecer la estabilidad de una partícula es imponiendo una simetría discreta Z2, de modo que todos los campos se transformen en la forma Ψ −→ Ψ, mientras que las candidatas a materia oscura se transformen como χ −→ −χ, de esta manera nos aseguramos de que no tengamos términos que denoten desintegraciones de χ. Este método se utilizará en 4HDM. Otra imposición requerida para proponer la candidatura de un campo del doblete Ha, es que su Valor de Espectación del Vacío (VEV) correspondiente sea igual a cero, va = 0.
Selecciones Matemáticas, 2024
Fourier analysis is currently one of the important parts of mathematical analysis. Fourier analys... more Fourier analysis is currently one of the important parts of mathematical analysis. Fourier analysis methods are used in physics, electrical engineering, and other sciences to solve various problems. In this article we will give the main concepts of Fourier analysis and its applications in spectral analysis in solving problems using R, as shown in the examples.
Revista de Investigación de Física , 2023
Modied Newtonian dynamics (MOND) is a hypothesis that proposes a modication of Newton's law of un... more Modied Newtonian dynamics (MOND) is a hypothesis that proposes a modication of Newton's law of universal gravitation to account for observed properties of galaxies. This theory is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics. In this work, we present a relativistic theory of gravitation for MOND.
Revista de Investigación de Física , 2023
Observations on the anisotropies of the Cosmic Microwave Background (CMB) have become a fundament... more Observations on the anisotropies of the Cosmic Microwave Background (CMB) have become a fundamental tool in Cosmology. We present a brief description of the formalism necessary to understand the evolution of the anisotropies, and how their power spectrum gives us information about the evolution and composition of the universe.
Revista de Investigación de Física, 2023
In this article, we present the fundamentals of Goldstone's theorem and the breaking of global sy... more In this article, we present the fundamentals of Goldstone's theorem and the breaking of global symmetries. As well as one of the important aspects to take into account in the process of spontaneous symmetry breaking are the possible topological defects generated by the breaking. For this reason, we will expose the concept of topological defect and the calculation of the relic density of the axion, considered as a candidate to dark matter.
Revista de Investigación de Física, 2023
In this work, we present the fundamentals of the general theory of relativity, the standard cosmo... more In this work, we present the fundamentals of the general theory of relativity, the standard cosmology and a description of current and interesting research topics about our current Universe, in addition the emergence of the dark matter problem has been raised, trying to outline possible dark matter candidates. This assumption seems realistic, however the analysis, from the point of view of standard cosmology, which is also studied in this work, turns out to be more complex than if dark matter were considered with a single species of elementary particle.
Revista de Investigación de Física , 2022
In writing out the eq. (43) for in paper [1], an
inadvertent error led to two errant numerical ex... more In writing out the eq. (43) for in paper [1], an
inadvertent error led to two errant numerical expressions
in Diferential identities. The main results and conclusions
remain unchanged. All of the aected formulas are
corrected below.
Revista de Investigación de Física , 2022
The last few decades have seen an explosive increase in the amount and precision of data obtained... more The last few decades have seen an explosive increase in the amount and precision of data obtained from cosmological observations. Theoretical cosmologists have not yet nished interpreting this amount of data. Likewise, the wonderful ideas we have for the beginning of the Universe have not yet been connected with concrete models of elementary particles. Currently, the existence of dark matter (DM) is accepted in the scientic community. Stars, planets, comets, cosmic dust and other forms of matter make up 5% of the matter in the Universe. The remaining 95% would be "dark matter" and "dark energy", if it is that, it is not known what it is, in fact they exist. In this work, the standard cosmological model is studied, as well as the production of relic particles with the Boltzmann equation applied to the decoupling of relic particles from a reservoir.
Revista de Investigación de Física, 2022
In writing out the equations in section of Hamilton principle in my recent paper [1], inadvertent... more In writing out the equations in section of Hamilton principle in my recent paper [1], inadvertents errors led to
errant numerical expressions in Field equations. The
main results and conclusions of my paper remain unchanged. All of the aected formulas are corrected below.
