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Cardona Hurtado, Oscar Abel - One of the best experts on this subject based on the ideXlab platform.
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Beneficios de la notación de Peirce para los conectivos proposicionales binarios
2016Co-Authors: Cardona Hurtado, Oscar AbelAbstract:Background: In traditional binary Notation for propositional connectives only some of these ones are taken into account. Throughout the twentieth century several Notations were proposed which overcome this flaw, leading to the proposal of interesting mathematical problems. Objective: This paper presents the Notation created by the American Charles Peirce, showing some of the properties of this symbols, and evidencing the advantages of these compared to the traditional. Method: the Notation proposed by Peirce is described, and some properties of the geometric and algebraic logical character among its connective are verified; also, the possible role of these properties in the traditional Notation is analyzed. Results: In addition to several individual properties and multiple relations between the connectives, the symmetries of the full set of binary propositional connective is visually evident in the signs proposed by Peirce. Conclusion: Different benefits of the Notation proposed by Peirce, support the conclusion that the Usual Notation is clearly surpassed by the symbolism designed by the American scientist.Antecedentes: Na notação tradicional para os conectivos proposicionais binários são tidos em conta somente alguns destes. Ao longo do século XX foram propostas várias notações que corrigem essa falência, dando lugar ao planejamento de interessantes problemas matemáticos. Objetivo: Neste artigo se apresenta a notação criada pelo norte-americano Charles Peirce, onde se mostram algumas das propriedades que tem está simbologia, e se evidenciam suas vantagens com respeito à tradicional. Método: Se descreve a notação proposta por Peirce, e se verificam algumas propriedades de carácter lógico geométrico e algébrico entre seus conectivos; também se analisa a possível atuação destas propriedades na notação Usual. Resultados: Ademais de várias propriedades individuais e de múltiplas relações entre os conectivos, as simetrias do sistema completo dos conectivos proposicionais binários se evidenciam de maneira visual nos signos propostos por Peirce. Conclusão: Diversas bondades se percebem na notação proposta por Peirce, permitindo afirmar que a notação Usual é superada de maneira clara pela simbologia desenhada pelo científico norte-americano.Palavras-chave: Charles S. Peirce, conectivo proposicional, operação, simetria, tabela de verdade.Antecedentes: En la notación tradicional para los conectivos proposicionales binarios son tenidos en cuenta solamente algunos de estos. A lo largo del siglo XX fueron propuestas varias notaciones que subsanan esa falencia, dando lugar al planteamiento de interesantes problemas matemáticos. Objetivo: En este escrito se presenta la notación creada por el norteamericano Charles Peirce, se muestran algunas propiedades de las cuales goza esta simbología, y se evidencian sus ventajas con respecto a la tradicional. Método: Se describe la notación propuesta por Peirce, y se verifican algunas propiedades de carácter lógico geométrico y algebraico entre sus conectivos; también se analiza la posible actuación de estas propiedades en la notación Usual. Resultados: Además de varias propiedades individuales y de múltiples relaciones entre los conectivos, las simetrías del sistema completo de los conectivos proposicionales binarios se evidencian de manera visual en los signos propuestos por Peirce. Conclusión: Diversas bondades de las cuales goza la notación propuesta por Peirce, permiten afirmar que la notación Usual es superada de manera clara por la simbología diseñada por el científico norteamericano
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Beneficios de la notación de Peirce para los conectivos proposicionales binarios
