Pseudofermion dynamical theory for the spin dynamical correlation functions of the half-filled 1D Hubbard model

A modified version of the metallic-phase pseudofermion dynamical theory (PDT) of the 1D Hubbard model is introduced for the spin dynamical correlation functions of the half-filled 1D Hubbard model Mott– Hubbard phase. The Mott–Hubbard insulator phase PDT is applied to the study of the model longitudinal and transverse spin dynamical structure factors at finite magnetic field h, focusing in particular on the sin- gularities at excitation energies in the vicinity of the lower thresholds. The relation of our theoretical results to both condensed-matter and ultra-cold atom systems is discussed.

On the temperature dependence of the absorption cross section for black holes in string theory

We study the low frequency absorption cross section of spherically symmetric nonextremal d-dimensional black holes. In the presence of α′ corrections, this quantity must have an explicit dependence on the Hawking temperature of the form 1/TH. This property of the low frequency absorption cross section is shared by the D1-D5 system from type IIB superstring theory already at the classical level, without α′ corrections. We apply our formula to the simplest example, the classical d-dimensional Reissner-Nordstr¨om solution, checking that the obtained formula for the cross section has a smooth extremal limit. We also apply it for a d-dimensional Tangherlini-like solution with α′3 corrections.

Absorption of scalars by nonextremal charged black holes in string theory

We analyze the low frequency absorption cross section of minimally coupled massless scalar fields by different kinds of charged static black holes in string theory, namely the D1–D5 system in d=5 and a four dimensional dyonic four-charged black hole. In each case we show that this cross section always has the form of some parameter of the solution divided by the black hole Hawking temperature. We also verify in each case that, despite its explicit temperature dependence, such quotient is finite in the extremal limit, giving a well defined cross section. We show that this precise explicit temperature dependence also arises in the same cross section for black holes with string \alpha' corrections: it is actually induced by them.

Verificación de Sistemas Basada en Teoría de Tipos. System verification in type theory

Este proyecto se enmarca en la utlización de métodos formales (más precisamente, en la utilización de teoría de tipos) para garantizar la ausencia de errores en programas. Por un lado se plantea el diseño de nuevos algoritmos de chequeo de tipos. Para ello, se proponen nuevos algoritmos basados en la idea de normalización por evaluación que sean extensibles a otros sistemas de tipos. En el futuro próximo extenderemos resultados que hemos conseguido recientemente [16,17] para obtener: una simplificación de los trabajos realizados para sistemas sin regla eta (acá se estudiarán dos sistemas: a la Martin Löf y a la PTS), la formulación de estos chequeadores para sistemas con variables, generalizar la noción de categoría con familia utilizada para dar semántica a teoría de tipos, obtener una formulación categórica de la noción de normalización por evaluación y finalmente, aplicar estos algoritmos a sistemas con reescrituras. Para los primeros resultados esperados mencionados, nos proponemos como método adaptar las pruebas de [16,17] a los nuevos sistemas. La importancia radica en que permitirán tornar más automatizables (y por ello, más fácilmente utilizables) los asistentes de demostración basados en teoría de tipos. Por otro lado, se utilizará la teoría de tipos para certificar compiladores, intentando llevar adelante la propuesta nunca explorada de [22] de utilizar un enfoque abstracto basado en categorías funtoriales. El método consistirá en certificar el lenguaje "Peal" [29] y luego agregar sucesivamente funcionalidad hasta obtener Forsythe [23]. En este período esperamos poder agregar varias extensiones. La importancia de este proyecto radica en que sólo un compilador certificado garantiza que un programa fuente correcto se compile a un programa objeto correcto. Es por ello, crucial para todo proceso de verificación que se base en verificar código fuente. Finalmente, se abordará la formalización de sistemas con session types. Los mismos han demostrado tener fallas en sus formulaciones [30], por lo que parece conveniente su formalización. Durante la marcha de este proyecto, esperamos tener alguna formalización que dé lugar a un algoritmo de chequeo de tipos y a demostrar las propiedades usuales de los sistemas. La contribución es arrojar un poco de luz sobre estas formulaciones cuyos errores revelan que el tema no ha adquirido aún suficiente madurez o comprensión por parte de la comunidad. This project is about using type theory to garantee program correctness. It follows three different directions: 1) Finding new type-checking algorithms based on normalization by evaluation. First, we would show that recent results like [16,17] extend to other type systems like: Martin-Löf´s type theory without eta rule, PTSs, type systems with variables (in addition to systems in [16,17] which are a la de Bruijn), systems with rewrite rules. This will be done by adjusting the proofs in [16,17] so that they apply to such systems as well. We will also try to obtain a more general definition of categories with families and normalization by evaluation, formulated in categorical terms. We expect this may turn proof-assistants more automatic and useful. 2) Exploring the proposal in [22] to compiler construction for Algol-like languages using functorial categories. According to [22] such approach is suitable for verifying compiler correctness, claim which was never explored. First, the language Peal [29] will be certified in type theory and we will gradually add funtionality to it until a correct compiler for the language Forsythe [23] is obtained. 3) Formilizing systems for session types. Several proposals have shown to be faulty [30]. This means that a formalization of it may contribute to the general understanding of session types.

Darwin and after Darwin. An exposition of the Darwinian theory and a discussion of post-Darwinian questions, by George John Romanes ...

3

Darwin and after Darwin. An exposition of the Darwinian theory and a discussion of post-Darwinian questions, by George John Romanes ...

2

Darwin and after Darwin. An exposition of the Darwinian theory and a discussion of post-Darwinian questions, by George John Romanes ...

1

A critique of the theory of evolution, by Thomas Hunt Morgan ... Lectures delivered at Princeton University, February 24, March 1, 8, 15, 1916.

1916:Feb.-Mar.

The mutation theory; experiments and observations on the origin of species in the vegetable kingdom, by Hugo de Vries ... tr. by Prof. J. B. Farmer and A. D. Darbishire ...

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