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Proportional reasoning instruction is prevalent in elementary, secondary, and post-secondary schooling. The concept of proportional reasoning is used in a variety of contexts for solving real-world problems. One of these contexts is the solving of dosage calculation proportional problems in the healthcare field. On the job, nurses perform drug dosage calculations which carry fatal consequences. As a result, nursing students are required to meet minimum competencies in solving proportion problems. The goal of this research is to describe the lived experiences of nurses in connection to their use of proportional reasoning in order to impact instruction of the procedures used to solve these problems. The research begins by clarifying and defining the conceptual field of proportional reasoning. Utilizing Vergnaud*s theory of conceptual fields and synthesizing the differing organizational frameworks used in the literature on proportional reasoning, the concept is organized and explicated into three components: concepts, procedures, and situations. Through the lens of this organizational structure, data from 44 registered nurses who completed a dosage calculation proportion survey were analyzed and connected to the framework of the conceptual field of proportional reasoning. Four nurses were chosen as a focus of in-depth study based upon their procedural strategies and ability to vividly describe their experiences. These qualitative results are synthesized to describe the lived experiences of nurses related to their education and use of proportional reasoning. Procedural strategies that are supported by textbooks, instruction, and practice are developed and defined. Descriptive statistics show the distribution of procedures used by nurses on a five question dosage calculation survey. The most common procedures used are the nursing formula, cross products, and dimensional analysis. These procedures correspond to the predominate procedures found in nursing dosage calculation texts. Instructional implications focus on the transition between elementary and secondary multiplicative structures, the confusion between equality and proportionality, and the difficulty that like quantities present in dealing with proportions.

We present an implementation of a very recent approximation algorithm for scheduling jobs on a single machine with precedence constraints, minimising the total weighted completion time. We also evaluate the performance of this implementation. The algorithm was published by Shi Li in 2021 and is a (6+ε)-approximation algorithm for the multiprocessor problem P|prec|∑j wjCj. We have implemented a version which is a (2+ε)-approximation algorithm for the single processor problem 1|prec|∑j wjCj. This special case can easily be generalised to the multiprocessor case, as the two algorithms are based on the same LP relaxation of the problem. Unlike other approximation algorithms for this and similar problems, for example, those published by Hall, Schulz, Shmoys and Wein in 1997, and by Li in 2020, this algorithm has been developed with a focus on obtaining a good asymptotic run time guarantee, rather than obtaining the best possible guarantee on the quality of solutions. Li’s algorithm has run time O((n+κ) · polylog(n+κ) · log3 pmax · 1/ε2), where n is the number of jobs, κ is the number of precedence constraints and pmax is the largest of the processing times of the jobs. We also present a detailed explanation of the algorithm aimed at readers who do not necessarily have a background in scheduling and/or approximation algorithms, based on the paper by Li. Finally, we empirically evaluate how well (our implementation of) this algorithm performs in practice. The performance was measured on a set of 96 randomly generated instances, with the largest instance having 1024 jobs and 32 768 precedence constraints. We can find a solution for an instance with 512 jobs and 11 585 precedence constraints in 25 minutes. / Vi presenterar en praktisk implementation av en ny approximationsalgoritm för schemaläggning av jobb på en maskin med ordningsbivillkor, under minimering av den viktade summan av sluttider. Algoritmen, som publicerades av Shi Li år 2021, är en (6+ε)-approximationsalgoritm för multiprocessorproblemet P|prec|∑j wjCj. Vi har implementerat en version som är en (2+ε)-approximationsalgoritm för enprocessorproblemet 1|prec|∑j wjCj. Detta specialfall kan enkelt generaliseras till multiprocessorfallet, eftersom de två algoritmerna baseras på samma LP-relaxation av problemet. Till skillnad från andra approximationsalgoritmer för detta och liknande problem, exempelvis de från Hall, Schulz, Shmoys och Wein år 1997, och från Li år 2020, har denna algoritm utvecklats med fokus på att uppnå en bra garanti på asymptotisk körtid, istället för att försöka uppnå den bästa möjliga garantin på lösningarnas kvalité. Lis algoritm har körtid O((n+κ) · polylog(n+κ) · log3 pmax · 1/ε2), där n är antalet jobb, κ antalet ordningsbivillkor och pmax är den största körtiden bland jobben. En detaljerad beskrivning av algoritmen riktad till personer som inte nödvändigtvis har förkunskaper inom schemaläggning och/eller approximationsalgoritmer, baserad på artikeln, ges också. Slutligen utvärderar vi empiriskt hur väl (vår implementation av) denna algoritm presterar i praktiken. Implementationens egenskaper mättes på en uppsättning av 96 slumplässigt genererade instanser, där den största instansen har 1024 jobb och 32768 ordningsbivillkor. Med vår implementation kan vi hitta en lösning för en instans med 512 jobb och 11 585 precedencensbivillkor på 25 minuter.

