Orientador: Marcelo Esteban Coniglio / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas / Made available in DSpace on 2018-08-25T12:43:36Z (GMT). No. of bitstreams: 1 Peron_NewtonMarques_D.pdf: 1773917 bytes, checksum: da2d2a1b1ecf8da6e26e419dee4888c5 (MD5) Previous issue date: 2014 / Resumo: Esse é um estudo sobre a viabilidade de matrizes finitas como semântica para lógica modal. Separamos nossa análise em dois casos: matrizes determinísticas e não-determinísticas. No primeiro caso, generalizamos o Teorema de Incompletude de Dugundji, garantindo que uma vasta família de lógicas modais não pode ser caracterizada por matrizes determinísticas finitas. No segundo caso, ampliamos a semântica de matrizes não- determinísticas para lógica modal proposta independentemente por Kearns e Ivlev. Essa ampliação engloba sistemas modais que, de acordo com nossa generalização, não podem ser caracterizados por matrizes determinísticas finitas / Abstract: This is a study on the feasibility of finite matrices as semantics for modal logics. We separate our analysis into two cases: deterministic and non-deterministic matrices. In the first case, we generalize Dugundji's Incompleteness Theorem, ensuring that a wide family of modal logic cannot be characterized by deterministic finite matrices. In the second, we extend the non-deterministic matrices semantics to modal logics proposed independently by Kearns and Ivlev. This extension embraces modal systems that, according to our generalization, cannot be characterized by finite deterministic matrices / Doutorado / Filosofia / Doutor em Filosofia

Matematik är ett ämne som elever över hela världen behöver lära sig. I de senare årskurserna bygger ämnet på att elever ska kunna behärska algebra. Vi har valt att fokusera på mönster vilket många anser vara inkörsporten till algebra. För att lärare ska kunna erbjuda elever en rättvis utbildning bör de ha kunskap om elevers svårigheter och lärande. Vår litteraturstudie har riktat in sig på att försöka svara på vad forskning säger om elevers lärande till växande geometriska mönster och explicit formel. I de elva studier som valts ut har vi kommit fram till att några gemensamma slutsatser finns men även sådana som skiljer sig åt. Att elever behöver utveckla sitt språk och få förståelse för innebörden av bokstavssymboler i matematiken är en viktig slutsats för lärande relaterad till mönster. Studierna har dessutom visat en stark relevans i att samordna olika delar till en helhet. Svenska elevers resultat i internationella undersökningar problematiseras och vad som kan tänkas vara orsaken till att de presterar sämre i mönsterrelaterade uppgifter än vad de gör i övriga delar i matematiken. Vårt resultat är till stor del överensstämmande med hur de svenska styrdokumenten förhåller sig till ämnet. Trots det har svenska elever svårigheter med att uttrycka en explicit formel till ett växande geometriskt mönster. Just den explicita formeln är viktig för elevers helhetsförståelse av mönster och tidig algebra.

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The present thesis considers the relation between Jacques Derrida and G.W.F. Hegel. In his Positions Derrida noted that differance is ‘at a point of almost absolute proximity to Hegel,’ and that he had ‘attempted to distinguish [differance] from Hegelian difference at the point at which Hegel, in the greater Logic, determines difference as contradiction only in order to resolve it.’ Nevertheless, scholarship on the relation between the two thinkers has largely neglected the detailed consideration of the relation of Derrida’s thinking to Hegel’s logic of essence, where the categories of difference and contradiction are located. This has often led to a simplification, from both Hegelian and Derridean perspectives, of the relation between Hegel and Derrida. Through a reading of Hegel’s logic of essence and of Derrida’s early texts in particular, the thesis first aims to determine the nature and degree of the proximity indicated by Derrida and then considers the manner in which the two thinkers depart from one another. The proximity between Hegel and Derrida is drawn out through an analysis of Hegel’s notion of reflection and his logic of identity and difference. This logic is compared with the ‘graphics’ of identity and difference elaborated by Derrida in his Limited Inc. I claim that Derrida departs from Hegel in thinking difference as the displacement of opposition. Nevertheless, I claim that in relating Hegel and Derrida to one another, it cannot be a question of simply comparing two logics or two philosophies, for Derrida does not and cannot have a general logic or ‘philosophy’ of ‘differance.’ Derrida thus departs from Hegel also insofar as he puts into question the possibility of, and the desire for, a general onto-logic.

M.Ed. / Please refer to full text to view abstract

M.Sc.

M.Sc. / Please refer to full text to view abstract

This dissertation analyzes the Wigner-Poisson system in the presence of an external Coulomb potential. In the first part, the Weyl transform is defined and used to derive an exact quantum mechanical equation for the Weyl transform of the density function ρw (the Wigner function) known as the Wigner equation. This equation holds for any Hamiltonian which is a function of the position and momentum operators. The Wigner-Poisson system is then formally derived by imposing various assumptions on the structure of the Hamiltonian. This system describes the behaviour of an effective one-particle distribution in the presence of a large ensemble of particles. Furthermore, it allows the particles to either attract or repel each other as well as attract or repel as a whole from a fixed Coulomb source located at the origin. The second part details the question of existence and uniqueness for the Wigner-Poisson system. It is shown that provided the initial Wigner function is sufficiently regular [special characters omitted] and is a valid Wigner distribution, then the Wigner-Poisson system has a unique global mild solution [special characters omitted]. This result is independent of both the nature of the external Coulomb potential as well as the interparticle interaction.The proof of this result is accomplished by first transforming the Wigner-Poisson system into a countably infinite set of Schrödinger equations which results in what is referred to as the Schrödinger Poisson system. Using standard semigroup theory arguments, existence and uniqueness of the Schrödinger-Poisson system is established. The properties of the Wigner-Poisson system are then obtained by reversing the transformation step. Regularity results for both the Schrödinger-Poisson and the Wigner-Poisson systems are compared to the case with no external Coulomb potential. In addition, the known regularity results are extended when there is no external field. The results illustrate that the introduction of an external Coulomb potential slightly reduces the regularity of the solution. This confirms a conjecture of Brezzi and Markowich. The third part analyzes the asymptotic behaviour of the Wigner-Poisson system. If the configurational energy Εₐ,ᵦ(t) is positive for all times then by considering the Schrödinger-Poisson system, solutions will decay in the sense of Lᵖ for 2 < p < 6. This generalizes a result of Illner, Lange and Zweifel. Moreover, If the total energy is negative then the solutions will not decay in the sense of Lᵖ for any 2 < p ≤ ∞. This generalizes a result of Chadam and Glassey. Decay estimates for both the Schrödinger-Poisson and the Wigner-Poisson systems are compared to the case with no external Coulomb field. As with the regularity results, the introduction of an external Coulomb field degrades the reported decay rates of the solution. / Graduate