Families of Singular and Subsingular Vectors of the Topological N=2 Superconformal Algebra

We analyze several issues concerning the singular vectors of the Topological N=2 Superconformal algebra. First we investigate which types of singular vectors exist, regarding the relative U(1) charge and the BRST-invariance properties, finding four different types in chiral Verma modules and twenty-nine different types in complete Verma modules. Then we study the family structure of the singular vectors, every member of a family being mapped to any other member by a chain of simple transformations involving the spectral flows. The families of singular vectors in chiral Verma modules follow a unique pattern (four vectors) and contain subsingular vectors. We write down these families until level 3, identifying the subsingular vectors. The families of singular vectors in complete Verma modules follow infinitely many different patterns, grouped roughly in five main kinds. We present a particularly interesting thirty-eight-member family at levels 3, 4, 5, and 6, as well as the complete set of singular vectors at level 1 (twenty-eight different types). Finally we analyze the D\"orrzapf conditions leading to two linearly independent singular vectors of the same type, at the same level in the same Verma module, and we write down four examples of those pairs of singular vectors, which belong to the same thirty-eight-member family.Comment: Latex, 51 pages. One figure. Many improvements. Major revisio

The Other Spectral Flow

Recently we showed that the spectral flow acting on the N=2 twisted topological theories gives rise to a topological algebra automorphism. Here we point out that the untwisting of that automorphism leads to a spectral flow on the untwisted N=2 superconformal algebra which is different from the usual one. This "other" spectral flow does not interpolate between the chiral ring and the antichiral ring. In particular, it maps the chiral ring into the chiral ring and the antichiral ring into the antichiral ring. We discuss the similarities and differences between both spectral flows. We also analyze their action on null states.Comment: Latex, 7 page

Aixecament fotogràmetric i registre de les majòliques de Montserrat

La digitalització del patrimoni és cada cop més important, amb l’objectiu de preservar-ho i difondre en el futur. En aquest treball està explicat pas per pas com es digitalitzaran les Majòliques de Montserrat, més de noranta ornaments, dedicats a advocacions marianes de diferents pobles i ciutats, que es troben al Camí dels Degotalls. S’explicarà que són i com han anat evolucionant al pas del temps.Es mostrarà de forma ordenada i detallada el procés per la generació d’un model 3D de cadascuna de les Majòliques, com i quines dades s’han pres per la seva elaboració. També es veurà com es recolliren totes aquestes dades en una fitxes per tal d’entregar-les a L’Abadia de Montserrat, òrgan que regula la creació de noves construccions.Posteriorment aprofitant les dades que s’han pres a camp, es prepararà un plànol CAD per la visualització rapida i clara de la ubicació de cadascuna d’elles. I de la mateixa manera també es detallarà com transformar aquestes dades en un format “shapefile” on quedaran emmagatzemades totes les dades geomètriques i la corresponent informació de cadascuna de les Majòliques.Per concloure, s’importarà aquest arxiu a una base de dades, amb el qual podrem tractar tota la informació de manera ràpida per a qualsevol tipus de consulta

Topological Descendants: DDK and KM Realizations

The "minimal matter + scalar" system can be embedded into the twisted N=2 topological algebra in two ways: a la DDK or a la KM. Here we present some results concerning the topological descendants and their DDK and KM realizations. In particular, we prove four "no-ghost" theorems (two for null states) regarding the reduction of the topological descendants into secon- daries of the "minimal matter + scalar" conformal field theory. We write down the relevant expressions for the case of level 2 descendants.Comment: 10 pgs, Late

Spectral Flows and Twisted Topological Theories

We analyze the action of the spectral flows on N=2 twisted topological theories. We show that they provide a useful mapping between the two twisted topological theories associated to a given N=2 superconformal theory. This mapping can also be viewed as a topological algebra automorphism. In particular null vectors are mapped into null vectors, considerably simplifying their computation. We give the level 2 results. Finally we discuss the spectral flow mapping in the case of the DDK and KM realizations of the topological algebra.Comment: The presentation of the results has been very much improved. Some references have been adde

The Adapted Ordering Method for Lie Algebras and Superalgebras and their Generalizations

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows: to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the Adapted Ordering Method for general Lie algebras and superalgebras, and their generalizations, provided they can be triangulated. We also review briefly the results obtained for the Virasoro algebra and for the N=2 and Ramond N=1 superconformal algebras.Comment: Many improvements in the redaction for pedagogical purposes. Latex, 11 page

A Narrative Approach to the Philosophical Interpretation of Dreams, Memories, and Reflections of the Unconscious Through the Use of Autoethnography/Biography

The purpose of the present study aimed to develop a comprehensive model that measures the autoethnographic/biographic relevance of dreams, memories, and reflections as they relate to understanding the self and others. A dream, memory, and reflection (DMR) ten item questionnaire was constructed using aspects of Freudian, Jungian, and Lacanian Theory of Dream Interpretation. Fifteen dreams, five memories, and five reflections were collected from the participant at the waking episode or during a moment of deep thought. The DMR analysis was used as the prime matter for creating a narrative document that uses autoethnography and autobiography to deliver a philosophical story about the unconscious reality of the participant. The results of the dissertation study produced a ten section narrative document titled The Shadow of Joaquin that portrayed the benchmarks of the life of the participant that led him to the completion of a doctoral degree in curriculum and instruction. At the final section of the narrative document the postmodern philosophical theory of Labor Percolation is proposed by the researcher as a direct result of the DMR analysis

24-hour Heart Rate is Related to Lower Extremity Venous Vascular Function in Persons with Paraplegia

Please refer to the pdf version of the abstract located adjacent to the title