Revista de Investigación de Física, 2022
In writing out the eq. (36) for ln √
−g in my recent paper [1], an inadvertent error led to two e... more In writing out the eq. (36) for ln √
−g in my recent paper [1], an inadvertent error led to two errant numerical
expressions in equations (37) and (38) that propagated
to the "Field equations". The main results and conclusions
of my paper remain unchanged. All of the aected
formulas are corrected below.
Revista de Investigación de Física, 2022
In this paper, we have given a presentation of the relativistic theory of asymmetric field. It is... more In this paper, we have given a presentation of the relativistic theory of asymmetric field. It is our aim to present a theory of gravitation and electomagnetism by a generalization of the concepts and mathematical methods of the general relativity. We look for the formally most simple expression for the law of gravitation in the absence of an electromagnetic field, and then the most natural generalization of this law. This theory contain Maxwell's theory in the Lambda transformation.
Selecciones Matemáticas, 2022
This work has three important purposes: first it is the study of Markov Chains, the second is to ... more This work has three important purposes: first it is the study of Markov Chains, the second is to show that Markov chains have different applications and finally it is to model a process of this behaves. Throughout this work we will describe a Markov chain, what these processes are for and how these chains are classified. We will describe a Markov Chain, that is, analyze what are the primary elements that make up a Markov chain, among others.
Revista de Investigación de Física , 2022
Lately the Cosmic Background Radiation (CMB) data have resulted in anomalies or deviations with r... more Lately the Cosmic Background Radiation (CMB) data have resulted in anomalies or deviations with respect to the standard model of cosmology, which has led several cosmologists to consider alternative models to the standard model (homogeneous and isotropic), such as the Bianchi models, which are homogeneous but anisotropic. Based on these motivations to consider alternative models, we propose to study, in the present work, the algebraic classification of the Bianchi models and each of the Bianchi space-times, applying the ADM formalism of general relativity in its Hamiltonian version and the groups G3. The dynamic equations are shown with the help of the Hamiltonian density H and the Poisson parentheses, in other words, the equation of motion are presented for each of the Bianchi space-times. Some theoretical consequences of these equations are discussed when we take the limit Ω → −∞ and the fixed parameters β+ and β−, consequently, we find that the dependent part of the gravitational potential from the Hamiltonian Density tends to zero and from the equations of motion we find the constant of motion, pΩ = p β + = p β − = constant.
Revista de Investigación de Física , 2022
As gravitation and electromagnetism are closely analogous long-range interactions, and the curren... more As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear throug the geometry. We look for the formally most simple expression for the law of gravitation in the absence of an electromagnetic field, and then the most natural generalization of this law. This theory contain Maxwell’s theory in first approximation. In the following we outline the scheme of the general theory and then show in which sense this contains the law of the pure gravitational field and Maxwell’s theory.
Revista de Investigación de Física , 2021
As gravitation and electromagnetism are closely analogous long-range interactions, and the curren... more As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry. Thence emerges a relativistic theory of the field by generalization of the general relativity. The derivation presented shows how naturally we can extend general relativity theory to a non-symmetric field, and that the field-equations are really the generalizations of the gravitational equations. With curvature tensor and the variational principle, we will deduce the field equations and Bianchi's identities. In consecuense, the field equations will find from Bianchi's identities.
Revista de Investigación de Física, 2021
As gravitation and electromagnetism are closely analogous long-range interactions, and the curren... more As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear through the geometry. This unication has however, remained an unfullled goal. Thence emerges a relativistic theory of the asymmetric field by generalization of the general relativity. It will demonstrate in a new way that the field-equations chosen for the non-symmetric fields are really the natural ones.
Thesis Chapters by Mississippi Valenzuela Durán
En el presente trabajo se muestran ciertas pruebas estadísticas basadas en el método de ”verosimi... more En el presente trabajo se muestran ciertas pruebas estadísticas basadas en el método de ”verosimilitud” y se aplican en la física de altas energías en el descubrimiento de nuevos fenómenos, al hacer uso de la construcción
de intervalos de confianza de los parámetros del modelo. Nos centramos
en las propiedades de los métodos llamados “pruebas” estadísticas que permiten incluir las incertidumbres sistemáticas. También, trabajamos con fórmulas explícitas para las distribuciones asintóticas de las pruebas estadísticas. Además, usaremos un conjunto de datos representativo, llamado el conjunto de datos “Asimov”, que proporciona un método para obtener la sensibilidad experimental de una búsqueda
o medición, así como las fluctuaciones en esa espera.
