Co-universal algebras associated to product systems, and gauge-invariant uniqueness theorems

Let X be a product system over a quasi-lattice ordered group. Under mild hypotheses, we associate to X a C*-algebra which is co-universal for injective Nica covariant Toeplitz representations of X which preserve the gauge coaction. Under appropriate amenability criteria, this co-universal C*-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced by Sims and Yeend. We prove two key uniqueness theorems, and indicate how to use our theorems to realise a number of reduced crossed products as instances of our co-universal algebras. In each case, it is an easy corollary that the Cuntz-Nica-Pimsner algebra is isomorphic to the corresponding full crossed product.Comment: 40 pages, 2 figures; v2: minor changes to the introduction, references added and update

Cryogen-Free dissolution Dynamic Nuclear Polarization polarizer operating at 3.35 T, 6.70 T and 10.1 T

Purpose: A novel dissolution dynamic nuclear polarization (dDNP) polarizer platform is presented. The polarizer meets a number of key requirements for in vitro, pre-clinical and clinical applications. Method: It uses no liquid cryogens, operates in continuous mode, accommodates a wide range of sample sizes up to and including those required for human studies, and is fully automated. Results: It offers a wide operational window both in terms of magnetic field, up to 10.1 T, and temperature, from room temperature down to 1.3 K. The polarizer delivers a 13C liquid state polarization for [1-13C]pyruvate of 70%. The build-up time constant in the solid state is approx. 1200 s (20 min), allowing a sample throughput of at least one sample per hour including sample loading and dissolution. Conclusion: We confirm the previously reported strong field dependence in the range 3.35 to 6.7 T, but see no further increase in polarization when increasing the magnetic field strength to 10.1 T for [1-13C]pyruvate and trityl. Using a custom dry magnet, cold head and recondensing, closed-cycle cooling system, combined with a modular DNP probe, automation and fluid handling systems; we have designed a unique dDNP system with unrivalled flexibility and performance.Comment: 16 pages, 8 figure

An Analysis of the Effectiveness of E-Commerce at United Parcel Service

This paper is an analysis of e-commerce at United Parcel Service (NYSE: UPS). The paper begins with a general overview of the company’s IT environment to establish awareness of the size and complexity of this corporation. The analysis includes a macro level breakdown of the technology infrastructure of UPS ranging from the amount of data centers the company has, to the amount of PCs currently in operation. The study also more closely analyzes the software and database structure of UPS. Furthermore, an analysis of the company’s E-commerce activities was conducted and includes an interview with Tom Creech, the North Florida District E-commerce manager at UPS. Finally, research was conducted to evaluate the emerging technologies that UPS will soon be implementing and should be employing in the future to support the business strategy and maintain its competitive edge

Razonamiento covariacional aplicado a la modelación de eventos dinámicos: un marco conceptual y un estudio

Se desarrolla la noción de razonamiento covariacional y se propone un marco conceptual para describir las acciones mentales involucradas al aplicar razonamiento covariacional cuando se interpretan y representan funciones asociadas a eventos dinámicos. Se reporta la habilidad para razonar sobre cantidades covariantes en situaciones dinámicas, de estudiantes de alto desempeño en un curso de cálculo. El estudio reveló que ellos eran capaces de construir imágenes de la variable dependiente de una función que cambia simultáneamente con el cambio imaginado de la variable independiente, y en algunas ocasiones eran capaces de construir imágenes de la razón de cambio para intervalos contiguos del dominio de una función. Sin embargo, al parecer, tuvieron dificultad para formar imágenes de una razón cambiante de manera continua y no pudieron representar con exactitud o interpretar los puntos de inflexión ni la razón creciente y decreciente para funciones asociadas a situaciones dinámicas. Estos hallazgos sugieren que el currículo y la instrucción deberían aumentar el énfasis en el cambio que debe darse en los alumnos de una imagen coordinada de dos variables que cambian simultáneamente a una imagen coordinada de razón de cambio instantánea con cambios continuos en la variable independiente para funciones asociadas a situaciones dinámicas

Proofs and refutations in the undergraduate mathematics classroom

Abstract In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional approaches that support the learning of mathematics through the process of guided reinvention

Expanding on Basis Risk Estimates for Pasture, Rangeland, and Forage Insurance

Basis risk or residual risk arising from disparity between an index’s estimate of losses and actual losses is inherent in index-based insurance products. We approximate basis risk as the false negative probability (FNP) within pasture, rangeland, and forage (PRF) rainfall index insurance for the south-central coastal region of California. We estimate the FNP on average that at least one of two selected coverage intervals will fail to provide an indemnity when a loss is realized at 48%. The average FNP is reduced to only 11% when considering whether both selected intervals fail to provide an indemnity when a loss is realized

When students prove a theorem without explicitly using a necessary condition: digging into a subtle problem from practice

Over the years, we have noticed our students constructing proofs that commutativity is preserved by isomorphism that do not explicitly use the fact that the isomorphism is surjective. These proofs are typically valid otherwise. However, such proofs are invalid because they would prove the false claim that commutativity is preserved by any homomorphism. This observation from practice raises researchable questions: How common is this phenomenon? What is the nature of this phenomenon and can we explain why students produce this type of argument? In this paper, we report a small-scale two-part survey study and a preliminary interview study designed to begin exploring these questions. Our results suggest that this phenomenon is likely quite common and goes beyond a simple omission of a proof detail. Drawing on the research literature and our follow-up interviews, we propose potential explanations for this phenomenon. Finally, we discuss two different ways to think about supporting students who make this error, one that focuses on refining the students’ proofs and one that involves encouraging students to use the conclusion of a statement to structure a proof.First author draf