Putting fractions in lowest terms is a common problem for basic algebra courses, but it is rarely discussed in abstract algebra. In a 1990 paper, D.D. Anderson, D.F. Anderson, and M. Zafrullah published a paper called Factorization in Integral Domains, which summarized the results concerning different factorization properties in domains. In it, they defined an LT domain as one where every fraction is equal to a fraction in lowest terms. That is, for any x/y in the field of fractions of D, there is some a/b with x/y=a/b and the greatest common divisor of a and b is 1. In addition, R. Gilmer included a brief exercise concerning lowest terms over a domain in his book Multiplicative Ideal Theory. In this thesis, we expand upon those definitions. First, in Chapter 2 we make a distinction between putting a fraction in lowest terms and reducing it to lowest terms. In the first case, we simply require the existence of an equal fraction which is in lowest terms, while the second requires an element which divides both the numerator and the denominator to reach lowest terms. We also define essentially unique lowest terms, which requires a fraction to have only one lowest terms representation up to unit multiples. We prove that a reduced lowest terms domain is equivalent to a weak GCD domain, and that a domain which is both a reduced lowest terms domain and a unique lowest terms domain is equivalent to a GCD domain. We also provide an example showing that not every domain is a lowest terms domain as well as an example showing that putting a fraction in lowest terms is a strictly weaker condition than reducing it to lowest terms. Next, in Chapter 3 we discuss how lowest terms in a domain interacts with the polynomial ring. We prove that if D[T] is a unique lowest terms domain, then D must be a GCD domain. We also provide an alternative approach to some of the earlier results using the group of divisibility. So far, all fractions have been representatives of the field of fractions of a domain. However, in Chapter 4 we examine fractions in other localizations of a domain. We define a necessary and sufficient condition on the multiplicatively closed set, and then examine how this relates to existing properties of multiplicatively closed sets. Finally, in Chapter 5 we briefly examine lowest terms in rings with zero divisors. Because many properties of GCDs do not hold in such rings, this proved difficult. However, we were able to prove some results from Chapter 2 in this more general case.

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Advantage of the single QD active layer is its potential for very low threshold current density, which in turn can produce low internal optical loss. The low threshold current density and low internal loss thus enable a significant increase in laser diode cavity length. Because of the importance of the threshold current density in heatsinking, future technology of broad-area monolithic laser diodes can be implemented. The dissertation describes the development and the unique characteristics of single QD active layer laser with long cavity. The data are presented on single layer QD laser diodes that reach threshold current densities values of 11.7 A/cm2 in a p-up mounted 2 cm long cavity and as low as 10 A/cm2, with CW output power of 2 W in a p-down mounted 1.6 cm long cavity. The 8.8 A/cm2 in a p-down mounted 2 cm long cavity is reported. To our knowledge the value 8.8 A/cm2 is the lowest threshold current density ever reported for a room temperature laser diode. These single layer QD laser diodes reach an internal loss of ~0.25 cm-1, which is also the lowest ever reported for a room temperature laser diode. These unique characteristics of single layer QD and laser diode size are potentially promising for the monolithic mode-locked laser because of relatively high peak power with a low repetition rate that is on the order of a few GHz, which can be the novel device for external clocking in the optical interconnect applications. In this dissertation, the stable optical pulse train in a 40 µm wide stripe with a repetition rate of 3.75 GHz with 1.1 cm cavity length through the passive mode-locked onto the monolithic two-section device fabricated from this single layer QD laser is observed.

Public procurement in the Czech Republic is a complex process directly settled by the legal procurement framework which defines various contract-awarding procedures. This study focuses on the part of selection process when procurers can decide between using lowest price criterion or most economically advantageous tender (MEAT). We found an evidence of preference of lowest price criterion, especially in the recent years. The main goal of the study is therefore to provide a comprehensive analysis of the leading drivers of selection of specific criteria and their consequential effects. Taking into account various characteristics of public procurement processes, we found out that in general lowest price criterion is preferred by public contracting authorities and by procurers with larger number of employees. This type of selection process also consequently provides an interesting trade-off between higher competition in terms of number of bidders, higher stability in terms of less interventions by the Office for the Protection of Competition (OPC) but also higher probability of consequent extraworks.