Últimamente los datos de la Radiación Cósmica de Fondo (CMB) han dado como resultado anomalías o ... more Últimamente los datos de la Radiación Cósmica de Fondo (CMB) han dado como resultado anomalías o desviaciones con respecto al modelo estándar de la cosmología, lo cual ha llevado a varios cosmólogos a considerar modelos alternativos al modelo estándar (homogeneo e isotrópico), como los modelos de Bianchi, los cuales son homogéneos pero anisotrópicos. Basándonos en estas motivaciones para considerar modelos alternativos, proponemos estudiar, en el presente trabajo de tesis, la clasificación algebraíca de los modelos de Bianchi y cada uno de los espacio-tiempo de Bianchi, aplicando el formalismo ADM de relatividad general en su versión Hamiltoniana y los grupos G3 . Se muestran las ecuaciones dinámicas con ayuda de la densidad Hamiltoniana H y los paréntesis de Poisson, en otras palabras, se presentan las ecuaciones de movimiento para cada uno de los espacio-tiempo de Bianchi. Se discuten algunas consecuencias de carácter teórico en dichas ecuaciones cuando tomamos el límite Ω → −∞ y los parámetros β+ y β− fijos, en consecuencia, encontramos que la parte dependiente del potencial gravitacional de la densidad Hamiltoniana tiende a cero y de las ecuaciones de movimiento encontramos la con stante de movimiento, pΩ = pβ+ = pβ− = constante.
Uploads
Papers by Mississippi Valenzuela Durán
in accelerators that are increasing in energy and complexity by the collaborations of thousands of
physicists from hundreds of institutes in a few dozen countries. In "big science" a research methodology
has been developed in which statistics is of great importance to interpret the results obtained from these
experiments. Despite the discovery of the Higgs boson in 2012, which contributed to the success of the
Standard Model and the award of the 2013 Nobel Prize in Physics. Based on these motivations, in the
present work certain statistical tests based on the "likelihood" method are shown and are applied in
high energy physics in the discovery of new phenomena, by making use of the construction of confidence
intervals of the model parameters. We focus on properties of methods called statistical "proofs" that
allow systematic uncertainties to be included. Also, we work with explicit formulas for the asymptotic
distributions of the statistical tests. In addition, we will use a representative data set, called the "Asimov"
data set, which provides a method for obtaining the experimental sensitivity of a search or measurement,
as well as the fluctuations in that expectation.
por lo que son invariantes ante transformaciones del grupo S3. Usando la simetría S3 tenemos a nuestra disposición 3 representaciones irreductibles, 2, 1s, 1a, donde podemos acomodar hasta cuatro dobletes de Higgs en un modelo que ocupa todas las representaciones irreductibles del grupo S3. Este modelo con cuatro dobletes de Higgs (4HDM) es de gran interés, gracias a que podemos tomar el cuarto doblete de Higgs como una partícula estable sin interacción con los fermiones por lo que se convierte en candidato a materia oscura, mientras que con los tres restantes las propiedades obtenidas se mantienen. Una condición importante para tener un candidato viable a materia oscura es su estabilidad, es decir, no se desintegra en partículas del modelo estándar. La forma más sencilla de establecer la estabilidad de una partícula es imponiendo una simetría discreta Z2, de modo que todos los campos se transformen en la forma Ψ −→ Ψ, mientras que las candidatas a materia oscura se transformen como χ −→ −χ, de esta manera nos aseguramos de que no tengamos términos que denoten desintegraciones de χ. Este método se utilizará en 4HDM. Otra imposición requerida para proponer la candidatura de un campo del doblete Ha, es que su Valor de Espectación del Vacío (VEV) correspondiente sea igual a cero, va = 0.
inadvertent error led to two errant numerical expressions
in Diferential identities. The main results and conclusions
remain unchanged. All of the aected formulas are
corrected below.
errant numerical expressions in Field equations. The
main results and conclusions of my paper remain unchanged. All of the aected formulas are corrected below.
