Let X be a space and let S ⊂ X with a measure of set size |S| and boundary size |∂S|. Fix a set C ⊂ X called the constraining set. The constrained isoperimetric problem asks when we can find a subset S of C that maximizes the Følner ratio FR(S) = |S|/|∂S|. We consider different measures for subsets of R^2,R^3,Z^2,Z^3 and describe the properties that must be satisfied for sets S that maximize the Folner ratio. We give explicit examples.

The focus of this research was to examine the performance of Florida public community college foundations from 2002-2004 using performance ratios. The findings from this study may assist community college foundation leaders to better understand the performance of their own organizations, compare this performance to other similar organizations, establish relative performance standards, and influence the strategic initiatives to improve an existing foundation. This study was designed to research the financial performance measurement ratios for the 28 public community college foundations in Florida. Ex post facto data that were publicly available were utilized to acquire the information needed for the statistical analyses; therefore, the population was comprised of all 28 Florida community college foundations. Data were collected from each institution's Form 990. A total of 27 ratios were calculated by year for 2002, 2003, and 2004 and were categorized into 6 areas: (a) measures of fiscal performance, (b) measures of fundraising efficiency, (c) measures of public support, (d) measures of adequacy of resources to support mission, (e) measures of use of resources to support mission, and (f) measures of investment performance and concentration. The study included benchmarking data in the form of descriptive statistics for these ratios and comprehensive analysis. In addition, three repeated measures analysis of variance models were computed to determine if the contributions and grants, fundraising expense, and program service expense ratios varied over time. There were no mean differences over time during the three-year period from 2002 to 2004.

Students with Emotional and Behavioral Disorders (EBD) in the United States are often underserved by the education system, which contributes to their academic difficulties and poor student outcomes. Research on Positive-to-Negative (PN) response ratios suggest that maintaining a high ratio helps decrease inappropriate behaviors and improve academic outcomes for students with EBD. The current study investigates the effects of a high PN ratio on the behavior of an educator of students with EBD by utilizing a tracking app to help meet a target PN ratio. One preservice special education teacher working as a paraeducator was recruited to participate in the study. The paraeducator was asked to meet PN ratio goals of 2:1, 5:1, and 10:1. Visual analysis of the data collected throughout the study indicated that each successively higher PN ratio was met by the paraeducator suggesting that access to the tracking app was functionally related to the paraeducator's ability increase her PN ratio goals. This is consistent with previous research suggesting that self-monitoring is an effective procedure to increase the use of praise and it extends access to effective interventions by adding real-time, app-based monitoring to the list of effective supports for educators. The limitations and implications of the study are discussed alongside the potential implications for practice suggested by these findings.

Control charts are fundamental SPC tools for process monitoring. When a control chart or combination of charts signals, knowing the change point, which distributional parameter changed, and/or the change size helps to identify the cause of the change, remove it from the process or adjust the process back in control correctly and immediately. In this study, we proposed using maximum likelihood (ML) estimation of the current process parameters and their ML confidence intervals after a signal to identify and estimate the changed parameters. The performance of this ML diagnostic procedure is evaluated for several different charts or chart combinations for the cases of sample sizes and , and compared to the traditional approaches to diagnostics. None of the ML and the traditional estimators performs well for all patterns of shifts, but the ML estimator has the best overall performance. The ML confidence interval diagnostics are overall better at determining which parameter has shifted than the traditional diagnostics based on which chart signals. The performance of the generalized likelihood ratio (GLR) chart in shift detection and in ML diagnostics is comparable to the best EWMA chart combination. With the application of the ML diagnostics naturally following a GLR chart compared to the traditional control charts, the studies of a GLR chart during process monitoring can be further deepened in the future. / Ph. D.