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No description available.

Cardiovascular workouts offer numerous health benefits, yet beginners often find it challenging to initiate them. Existing wearable technologies, although providing valuable feedback such as heart rate zones, often disrupt the workout flow and distract users due to the need for interaction with the wearable display. In response, we propose an alternative feedback mechanism: cadence, measured in steps per minute. This feedback mechanism uses multiplicative control to produce the correct cadence for the user’s target heart rate (HR). To model the HR and cadence relationship, a first-order system was used. The prototype implementation of this system was completed in Arduino, using a force sensitive resistor (FSR) to measure the user’s cadence and a POLAR HR strap to measure the user’s HR. The cadence is updated every 10 seconds to allow the user to sync to the cadence metronome provided by earbuds. This proposed system has shown promising experimental results for both moderate-intensity and high-intensity workouts, skipping the transition zone between them. This allows the user to avoid awkward workout intensities between a fast walk and a jog.

Non-intrusive acoustic thermometry using an acoustic impulse generator and two microphones is developed and integrated with tomographic techniques to reconstruct temperature contours. A low velocity plume at around 450 °F exiting through a rectangular duct (3.25 by 10 inches) was used for validation and reconstruction. 0.3 % static temperature relative error compared with thermocouple-measured data was achieved using a cross-correlation algorithm to calculate speed of sound. Tomographic reconstruction algorithms, the simplified multiplicative algebraic reconstruction technique (SMART) and least squares method (LSQR), are investigated for visualizing temperature contours of the heated plume. A rectangular arrangement of transmitter and microphones with a traversing mechanism collected two orthogonal sets of acoustic projection data. Both reconstruction techniques have successfully recreated the overall characteristic of the contour; however, for the future work, the integration of the refraction effect and implementation of additional angled projections are required to improve local temperature estimation accuracy. The root-mean-square percentage errors of reconstructing non-uniform, asymmetric temperature contours using the SMART and LSQR method are calculated as 20% and 19%, respectively. / Master of Science

In recent years, as the availability of remote sensing imagery of varying resolution has increased, merging images of differing spatial resolution has become a significant operation in the field of digital remote sensing. This practice, known as data fusion, is designed to enhance the spatial resolution of multispectral images by merging a relatively coarse-resolution image with a higher resolution panchromatic image of the same geographic area. This study examines properties of fused images and their ability to preserve the spectral integrity of the original image. It analyzes five current data fusion techniques for three complex scenes to assess their performance. The five data fusion models used include one spatial domain model (High-Pass Filter), two algebraic models (Multiplicative and Brovey Transform), and two spectral domain models (Principal Components Transform and Intensity-Hue-Saturation). SPOT data were chosen for both the panchromatic and multispectral data sets. These data sets were chosen for the high spatial resolution of the panchromatic (10 meters) data, the relatively high spectral resolution of the multispectral data, and the low spatial resolution ratio of two to one (2:1). After the application of the data fusion techniques, each merged image was analyzed statistically, graphically, and for increased photointerpretive potential as compared with the original multispectral images. While all of the data fusion models distorted the original multispectral imagery to an extent, both the Intensity-Hue-Saturation Model and the High-Pass Filter model maintained the original qualities of the multispectral imagery to an acceptable level. The High-Pass Filter model, designed to highlight the high frequency spatial information, provided the most noticeable increase in spatial resolution. / Master of Science

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25093号 / 理博第5000号 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 Croydon David Alexander, 教授 大木谷 耕司, 准教授 梶野 直孝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

<p dir="ltr">Applications of the Hardy-Littlewood Method to a class of partition generating functions, in which partitions are weighted (or "signed") using certain functions from multiplicative number theory.</p>