Structure and enumeration of (3+1)-free posets

A poset is (3+1)-free if it does not contain the disjoint union of chains of length 3 and 1 as an induced subposet. These posets play a central role in the (3+1)-free conjecture of Stanley and Stembridge. Lewis and Zhang have enumerated (3+1)-free posets in the graded case by decomposing them into bipartite graphs, but until now the general enumeration problem has remained open. We give a finer decomposition into bipartite graphs which applies to all (3+1)-free posets and obtain generating functions which count (3+1)-free posets with labelled or unlabelled vertices. Using this decomposition, we obtain a decomposition of the automorphism group and asymptotics for the number of (3+1)-free posets.Comment: 28 pages, 5 figures. New version includes substantial changes to clarify the construction of skeleta and the enumeration. An extended abstract of this paper appears as arXiv:1212.535

Building Racial Coalitions: Limitations and New Directions to Teaching “White Privilege”

In this article, I pull from critical race theory, psychology, and philosophy to deconstruct the underlying psychological components that lead to “white fragility,” and I explore the limitations in current pedagogical approaches to teaching privilege. I argue that we adopt a more nuanced and context based understanding of “white privilege,” one that breaks down the concept into its two constituent parts: the “privilege/adversity paradigm” and “colonizer alignment privilege.” In the former, basic human physical or cultural traits are presented to students as capable of being beneficial or detrimental depending on context. In the latter, the ways in which people create contexts to favor specific traits as well as the various contexts individuals shift between are analyzed. If done properly, these approaches can validate the personal struggles of all students, help them to acknowledge their advantages, and guide them towards overcoming the psychological hurdles that prevent effective coalition building

Producción de metanol por hidrogenación de CO2 mediante rectificación reactiva

Treballs Finals de Màster d'Enginyeria Química, Facultat de Química, Universitat de Barcelona. Curs: 2021-2022. Tutors: Jordi Bonet i Ruiz, Alexandra Elena PlesuMethanol is a very versatile product that can be found in a large number of industrial applications such as it’s use as a solvent or as a raw material for the synthesis of methyl ether, methylamine, etc. Due to the current environmental situation, many research projects are starting to focus on the reduction of greenhouse gases pollution, which directly affects fossil fuels and certain industries that have a large CO2 stream as their major waste (cement plants, thermal power plants, etc.). One of the most studied projects nowadays is the synthesis of carbon-based fuels using CO2 as raw material, which could be used to store the surplus energy obtained from renewable sources in chemical products, to be reused later on. This method has great advantages since with renewable energy and a carbon source (such as CO2) "green" fuels could be produced and these could be easily transported with current logistics and used by many facilities, due to their similarity to fossil fuels. One of the carbon-based fuels with the greatest potential is methanol due to its high energy density. Currently there are several plants producing methanol from CO2 and hydrogen, but they are still too unprofitable to be implemented worldwide. This project studies an intensified process, the reactive distillation process, as an alternative to the current methanol synthesis process to make it more cost effective and efficient. Reactive distillation is an intensified process which allows to reduce the number of equipment required to carry out a process, since several unit operations take place simultaneously inside the column. As it is a process that has not been studied yet, in this project a model has been proposed (simulated using Aspen plus technology) and different points have been evaluated: - Proposal for the process using assumptions and calculation bases. - Process parameters: column reflux, total distillation column stages, feed stages and product obtained by column bottom-head flow stream. - Improvement proposals for the process studied: equipment adjacent to the main column. The different stages of the whole process have been simulated with the ASPEN program and it has been demonstrated that this initial study opens the possibility for future studies since the results are optimistic for the viability of the project in the industrial fiel

