Cyclotomic factors of the descent set polynomial

We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting factorization patterns. We explore the question of when particular cyclotomic factors divide these polynomials. As an instance we deduce that the proportion of odd entries in the descent set statistics in the symmetric group S_n only depends on the number on 1's in the binary expansion of n. We observe similar properties for the signed descent set statistics.Comment: 21 pages, revised the proof of the opening result and cleaned up notatio

Active Sensing for Dynamic, Non-holonomic, Robust Visual Servoing

We consider the problem of visually servoing a legged vehicle with unicycle-like nonholonomic constraints subject to second-order fore-aft dynamics in its horizontal plane. We target applications to rugged environments characterized by complex terrain likely to perturb significantly the robot’s nominal dynamics. At the same time, it is crucial that the camera avoid “obstacle” poses where absolute localization would be compromised by even partial loss of landmark visibility. Hence, we seek a controller whose robustness against disturbances and obstacle avoidance capabilities can be assured by a strict global Lyapunov function. Since the nonholonomic constraints preclude smooth point stabilizability we introduce an extra degree of sensory freedom, affixing the camera to an actuated panning axis mounted on the robot’s back. Smooth stabilizability to the robot-orientation-indifferent goal cycle no longer precluded, we construct a controller and strict global Lyapunov function with the desired properties. We implement several versions of the scheme on a RHex robot maneuvering over slippery ground and document its successful empirical performance. For more information: Kod*La

Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids

To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid

Tropical types and associated cellular resolutions

An arrangement of finitely many tropical hyperplanes in the tropical torus leads to a notion of `type' data for points, with the underlying unlabeled arrangement giving rise to `coarse type'. It is shown that the decomposition of the tropical torus induced by types gives rise to minimal cocellular resolutions of certain associated monomial ideals. Via the Cayley trick from geometric combinatorics this also yields cellular resolutions supported on mixed subdivisions of dilated simplices, extending previously known constructions. Moreover, the methods developed lead to an algebraic algorithm for computing the facial structure of arbitrary tropical complexes from point data.Comment: minor correction

Affine and toric hyperplane arrangements

We extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.Comment: 32 pages, 4 figure

Thermochemical equilibrium model of synthetic natural gas production from coal gasification using aspen plus

ABSTRACT: The production of synthetic or substitute natural gas (SNG) from coal is a process of interest in Colombia where the reserves-to-production ratio (R/P) for natural gas is expected to be between 7 and 10 years, while the R/P for coal is forecasted to be around 90 years. In this work, the process to produce SNG by means of coal-entrained flow gasifiers is modeled under thermochemical equilibrium with the Gibbs free energy approach. The model was developed using a complete and comprehensive Aspen Plus model. Two typical technologies used in entrained flow gasifiers such as coal dry and coal slurry are modeled and simulated. Emphasis is put on interactions between the fuel feeding technology and selected energy output parameters of coal-SNG process, that is, energy efficiencies, power, and SNG quality. It was found that coal rank does not significantly affect energy indicators such as cold gas, process, and global efficiencies. However, feeding technology clearly has an effect on the process due to the gasifying agent. Simulations results are compared against available technical data with good accuracy. Thus, the proposed model is considered as a versatile and useful computational tool to study and optimize the coal to SNG process

Periodisation as an approach in historiographic research in mathematics teaching: reflections on two case studies

Background: the study of the history of mathematics teaching can be approached from different perspectives, defining contours from which the researcher performs the analysis focused on a process characterised by continuity, or by adopting periodisation. Objective: in this article, we seek to conduct a study based on the delimitation of periods, according to Le Goff’s (2014) argument, and in the light of the depth hermeneutics, based on Thompson (2011). Design: given the premises above, we conducted a documentary analysis of two historical processes within the scope of mathematics teaching, one focusing on the municipal public schools of canoas, and the other on a technical course in chemistry of a school in the city of novo Hamburgo, both in the state of Rio Grande do Sul. Setting and participants: a timeline with conspicuous events used to periodicise both historical processes analysed by the authors. Data collection and analysis: analysis of documents relevant to the history of the technical school investigated and education in the municipality of canoas. Results: in both cases, it was possible to characterise the historical processes in periods based on events and official documents that generate changes in mathematics teaching. Conclusions: the historical processes analysed are characterised by ruptures resulting from changes, especially in the legislation, both in the municipal public network and in the technical education institution researched, enabling the realisation of changes and the characterisation of distinct periods, with their nuances

