On the Path Integral Loop Representation of (2+1) Lattice Non-Abelian Theory

A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The corresponding path integral for SU(2) lattice gauge theory is expressed as a sum over colored surfaces, i.e. only involving the $j_p$ attached to the lattice plaquettes. This surfaces may be interpreted as the world sheets of the spin networks In 2+1 dimensions, this can be accomplished by working in a lattice dual to a tetrahedral lattice constructed on a face centered cubic Bravais lattice. On such a lattice, the integral of gauge variables over boundaries or singular lines -- which now always bound three coloured surfaces -- only contributes when four singular lines intersect at one vertex and can be explicitly computed producing a 6-j or Racah symbol. We performed a strong coupling expansion for the free energy. The convergence of the series expansions is quite different from the series expansions which were performed in ordinary cubic lattices. In the case of ordinary cubic lattices the strong coupling expansions up to the considered truncation number of plaquettes have the great majority of their coefficients positive, while in our case we have almost equal number of contributions with both signs. Finally, it is discused the connection in the naive coupling limit between this action and that of the B-F topological field theory and also with the pure gravity action.Comment: 16 pages, REVTEX, 8 Encapsulated Postscript figures using psfig, minor changes in text and reference

Implementaci?n de una metodolog?a estocastica en programaci?n secuencial

71 p. Recurso Electr?nicoEn el presente trabajo se ha implementado una metodolog?a estad?stica en algunos problemas de programaci?n secuencial. Se ha hecho uso de Modelos Lineales, mediante el uso de las siguientes propuestas: dos tareas con una sola operaci?n, varias tareas, varias m?quinas con sola una operaci?n. Por ultimo se plantea un problema con varias tareas y varias m?quinas interactuando 2 y 3 operaciones dependientes, igualmente se dise?o una mezcla de Distribuciones la cual es muy ?til en este tipo de problema

Continuum spin foam model for 3d gravity

An example illustrating a continuum spin foam framework is presented. This covariant framework induces the kinematics of canonical loop quantization, and its dynamics is generated by a {\em renormalized} sum over colored polyhedra. Physically the example corresponds to 3d gravity with cosmological constant. Starting from a kinematical structure that accommodates local degrees of freedom and does not involve the choice of any background structure (e. g. triangulation), the dynamics reduces the field theory to have only global degrees of freedom. The result is {\em projectively} equivalent to the Turaev-Viro model.Comment: 12 pages, 3 figure

In-situ fabrication of gold nanoparticle functionalized probes for tip-enhanced Raman spectroscopy by dielectrophoresis

We report the use of dielectrophoresis to fabricate in-situ probes for tip-enhanced Raman spectroscopy (TERS) based on Au nanoparticles. A typical conductive atomic force microscope (AFM) was used to functionalize iridium-coated conductive silicon probes with Au nanoparticles of 10-nm diameter. Suitable TERS probes can be rapidly produced (30 to 120 s) by applying a voltage of 10 Vpp at a frequency of 1 MHz. The technique has the advantage that the Au-based probes are ready for immediate use for TERS measurements, minimizing the risks of tip contamination and damage during handling. Scanning electron microscopy and energy dispersive x-ray spectroscopy were used to confirm the quality of the probes, and used samples of p-ATP monolayers on silver substrates were used to demonstrate experimentally TERS measurements

Ethnomathematical and Mathematical Connections Activated by a Teacher in Mathematical Problems Posing and Solving

Background: Connections are essential for understanding concepts, but difficulties have been evidenced in connecting representations and meanings of concepts and creating contextualised mathematical problems by teachers and students. Objective: Therefore, ethnomathematical and mathematical connections were analysed in a teacher's mathematical activity when posing and solving mathematical problems. Design: The methodology was qualitative-ethnographic, developed in a workshop done in stages. Setting and participants: An indigenous Mokaná teacher from Sibarco was selected. Data collection and analysis: Semi-structured interviews were conducted in the workshop, and the data were analysed based on the connections; the workshop was initially designed considering previous literature on the issue, and the researchers were familiarised with the teacher. Results: For the analysis of the mathematics used by the teacher in the classroom, we considered his sociocultural context, where he set problems about the area and perimeter of lots of land and enclosures. Then, the researchers presented the ethnomathematical connections that emerged in the elaboration and commercialisation of the pigeon peas sancocho, which was the basis for the teacher to pose and solve problems involving conversions between units of measurement, volume of the totumas (ellipsoid), etc. Simultaneously, mathematical connections of different representations, procedural, meaning, and modelling were identified. Finally, the researchers gave feedback by assessing the Acta Sci. (Canoas), 25(1), 86-121, Jan./Fev. 2023 87 potential of the mathematics known and explained by the teacher. Conclusion: This research provides input for teachers to pose and solve problems contextualised through connections