Yes / This study presents a compact broadband wide-slot antenna with broadband left-hand circular polarization compatible with both LTE 42 and LTE 43 standards of 5G mid-band applications. The proposed antenna is fabricated on an FR4 dielectric substrate with overall dimensions of , where is the free space wavelength at the resonant frequency of the antenna. The antenna ground plane is etched to form a square radiating slot with a pair of rectangular ground stubs that are diagonally placed inside the slot. On the other side of the antenna, the feed line is loaded by horizontal and vertical stubs to improve the coupling between the feed line and the square slot. To generate a circular polarization, the feeding stubs cooperate with the pair of rectangular ground stubs to excite the radiating slot of the antenna at two different feeding points whose currents have approximately equal amplitude and 90o phase shift. The measured impedance bandwidth (BW) of the proposed wide-slot antenna is 16.2% (580 MHz along the band 3.3-3.88 GHz), while the observed axial ratio bandwidth (ARBW) is 12.2% (440 MHz in the 3.4-3.84 GHz band). The measured gain values are found to be larger than 2.5 dB along both standards of the 5G mid-band applications. / This work was supported in part by the U.K. Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/E022936/1, and in part by the European Union’s Horizon 2020 Research and Innovation Programme under Grant H2020-MSCA-ITN-2016 SECRET-722424.

Hadronic collisions at the LHC at CERN probe particle interactions at the highest energy scale of any experiment to date. We present a research program measuring Rjet = &sigmaWBR(W&rarr&mu&nu) / (&sigmaZBR(Z&rarr&mu&mu)) as a function of a number of hadronic variables. The measurements are performed with the ATLAS detector at the LHC, using the 2011 data set, consisting of 4.64 fb-1 of pp collisions at a center of mass energy of 7 TeV. This measurement is a robust way to test the Standard Model and the modeling of perturbative QCD, and is sensitive to a wide variety of possible new physics in events with high jet ET, including some variations of Supersymmetry. By taking the ratio of W/Z production, a large number of systematic uncertainties cancel, including those associated with luminosity, jet energy scale and resolution, and many theoretical uncertainties. The measurement of Rjet is performed as a function of the pT and rapidity of the 1st-4th leading jet, ST, HT, and a number of dijet variables, including invariant mass and angular separations. The measurements are compared with NLO theoretical predictions from Blackhat+Sherpa, as well as using leading order simulations from Alpgen and Sherpa. Over most of the kinematic phase-space, there is good agreement between the data and theoretical predictions. There is a significant deviation for exactly one selected jet above 30 GeV, where Blackhat+Sherpa over-estimates the ratio Rjet by 12%.

Within commercial broiler production, feed and feed manufacturing costs account for 60 to 70% of production costs. Of these feed costs specifically, ingredients that supply energy and protein represent the highest expenditure, verifying the importance of knowing the nutrient requirements of current broiler strains to ensure accurate least-cost formulation. To reduce these production costs and optimize performance, primary breeder companies and nutritionists continuously strive to improve nutrient utilization of commercial broiler strains. As a result of this, a great magnitude of work is conducted to determine the nutrient requirements for broilers, especially amino acids. Therefore, the overall objective of this dissertation was to utilize processing measurements, multiple statistical models, and economics as a whole to determine the optimal percent digestible Isoleucine:digestible Lysine ratio (dIle:dLys) for Ross 708 x Ross YP male broilers to improve growth performance and economic return. Chapter 2 determined the optimal dIle:dLys ratio for the starter phase (d 0-18), while Chapter 3 determined the optimal ratio for the grower phase (d 14-28), and Chapter 4 determined the optimal ratio for the finisher phase (d 28-42). All experimental diets for each respective growth phase were created from a common deficient corn and soybean meal-based diet. After manufacturing, half was retained to create the summit diet through the addition of crystalline Ile. The remaining five experimental diets for each respective growth phase were obtained by blending proportions of the deficient and summit diets. All dIle:dLys ratios were estimated using quadratic regression (QR; 95% of the asymptote), as well as linear and quadratic broken line models (LBL; QBL). Regression analysis from d 0-18 using multiple regression models estimated the ratios to range from 63-73% for BW and BWG and 68-74% for FCR. Based on the data from the grower phase and using multiple regression models, the estimated ratios ranged from 62-68% for BW and BWG and 67-70% for FCR and are similar to the current breeder nutrient specifications. Data from the finisher phase and once again using multiple regression models estimated the ratios to range from 62-66% for BW and BWG and 63-66% for FCR.