'Universidad Francisco de Paula Santander', 2016Co-Authors: Cardona Hurtado, Oscar AbelAbstract:Antecedentes: En la notación tradicional para los conectivos proposicionales binarios son tenidos en cuenta solamente algunos de estos. A lo largo del siglo XX fueron propuestas varias notaciones que subsanan esa falencia, dando lugar al planteamiento de interesantes problemas matemáticos. Objetivo: En este escrito se presenta la notación creada por el norteamericano Charles Peirce, se muestran algunas propiedades de las cuales goza esta simbología, y se evidencian sus ventajas con respecto a la tradicional. Método: Se describe la notación propuesta por Peirce, y se verifican algunas propiedades de carácter lógico geométrico y algebraico entre sus conectivos; también se analiza la posible actuación de estas propiedades en la notación Usual. Resultados: Además de varias propiedades individuales y de múltiples relaciones entre los conectivos, las simetrías del sistema completo de los conectivos proposicionales binarios se evidencian de manera visual en los signos propuestos por Peirce. Conclusión: Diversas bondades de las cuales goza la notación propuesta por Peirce, permiten afirmar que la notación Usual es superada de manera clara por la simbología diseñada por el científico norteamericano.Palabras clave: Conectivo proposicional, Charles S. Peirce, operación, simetría, tabla de verdad. AbstractBackground: In traditional binary Notation for propositional connectives only some of these ones are taken into account. Throughout the twentieth century several Notations were proposed which overcome this flaw, leading to the proposal of interesting mathematical problems. Objective: This paper presents the Notation created by the American Charles Peirce, showing some of the properties of this symbols, and evidencing the advantages of these compared to the traditional. Method: the Notation proposed by Peirce is described, and some properties of the geometric and algebraic logical character among its connective are verified; also, the possible role of these properties in the traditional Notation is analyzed. Results: In addition to several individual properties and multiple relations between the connectives, the symmetries of the full set of binary propositional connective is visually evident in the signs proposed by Peirce. Conclusion: Different benefits of the Notation proposed by Peirce, support the conclusion that the Usual Notation is clearly surpassed by the symbolism designed by the American scientist.Keywords: Propositional connective, Charles S. Peirce, operation, symmetry, truth table. Resumo Antecedentes: Na notação tradicional para os conectivos proposicionais binários são tidos em conta somente alguns destes. Ao longo do século XX foram propostas várias notações que corrigem essa falência, dando lugar ao planejamento de interessantes problemas matemáticos. Objetivo: Neste artigo se apresenta a notação criada pelo norte-americano Charles Peirce, onde se mostram algumas das propriedades que tem está simbologia, e se evidenciam suas vantagens com respeito à tradicional. Método: Se descreve a notação proposta por Peirce, e se verificam algumas propriedades de carácter lógico geométrico e algébrico entre seus conectivos; também se analisa a possível atuação destas propriedades na notação Usual. Resultados: Ademais de várias propriedades individuais e de múltiplas relações entre os conectivos, as simetrias do sistema completo dos conectivos proposicionais binários se evidenciam de maneira visual nos signos propostos por Peirce. Conclusão: Diversas bondades se percebem na notação proposta por Peirce, permitindo afirmar que a notação Usual é superada de maneira clara pela simbologia desenhada pelo científico norte-americano.Palavras-chave: Charles S. Peirce, conectivo proposicional, operação, simetria, tabela de verdade
Maxime Hauray - One of the best experts on this subject based on the ideXlab platform.
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Propagation of chaos for the Landau equation with moderately soft potentials
Annals of Probability, 2016Co-Authors: Nicolas Fournier, Maxime HaurayAbstract:We consider the 3D Landau equation for moderately soft potentials ($\gamma\in(-2,0)$ with the Usual Notation) as well as a stochastic system of $N$ particles approximating it. We first establish some strong/weak stability estimates for the Landau equation, which are satisfying only when $\gamma \in [-1,0)$. We next prove, under some appropriate conditions on the initial data, the so-called propagation of molecular chaos, i.e. that the empirical measure of the particle system converges to the unique solution of the Landau equation. The main difficulty is the presence of a singularity in the equation. When $\gamma \in (-1,0)$, the strong-weak uniqueness estimate allows us to use a coupling argument and to obtain a rate of convergence. When $\gamma \in (-2,-1]$, we use the classical martingale method introduced by McKean. To control the singularity, we have to take advantage of the regularity provided by the entropy dissipation. Unfortunately, this dissipation is too weak for some (very rare) aligned configurations. We thus introduce a perturbed system with an additional noise, show the propagation of chaos for that perturbed system and finally prove that the additional noise is almost never used in the limit.