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The U.S. Air Force (USAF) estimates it has a $33 billion (about 10 percent is airfield pavements) deferred maintenance backlog within its $263 billion infrastructure portfolio. Given the scope of this backlog and the importance of airfields, the USAF has a vested interest in finding strategies to help reverse this growing trend. Without an increase in funding, divestiture of excess infrastructure, or change in strategy, this backlog is estimated to climb to over $50 billion by 2030. Reversing the growing infrastructure backlog trend requires new methods and strategies to rethink how the USAF invests in its infrastructure. As such, the overall goal of this research is to develop a comprehensive and practical asset management approach to reduce the total cost of ownership of USAF airfield pavements. By reducing the cost of ownership, the goal is to reverse the growing maintenance backlog while maintaining a pavement portfolio capable of supporting USAF flying operations into the future. While this research is particularly relevant to the USAF, it seeks to fill research gaps within the current body of knowledge related to pavement management strategies for other agency types by presenting a practical, simulation-based methodology for work planning and budget allocation across a large pavement portfolio over a thirty-year period. The dissertation presents the development of the BEAST and RAMPSS algorithms. The BEAST algorithm is a simulation tool capable of modeling behaviors and decisions of 109 organizations managing a global network of airfield pavements over thirty years. Additionally, the BEAST is used to forecast outcomes of USAF investment decisions utilizing its current management strategies and historical behaviors. The RAMPSS is a simulation algorithm designed to select the most economical maintenance strategy for each pavement section in the USAF’s portfolio (i.e., individualized maintenance recommendation strategy for each pavement section). Analysis from the RAMPSS algorithm of the USAF’s pavement portfolio suggests that airfields are generally more cost-effective to maintain if kept in better conditions with strategies other than localized preventative maintenance. The USAF’s current maintenance strategy is unsustainable; however, switching to recommendations from RAMPSS (incorporated and modeled in the BEAST) provides a potentially significant course correction.

Wearable activity classifiers, so far, have been able to perform well with simple activities, strictly-scripted activities, and application-specific activities. In addition, current classification systems suffer from using impractical tight-fitting sensor networks, or only use one loose-fitting sensor node that cannot capture much movement information (e.g., smartphone sensors and wrist-worn sensors). These classifiers either do not address the bigger picture of making activity recognition more practical and being able to recognize more complex and naturalistic activities, or try to address this issue but still perform poorly on many fronts. This dissertation works toward having practical, in-the-wild, and reusable wearable activity classifiers by taking several steps that include the four following main contributions. The dissertation starts by quantifying users' needs and expectations from wearable activity classifiers to set a framework for designing ideal wearable activity classifiers. Data collected from user studies and interviews is gathered and analyzed, then several conclusions are made to set a framework of essential characteristics that ideal wearable activity classification systems should have. Afterwards, this dissertation introduces a group of datasets that can be used to benchmark different types of activity classifiers and can accommodate for a variety of goals. These datasets help comparing different algorithms in activity classification to assess their performance under various circumstances and with different types of activities. The third main contribution consists of developing a technique that can classify complex activities with wide variations. Testing this technique shows that it is able to accurately classify eight complex daily-life activities with wide variations at an accuracy rate of 93.33%, significantly outperforming the state-of-the-art. This technique is a step forward toward classifying real-life natural activities performed in an environment that allows for wide variations within the activity. Finally, this dissertation introduces a method that can be used on top of any activity classifier that allows access to its matching scores in order to improve its classification accuracy. Testing this method shows that it improves classification results by 11.86% and outperforms the state-of-the-art, therefore taking a step forward toward having reusable activity classification techniques that can be used across users, sensor domains, garments, and applications. / Ph. D. / Wearable activity classifiers are wearable systems that can recognize human activities. These systems are needed in many applications. Nowadays, they are mainly used for fitness purposes – e.g., Fitbits and Apple Watches – and in gaming consoles – e.g., Microsoft Kinect. However, these systems are still far from being ideal. They still miss many characteristics that would make them practical and usable for different purposes, such as in medical applications, industrial applications, and other types of applications where recognizing human activities can be useful. This dissertation works toward having practical wearable activity classifiers that can be reused for different purposes in real-life scenarios. Four contributions are introduced in this dissertation. The dissertation starts by quantifying users’ needs and expectations from wearable activity classifiers and sets a framework for designing them. Afterward, this dissertation introduces a group of datasets that can be used to benchmark and compare different types of activity classifiers. The third main contribution consists of a technique that enables activity classifiers to recognize complex activities having a wide range of variations within each activity. Finally, this dissertation introduces a method that can be used to improve the recognition accuracy of activity classifiers.

Public procurement below the lowest threshold This thesis describes and analyses the legal regulations and practice in the Czech public procurement below the lowest threshold. In particular, it focuses on the principles governing the procedures, i.e. transparency, proportionality, equality and non-discrimination. The first chapter deals with the purpose of the Czech Public Procurement Act, the concept and development of the legal regulation of public procurement below the lowest threshold emphasising the financial limits of the contract's value, which separates these public contracts from other procedures. The second chapter deals with the principles that apply to public procurement which represent the source for the regulation of public procurement below the lowest threshold. The law does not define their precise meaning, leaving it to the case law, decisions of the public authorities and opinions of the experts. These principles are necessarily conncected to the principles of financial management known as the 3E. The third chapter focuses on the procedure of contracting authorities during the public procurement. Since contracting authorities may, with certain restrictions, create their own rules for the procedure, the chapter contains examples and evaluation of these regulations of the individual...

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