The safe and efficient propagation of the Deflagration to Detonation Transition (DDT) is a topic that has been researched for many years due to its applications in Aerospace and Mechanical Engineering. DDT is when fire caused by the burning of fuel is accelerated to the upper CJ point on the Rankine Hugoniot curve due to instabilities in the flame and the turbulence caused by these instabilities. The complex flame dynamics that go along with DDT have ensured that the process is yet to be fully understood and defined. This research will work towards observing the early stages of burning hydrogen-air mixtures in DDT conditions in order to better understand the processes that cause DDT. The research will also involve the testing of multiple different equivalence ratios of hydrogen known to undergo DDT. This research will assist in making places that store reactive gasses such as hydrogen safer by searching for the method of DDT formation and ways to prevent it. This research will also allow for safer commercial use of DDT in Detonation Based Engines. The research was tested in a secure facility and observed the first four inches of ignition and deflagration using schlieren and chemiluminescence imaging techniques. Through the research, it was found that flames at higher equivalence ratios tend to be longer, more top-biased, and have more instabilities than flames of lower equivalence ratios, better preparing them for DDT. This study will be elaborated on in future research using a variety of different fuels to solidify the findings of the research performed and to assist in the ability to innovate using DDT.

Thesis advisor: Arthur Lewbel / This dissertation consists of two independent studies that seek to improve public policies in developing country context. I first study how anti-poverty programs in developing countries can improve their screening procedure so that they can better direct resources to the poor over time. Then, I investigate the impacts of trade openness on fertility decisions in countries known for son preference, thereby informing governments in those countries of the unintended consequences of such growth-focused trade policies. In the first chapter, “Bunching and Learning in Targeting Poverty: Evidence from Vietnam,” I examine how households manipulate eligibility criteria in order to appear eligible for an anti-poverty program. Despite ample evidence that households manipulate these criteria, little is known about how such behaviors evolve over time in a long-term program. Using data from Vietnam, I find that, early on in each phase of its National Anti-Poverty Program, about 1-2% of the population (or 8-18% relative to the program size) bunch at the official income cutoff in order to appear eligible. However, this fraction falls by 60-100% towards the end of the phase, only to increase yet again when a new phase starts with a new income cutoff. To explain this temporal pattern of bunching, I develop a model in which over time the program staff learn to rely on housing conditions, a less-manipulable criteria, to select households. This refined information, in turns, discourages households from manipulating their income. I find that an increase of 0.5 standard deviation in the housing quality index further reduces the chance of being accepted to the program by 25.11% after two years. Meanwhile, other criteria, including reported income and asset holdings, do not contribute any additional predictive power to the program status over the same period. Without this learning process, the program would have misallocated about 1.7%, or equivalently 32.3-36.4 million USD (PPP), of its budget to non-poor households during the first phase of the program. In the second chapter, “Why does the sex ratio at birth rise? Evidence from Vietnam,” joint with Nghiem Huynh, we investigate the causal link between a major trade agreement between the US and Vietnam and the rise in sex ratio at birth in Vietnam. We test three theories of the rise in sex ratio at birth and find evidence that the fertility mechanism explains the recent increase in Vietnam. Using the 2001 US-Vietnam Bilateral Trade Agreement as an exogenous shock, we show that mothers exposed to larger tariff cuts are more likely to have boys, work more hours and less likely to give birth. These results hold up when we account for other competing mechanisms, including changes in fathers' exposure to the policy and daughters’ economic returns in repeated cross-sectional and panel data. This chapter highlights the trade-off between work and children for mothers, and the potential role of trade policy in heightening this trade-off, leading to lower fertility and higher sex selection. Although both studies are situated in Vietnam, their results and implications are relevant to policy discussions in many developing countries. / Thesis (PhD) — Boston College, 2023. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

Particle technology affects the entire human population. It is involved in the manufacture of agriculture chemicals, asphalt, paint, and pharmaceuticals, just to name a few. The size and shape of the particles play an important role in the manufacturing processes. A change in size or shape can change the product produced. Experiments were run to test the effects of agitation rate, magma density, and residence time on adipic acid and sodium chloride crystals. Experiments were executed in a one-liter, double-jacketed, stirred vessel. Digital images of the broken crystals were taken with a microscope/digital camera combo. ImagePro Plus was used to analyze the size of the broken crystals. The greatest change was seen between the two magma densities. It can be determined that change in size and shape based on the variables does exist. A specific set of variables should be introduced for each process in industry to achieve the desired results.