Nicolas Fournier - One of the best experts on this subject based on the ideXlab platform.
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On exponential moments of the homogeneous Boltzmann equation for hard potentials without cutoff
2021Co-Authors: Nicolas FournierAbstract:We consider the spatially homogeneous Boltzmann equation for hard potentials without cutoff. We prove that an exponential moment of order $\rho=\min\{2\gamma/(2-\nu),2\}$, with the Usual Notation, is immediately created. This is stronger than what happens in the case with cutoff. We also show that exponential moments of order $\rho\in (0,2]$ are propagated.
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Propagation of chaos for the Landau equation with moderately soft potentials
Annals of Probability, 2016Co-Authors: Nicolas Fournier, Maxime HaurayAbstract:We consider the 3D Landau equation for moderately soft potentials ($\gamma\in(-2,0)$ with the Usual Notation) as well as a stochastic system of $N$ particles approximating it. We first establish some strong/weak stability estimates for the Landau equation, which are satisfying only when $\gamma \in [-1,0)$. We next prove, under some appropriate conditions on the initial data, the so-called propagation of molecular chaos, i.e. that the empirical measure of the particle system converges to the unique solution of the Landau equation. The main difficulty is the presence of a singularity in the equation. When $\gamma \in (-1,0)$, the strong-weak uniqueness estimate allows us to use a coupling argument and to obtain a rate of convergence. When $\gamma \in (-2,-1]$, we use the classical martingale method introduced by McKean. To control the singularity, we have to take advantage of the regularity provided by the entropy dissipation. Unfortunately, this dissipation is too weak for some (very rare) aligned configurations. We thus introduce a perturbed system with an additional noise, show the propagation of chaos for that perturbed system and finally prove that the additional noise is almost never used in the limit.
Oscar Abel Cardona-hurtado - One of the best experts on this subject based on the ideXlab platform.
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Beneficios de la notación de Peirce para los conectivos proposicionales binarios
Universidad Francisco de Paula Santander, 2016Co-Authors: Oscar Abel Cardona-hurtadoAbstract:Background: In traditional binary Notation for propositional connectives only some of these ones are taken into account. Throughout the twentieth century several Notations were proposed which overcome this flaw, leading to the proposal of interesting mathematical problems. Objective: This paper presents the Notation created by the American Charles Peirce, showing some of the properties of this symbols, and evidencing the advantages of these compared to the traditional. Method: the Notation proposed by Peirce is described, and some properties of the geometric and algebraic logical character among its connective are verified; also, the possible role of these properties in the traditional Notation is analyzed. Results: In addition to several individual properties and multiple relations between the connectives, the symmetries of the full set of binary propositional connective is visually evident in the signs proposed by Peirce. Conclusion: Different benefits of the Notation proposed by Peirce, support the conclusion that the Usual Notation is clearly surpassed by the symbolism designed by the American scientist
Mikhail Malt - One of the best experts on this subject based on the ideXlab platform.
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A CAP for graphic scores. Graphic Notation and performance
Universidade da Coruña, 2017Co-Authors: Benny Sluchin, Mikhail MaltAbstract:Many graphic scores use the pitch versus time presentation, as a natural extension of the Usual Notation. In the general case, it displays discrete pitches, in a fixed timeline. Nevertheless, graphic scores use a lot of continuous lines, and the vertical dimension can be adapted to a particular performance. In such a way, the instrumentation is free, and the actual range of a particular instrument can be adapted according to the Notation. The present article is initiated by a search to provide the performer with adequate tools to approach the execution of such works. A computer assisted performance approach helps the player in the preparation process for both: the time and the pitch approximations. The simulation can enhance the performance in approaching the graphical Notation
