Antiprismless, or: Reducing Combinatorial Equivalence to Projective Equivalence in Realizability Problems for Polytopes

This article exhibits a 4-dimensional combinatorial polytope that has no antiprism, answering a question posed by Bernt Lindst\"om. As a consequence, any realization of this combinatorial polytope has a face that it cannot rest upon without toppling over. To this end, we provide a general method for solving a broad class of realizability problems. Specifically, we show that for any semialgebraic property that faces inherit, the given property holds for some realization of every combinatorial polytope if and only if the property holds from some projective copy of every polytope. The proof uses the following result by Below. Given any polytope with vertices having algebraic coordinates, there is a combinatorial "stamp" polytope with a specified face that is projectively equivalent to the given polytope in all realizations. Here we construct a new stamp polytope that is closely related to Richter-Gebert's proof of universality for 4-dimensional polytopes, and we generalize several tools from that proof

Transforming education policy in New Zealand: a case study analysis

This study provides a comprehensive analysis of the changing face of New Zealand education policy over the past 25 years. It highlights the phase of socio-economic trans-formation in the late 1980s and its far-reaching impact on the education system, before turning to the last two decades, in which New Zealand's education policy has been in-creasingly shaped by its system of education export, its willingness to engage in interna-tional comparison and its close cooperation with international organizations. The article also emphasizes the various domestic forces, which have shaped education policy-making. They include a unique willingness to experiment, pragmatism, and an underly-ing culture of balance and inclusion, which account for the high degree of flexibility and adaptiveness of the country's secondary and tertiary education systems. -- Diese Studie gibt einen umfassenden Überblick des Wandels in der neuseeländischen Bildungspolitik, der bereits vor ca. 25 Jahren begann. Der Fokus wird zuerst auf die Phase der sozioökonomischen Transformation Ende der 1980er Jahre und deren Auswirklungen auf das Bildungssystem gelegt. Danach werden die Reformen der letzten zwei Jahrzehnte skizziert. Sowohl im tertiären als auch im sekundären Bildungsbereich wird Bildung in diesem Zeitraum zunehmend as liberalisiertes Servicegut interpretiert, welches zudem exportierbar ist. Gleichzeitig wurde die neuseeländische Hochschulpolitik durch die Ergebnisse internationaler Leistungsvergleiche und durch enge Zusammenarbeit mit internationalen Organisationen stark geprägt. Der Artikel zeigt außerdem wie verschiedene innenpolitische Faktoren bildungspolitische Reformen in Neuseeland beschleunigt haben. Dazu gehören eine starke Bereitschaft mit neuen Lösungsansätzen zu experimentieren, ein stark ausgeprägter Pragmatismus und eine für Neuseeland charakteristische Kultur des sozialen Gleichgewichtes und Ausgleiches. Diese Faktoren erklären den hohen Grad an Flexibilität sowie die Anpassungsfähigkeit des sekundären und tertiären Bildungssystems des Landes.

Particle size of aluminum oxide produced by a small rocket motor

Spectrophotometric method for measurement of aluminum oxide particle sizes during burning of solid propellant rocket engin

A comparison of two methods of measuring particle size of Al2O3 produced by a small rocket motor

The size of aluminum oxide particles produced by small rocket motors is determined by tank collection and spectrophotometry. The size of the particulate determines loss in thrust due to particle lag, particulate radiant heat transfer, acoustic attenuation and impingement and rocket plume structure and properties

The New Grid

The New Grid seeks to provide mobile users with an additional method for off-grid communication, or communication without connection to Internet infrastructure. The motivation for this project was to find another alternative to Internet-dependent communication. Current Internet infrastructure is antiquated; it is expensive to maintain and expand, it has numerous vulnerabilities and high-impact points of failure, and can be rendered unusable for lengthy periods of time by natural disasters or other catastrophes. This current grid will eventually need to be replaced by a more modern, scalable, and adaptive infrastructure. The results of the projects research showed that implementing a library to allow for the creation of mobile peer-to-peer mesh networks could serve as a starting point for a transition from current Internet infrastructure to a more scalable, adaptive, and reliable Internet- independent network grid. Development of The New Grid largely followed the Rational Unified Process, in which the development process is split into four phases: requirements gathering, system design, implementation, and testing. Most of fall quarter was spent outlining functional requirements for the system, designing possible methods of implementation, and researching similar solutions that seek to transition mass mobile communication to a newer, more modern network grid. The New Grid differs from similar solutions because it has been implemented as a modular library. Current systems that allow for off-grid mobile connection exist as independent applications with a defined context and predetermined usability scope. We, the design team, found that implementing the system in the form of a modular library has multiple benefits. Primarily, this implementation would allow The New Grid to be deployed as widely as possible. Developers can both write applications around our library as well as include specific modules into existing applications without impacting other modules or introducing additional overhead into a system. Another benefit of deploying the system as a modular library is adaptability. The current, initial stable build of The New Grid uses Bluetooth Low Energy as its backbone for facilitating communication within large networks of mobile devices; however, this library could use any existing or future communication protocol to facilitate connection as long as a hook is written to allow The New Grid to interface with that protocol. Thus, The New Grid is not limited by which connection protocols currently exist, a property that other similar systems do not possess. The New Grid can be used in any application that requires connection between users. The most common applications would likely be messaging, file sharing, or social networking. While developers may find a variety of uses for The New Grid, its primary purpose is to facilitate reliable connection and secure data transfer in an environment with a large user base. Achieving this goal was proven feasible through research and testing the library with a small cluster of Android devices communicating solely with Bluetooth Low Energy. Expanding this group of a few phones to a larger mesh network of hundreds of devices was shown to be feasible through testing the librarys algorithms and protocols on a large network of virtual devices. As long as developers seek to create applications that allow users to communicate independent of Internet infrastructure, The New Grid will allow smartphone users to communicate off-grid and hopefully spur a switch from infrastructure-dependent mobile communication to user-centric, adaptive, and flexible connection

Regular systems of paths and families of convex sets in convex position

In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamily of size five is in convex position. (If each pair of bodies have at most two common tangents it is enough to assume that every triple is in convex position, and likewise, if each pair of bodies have at most four common tangents it is enough to assume that every quadruple is in convex position.) This confirms a conjecture of Pach and Toth, and generalizes a theorem of Bisztriczky and Fejes Toth. Our results on families of convex bodies are consequences of more general Ramsey-type results about the crossing patterns of systems of graphs of continuous functions $f:[0,1] \to \mathbb{R}$. On our way towards proving the Pach-Toth conjecture we obtain a combinatorial characterization of such systems of graphs in which all subsystems of equal size induce equivalent crossing patterns. These highly organized structures are what we call regular systems of paths and they are natural generalizations of the notions of cups and caps from the famous theorem of Erdos and Szekeres. The characterization of regular systems is combinatorial and introduces some auxiliary structures which may be of independent interest

Recent Measurements at JPL of Particle Size of Aluminum Oxide from Small Rocket Motors

Small rocket engine test firings conducted to measure particle size distribution of aluminum oxide exhaust