Deformations of Quantum Field Theories on Curved Spacetimes

The construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of globally hyperbolic spacetimes. First, we show that any four-dimensional spacetime which admits two commuting and spacelike Killing vector fields carries a family of wedge regions with causal properties analogous to the Minkowski space wedges. Deformations of quantum field theories on these spacetimes are carried out within the operator-algebraic framework - the emerging models share many structural properties with deformations of field theories on flat spacetime. In particular, deformed quantum fields are localized in the wedges of the considered spacetime. As a concrete example, the deformation of the free Dirac field is studied. Second, quantum field theories on de Sitter spacetime with global U(1) gauge symmetry are deformed using the joint action of the internal symmetry group and a one-parameter group of boosts. The resulting theories turn out to be wedge-local and non-isomorphic to the initial one for a class of theories, including the free charged Dirac field. The properties of deformed models coming from inclusions of CAR-algebras are studied in detail. Third, the deformation of the scalar free field in the Araki-Wood representation on Minkowski spacetime is discussed as a motivating example.Comment: PhD thesis, University of Vienna, 2012 (advisors: J. Yngvason and G. Lechner) 107 pages, 3 figure

Montana Canvas Tent Structure Design

Montana Canvas is one of the premier tent building companies in the world. Their product line includes backcountry tents, wall tents, and large scale shipping tarps. Currently they are looking to expand their product line to include large party tents of up to 60’ in width. Eric Schowengerdt and Nick Morales, both Mechanical Engineering students at Montana Tech, have both designed fixtures and verified several of the fixtures already in use by Montana Canvas. These fixtures were put through finite element analysis on a computer and many static hand calculations, which simulated the loading on them from 120 mph to 85 mph wind conditions. This report will outline the processes used to determine the max loading area, alternative solutions to the structure, and finite element analysis on the structure

Transit Timing Observations of the Extrasolar Hot-Neptune Planet GL 436b

Gliese 436 is an M dwarf with a mass of 0.45 Msun and hosts the extrasolar planet GL 436b [3, 6, 7, 2], which is currently the least massive transiting planet with a mass of ~23.17 Mearth [10], and the only planet known to transit an M dwarf. GL 436b represents the first transiting detection of the class of extrasolar planets known as "Hot Neptunes" that have masses within a few times that of Neptune's mass (~17 Mearth) and orbital semimajor axis <0.1 AU about the host star. Unlike most other known transiting extrasolar planets, GL 436b has a high eccentricity (e~0.16). This brings to light a new parameter space for habitability zones of extrasolar planets with host star masses much smaller than typical stars of roughly a solar mass. This unique system is an ideal candidate for orbital perturbation and transit-time variation (TTV) studies to detect smaller, possibly Earth-mass planets in the system. In April 2008 we began a long-term intensive campaign to obtain complete high-precision light curves using the Apache Point Observatory's 3.5-meter telescope, NMSU's 1-meter telescope (located at APO), and Sommers Bausch Observatory's 24" telescope. These light curves are being analyzed together, along with amateur and other professional astronomer observations. Results of our analysis are discussed. Continued measurements over the next few years are needed to determine if additional planets reside in the system, and to study the impact of other manifestations on the light curves, such as star spots and active regions.Comment: 4 pages, 3 figures. To appear in "Proceedings of the 15th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun", 2009, AIP Conference Proceedings vol. 1094, ed. Eric Stempel

Atomic-Scale Interface Engineering of Majorana Edge Modes in a 2D Magnet-Superconductor Hybrid System

Topological superconductors are predicted to harbor exotic boundary states - Majorana zero-energy modes - whose non-Abelian braiding statistics present a new paradigm for the realization of topological quantum computing. Using low-temperature scanning tunneling spectroscopy (STS), we here report on the direct real-space visualization of chiral Majorana edge states in a monolayer topological superconductor, a prototypical magnet-superconductor hybrid system comprised of nano-scale Fe islands of monoatomic height on a Re(0001)-O(2$\times$1) surface. In particular, we demonstrate that interface engineering by an atomically thin oxide layer is crucial for driving the hybrid system into a topologically non-trivial state as confirmed by theoretical calculations of the topological invariant, the Chern number.Comment: 26 pages, 9 figure