−g in my recent paper [1], an inadvertent error led to two errant numerical
expressions in equations (37) and (38) that propagated
to the "Field equations". The main results and conclusions
of my paper remain unchanged. All of the aected
formulas are corrected below.
Thesis Chapters by Mississippi Valenzuela Durán
de intervalos de confianza de los parámetros del modelo. Nos centramos
en las propiedades de los métodos llamados “pruebas” estadísticas que permiten incluir las incertidumbres sistemáticas. También, trabajamos con fórmulas explícitas para las distribuciones asintóticas de las pruebas estadísticas. Además, usaremos un conjunto de datos representativo, llamado el conjunto de datos “Asimov”, que proporciona un método para obtener la sensibilidad experimental de una búsqueda
o medición, así como las fluctuaciones en esa espera.
in accelerators that are increasing in energy and complexity by the collaborations of thousands of
physicists from hundreds of institutes in a few dozen countries. In "big science" a research methodology
has been developed in which statistics is of great importance to interpret the results obtained from these
experiments. Despite the discovery of the Higgs boson in 2012, which contributed to the success of the
Standard Model and the award of the 2013 Nobel Prize in Physics. Based on these motivations, in the
present work certain statistical tests based on the "likelihood" method are shown and are applied in
high energy physics in the discovery of new phenomena, by making use of the construction of confidence
intervals of the model parameters. We focus on properties of methods called statistical "proofs" that
allow systematic uncertainties to be included. Also, we work with explicit formulas for the asymptotic
distributions of the statistical tests. In addition, we will use a representative data set, called the "Asimov"
data set, which provides a method for obtaining the experimental sensitivity of a search or measurement,
as well as the fluctuations in that expectation.
por lo que son invariantes ante transformaciones del grupo S3. Usando la simetría S3 tenemos a nuestra disposición 3 representaciones irreductibles, 2, 1s, 1a, donde podemos acomodar hasta cuatro dobletes de Higgs en un modelo que ocupa todas las representaciones irreductibles del grupo S3. Este modelo con cuatro dobletes de Higgs (4HDM) es de gran interés, gracias a que podemos tomar el cuarto doblete de Higgs como una partícula estable sin interacción con los fermiones por lo que se convierte en candidato a materia oscura, mientras que con los tres restantes las propiedades obtenidas se mantienen. Una condición importante para tener un candidato viable a materia oscura es su estabilidad, es decir, no se desintegra en partículas del modelo estándar. La forma más sencilla de establecer la estabilidad de una partícula es imponiendo una simetría discreta Z2, de modo que todos los campos se transformen en la forma Ψ −→ Ψ, mientras que las candidatas a materia oscura se transformen como χ −→ −χ, de esta manera nos aseguramos de que no tengamos términos que denoten desintegraciones de χ. Este método se utilizará en 4HDM. Otra imposición requerida para proponer la candidatura de un campo del doblete Ha, es que su Valor de Espectación del Vacío (VEV) correspondiente sea igual a cero, va = 0.
inadvertent error led to two errant numerical expressions
in Diferential identities. The main results and conclusions
remain unchanged. All of the aected formulas are
corrected below.
errant numerical expressions in Field equations. The
main results and conclusions of my paper remain unchanged. All of the aected formulas are corrected below.
−g in my recent paper [1], an inadvertent error led to two errant numerical
expressions in equations (37) and (38) that propagated
to the "Field equations". The main results and conclusions
of my paper remain unchanged. All of the aected
formulas are corrected below.
de intervalos de confianza de los parámetros del modelo. Nos centramos
en las propiedades de los métodos llamados “pruebas” estadísticas que permiten incluir las incertidumbres sistemáticas. También, trabajamos con fórmulas explícitas para las distribuciones asintóticas de las pruebas estadísticas. Además, usaremos un conjunto de datos representativo, llamado el conjunto de datos “Asimov”, que proporciona un método para obtener la sensibilidad experimental de una búsqueda
o medición, así como las fluctuaciones en esa espera.