Resonant nature of phonon-induced damping of Rabi oscillations in quantum dots

Optically controlled coherent dynamics of charge (excitonic) degrees of freedom in a semiconductor quantum dot under the influence of lattice dynamics (phonons) is discussed theoretically. We show that the dynamics of the lattice response in the strongly non-linear regime is governed by a semiclassical resonance between the phonon modes and the optically driven dynamics. We stress on the importance of the stability of intermediate states for the truly coherent control.Comment: 4 pages, 2 figures; final version; moderate changes, new titl

Efecto del rango de carbones colombianos y su tecnología de alimentación en la producción de gas natural sustituto, mediante gasificación en lecho arrastrado

RESUMEN: Presenta los resultados de un estudio del efecto del rango del carbón usado (desde subbituminoso hasta semiantracita) y de la tecnología de alimentación (seca o húmeda) sobre el proceso de producción de gas natural sustituto (GNS) en gasificadores de flujo arrastrado. Se analizaron diez carbones provenientes de importantes minas de Colombia. El proceso de producción de GNS a partir de gasificación de carbón se modeló bajo equilibrio termoquímico en Aspen Plus. El rendimiento del proceso se evaluó en términos de parámetros de salida, que incluyen el poder calórico del GNS, el índice de Wobbe, la eficiencia de conversión de carbón, la eficiencia en frío, la eficiencia del proceso, la eficiencia global y la tasa de producción de GNS, entre otros. En orden descendente, el proceso carbón-GNS mejora energéticamente con el uso de carbones con alta relación material volátil/carbón fijo, bajo contenido de ceniza, alta relación C+H/O y alto valor calórico del carbón. La eficiencia energética global para la producción de GNS vía gasificación es 17% mayor para la tecnología de alimentación en húmedo con respecto a la tecnología de alimentación en seco; esto posiblemente se da por la mayor concentración de CH4 en el syngas (alrededor del 7% vol.) cuando se usa alimentación en húmedo. El GNS simulado cumple los estándares de calidad de gas natural (GN) en Colombia; por lo tanto, el combustible gaseoso sustituto podría transportarse directamente por gasoductos. Por lo anterior, es técnicamente viable considerar el proceso carbón-GNS como una alternativa no convencional para la producción de GN.ABSTRACT: The effect of coal rank (from sub-bituminous to semi-anthracite) and type of fuel feeding technology (slurry and dry) on the production of substitute natural gas (SNG) in entrained flow gasifiers is studied. Ten coals from important Colombian mines were selected. The process is modeled under thermochemical equilibrium using Aspen Plus, and its performance is evaluated in function of output parameters that include SNG heating value, Wobbe index, coal conversion efficiency, cold gas efficiency, process efficiency, global efficiency, and SNG production rate, among others. In descending order, the coal-to-SNG process improves energetically with the use of coals with: higher volatile-matter to fixed-carbon ratio, lower ash content, higher C+H/O ratio, and higher coal heating value. The overall energy efficiency of the slurry-feed technology (S-FT) to produce SNG by gasification is 17% higher than the dry-feed technology (D-FT), possibly as a consequence of the higher CH4 concentration in the syngas (around 7 vol. %) when the coal is fed as aqueous slurry. As the simulated SNG meets the natural gas (NG) quality standards in Colombia, the substitute gaseous fuel could be directly transported through pipelines. Therefore, the coal-to-SNG process is a technically feasible and unconventional alternative for NG production