Set Theory or Higher Order Logic to Represent Auction Concepts in Isabelle?

When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL system, and we have produced verified code for combinatorial Vickrey auctions. A fundamental question in this was how to represent some basic concepts: since set theory is available inside Isabelle/HOL, when introducing new definitions there is often the issue of balancing the amount of set-theoretical objects and of objects expressed using entities which are more typical of higher order logic such as functions or lists. Likewise, a user has often to answer the question whether to use a constructive or a non-constructive definition. Such decisions have consequences for the proof development and the usability of the formalization. For instance, sets are usually closer to the representation that economists would use and recognize, while the other objects are closer to the extraction of computational content. In this paper we give examples of the advantages and disadvantages for these approaches and their relationships. In addition, we present the corresponding Isabelle library of definitions and theorems, most prominently those dealing with relations and quotients.Comment: Preprint of a paper accepted for the forthcoming CICM 2014 conference (cicm-conference.org/2014): S.M. Watt et al. (Eds.): CICM 2014, LNAI 8543, Springer International Publishing Switzerland 2014. 16 pages, 1 figur

Thrust-induced effects on subsonic longitudinal aerodynamic characteristics of a vectored-engine-over-wing configuration

An investigation was conducted in the Langley 4 by 7 Meter Tunnel of the thrust induced effects on the longitudinal aerodynamic characteristics of a vectored-engine-over-wing fighter aircraft. The investigation was conducted at Mach numbers from 0.14 to 0.17 over an angle-of-attack range from -2 deg to 26 deg. The major model variables were the spanwise blowing nozzle sweep angle and main nozzle vector angle along with trailing edge, flap deflections. The overall thrust coefficient (main and spanwise nozzles) was varied from 0 (jet off) to 2.0. The results indicate that the thrust-induced effects from the main nozzle alone were small and mainly due to boundary-layer control affecting a small area behind the nozzle. When the spanwise blowing nozzles were included, the induced effects were larger than the main nozzle alone and were due to both boundary layer control and induced circulation lift. No leading edge vortex effects were evident

Free to Hate: Hate Crimes\u27 Intertwinement with the Evolution of Free Speech in the United States

In response to the growing tension between civil liberties and civil rights, this research investigates the relationship between the relative expansiveness of free speech and a the nationwide propensity for hate crimes. I argue that government’s legal limitations of speech influence the development of linguistic and hierarchical norms in a national culture. Given structural inequality’s association to violence and crimes of intimidation, I hypothesize that as the government expands the legal bounds of free speech, the national propensity for hate crimes decreases. Text analyses of 50 influential freedom of expression rulings in the United States (U.S.) Supreme Court from 1919-2019 demonstrate the United States’ increased tendency over the past century to rule with an increasingly expansive interpretation of freedom of expression. A conglomeration of secondary source data of prejudice-motivated victimizations in the U.S. over the same century creates an image of a rising annual hate crime victimization. This data and other findings within the research suggest that the national attention to hate crimes and tendency to record these incidents was deeply intertwined with cultural development in the U.S., specifically as it relates to social movements and attitudes towards diversity

Investigation of trailing-edge-flap, spanwise-blowing concepts on an advanced fighter configuration

The aerodynamic effects of spanwise blowing on the trailing edge flap of an advanced fighter aircraft configuration were determined in the 4 by 7 Meter Tunnel. A series of tests were conducted with variations in spanwise-blowing vector angle, nozzle exit area, nozzle location, thrust coefficient, and flap deflection in order to determine a superior configuration for both an underwing cascade concept and an overwing port concept. This screening phase of the testing was conducted at a nominal approach angle of attack from 12 deg to 16 deg; and then the superior configurations were tested over a more complete angle of attack range from 0 deg to 20 deg at tunnel free stream dynamic pressures from 20 to 40 lbf/sq ft at thrust coefficients from 0 to 2

Thrust-induced effects on low-speed aerodynamics of fighter aircraft

Results of NASA Langley has conducted wind-tunnel investigations of several fighter configurations conducted to determine the effects of both thrust vectoring and spanwise blowing are reviewed. A recent joint NASA/Grumman Aerospace Corporation/U.S. Air Force Wright Aeronautical Laboratory wind-tunnel investigation was conducted to examine the effects of spanwise blowing on the trailing-edge flap system. This application contrasts with the more familiar method of spanwise blowing near the wing leading edge. Another joint program among NASA/McDonnell Aircraft Company/U.S. Air Force Wright Aeronautical Laboratory investigated the effects of reverse thrust on the low-speed aerodynamics of an F-15 configuration. The F-15 model was fitted with a rotating van thrust reverser concept which could simulate both in-flight reversing for approach and landing or full reversing for ground roll reduction. The significant results of these two joint programs are reported

Translational energy dependence of cross sections for reactions of OH− (H2O) n with CO2 and SO2

This is the publisher's version, also available electronically from http://scitation.aip.org/content/aip/journal/jcp/80/10/10.1063/1.446510.A tandem mass spectrometer has been used to measure cross sections for reactions of the solvated negative ions OH−(H2O) n , where 0≤n≤3, with the neutral molecules CO2 and SO2 over the range of reactant translational energy 0.15–25.0 eV (LAB). The reactions observed include solvent switching, collisional dissociation, and charge transfer. The exoergic solvent switching reactions are very rapid, having cross sections which exceed a hundred square Angstroms at low energies. These cross sections decrease approximately as (energy)−0.5 up to 1 eV and then decrease much more rapidly at higher collision energies. Estimates of bond dissociation energies for the cluster ions are derived from the measured translational energy thresholds for the endothermic collisional dissociationreactions

Differential Radial Velocities and Stellar Parameters of Nearby Young Stars

Radial velocity searches for substellar mass companions have focused primarily on stars older than 1 Gyr. Increased levels of stellar activity in young stars hinders the detection of solar system analogs and therefore there has been a prejudice against inclusion of young stars in radial velocity surveys until recently. Adaptive optics surveys of young stars have given us insight into the multiplicity of young stars but only for massive, distant companions. Understanding the limit of the radial velocity technique, restricted to high-mass, close-orbiting planets and brown dwarfs, we began a survey of young stars of various ages. While the number of stars needed to carry out full analysis of the problems of planetary and brown dwarf population and evolution is large, the beginning of such a sample is included here. We report on 61 young stars ranging in age from beta Pic association (~12 Myr) to the Ursa Majoris association (~300 Myr). This initial search resulted in no stars showing evidence for companions greater than ~1-2 M_Jup in short period orbits at the 3 sigma-level. Additionally, we present derived stellar parameters, as most have unpublished values. The chemical homogeneity of a cluster, and presumably of an association, may help to constrain true membership. As such, we present [Fe/H] abundances for the stars in our sample.Comment: Accepted for publication in the PAS

Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated Deduction, 2015. Proceedings to be published by Springer-Verla