This work summarizes the development of a dynamic measurement platform in a cryostat to measure sample temperature response to space-like conditions and the creation a MATLAB theoretical model to predict sample temperature responses in the platform itself. An interesting variable-emittance sample called a Fabry-Perot emitter was studied for its thermal homeostasis behavior using the two developments. Using the measurement platform, it was shown that there was no thermal homeostatic behavior demonstrated by the sample at steady state temperatures. Theoretical calculations show other ways to demonstrate the cooling homeostasis behavior through time-varying heat inputs. Factors within the system such as heat loss and thermal mass contributed to an inhibited sample performance in the platform. Future work will have to be conducted, not only to verify the findings of the initial experiments but also to improve the measurement platform and the theoretical model.

A thermochromic mid-infrared filter is designed, where a spectrally-selective transmittance peak exists while vanadium dioxide layers are below their transition temperature but broad opaqueness is observed below the transition temperature. This filter takes advantage of interference effects between a silicon spacer and insulating vanadium dioxide to create the transmittance peak and the drastic optical property change between insulating and metallic vanadium dioxide. The theoretical performance of the filter in energy dissipation and thermal camouflaging applications is analyzed and can be optimized by tuning the thicknesses of the thin-film layers.

Sanctuary jurisdictions are jurisdictions that do not enforce one or more aspects of federal immigration policy in regards to unauthorized immigrants. Some states maintain state-wide sanctuary policies while others are adamantly against them. Estimates of taxes that unauthorized immigrants pay and estimates of the amount of state funding that unauthorized immigrants can access (education, financial aid, corrections, and welfare) reveal that regardless of sanctuary status, unauthorized immigrants may “pay in” more than they “take out” from the system. The status of “sanctuary jurisdiction” does not appear to have much if any effect on the net state budget. However, unauthorized immigrants are able to access more welfare programs in sanctuary states.

With the rise of fast fashion and its now apparent effects on climate change, there is an evident need for change in terms of how we as individuals use our clothing and footwear. Our team has created Ray Fashion Inc., a sustainable footwear company that focuses on implementing the circular economy to reduce the amount of waste generated in shoe creation. We have designed a sandal that accommodates the rapid consumption element of fast fashion with a business model that promotes sustainability through a buy-back method to upcycle and retain our materials.

The COVID-19 pandemic has resulted in preventative measures and has led to extensive changes in lifestyle for the vast majority of the American population. As the pandemic progresses, a growing amount of evidence shows that minority groups, such as the Deaf community, are often disproportionately and uniquely affected. Deaf people are directly affected in their ability to personally socialize and continue with daily routines. More specifically, this can constitute their ability to meet new people, connect with friends/family, and to perform in their work or learning environment. It also may result in further mental health changes and an increased reliance on technology. The impact of COVID-19 on the Deaf community in clinical settings must also be considered. This includes changes in policies for in-person interpreters and a rise in telehealth. Often, these effects can be representative of the pre-existing low health literacy, frequency of miscommunication, poor treatment, and the inconvenience felt by Deaf people when trying to access healthcare. Ultimately, these effects on the Deaf community must be taken into account when attempting to create a full picture of the societal shift caused by COVID-19.

This thesis is a supplement textbook designed with ASU’s MAT 370, or more generally, a course in introductory real analysis (IRA). With research in the realms of mathematics textbook creation and IRA pedagogy, this supplement aims to provide students or interested readers an additional presentation of the materials. Topics discussed include the real number system, some topology of the real line, sequences of real numbers, continuity, differentiation, integration, and the Fundamental Theorem of Calculus. Special emphasis was placed on worked examples of proven results and exercises with hints at the end of every chapter. In this respect, this supplement aims to be both versatile and self-contained for the different mathematics skill levels of readers.

This thesis project focuses on algorithms that generate good sampling points for function approximation. In one dimension, polynomial interpolation using equispaced points is unstable, with high Oscillations near the endpoints of the interpolated interval. On the other hand, Chebyshev nodes provide both stable and highly accurate points for polynomial interpolation. In higher dimensions, optimal sampling points are unknown. This project addresses this problem by finding algorithms that are robust in various domains for polynomial interpolation and least-squares. To measure the quality of the nodes produced by said algorithms, the Lebesgue constant will be used. In the algorithms, a number of numerical techniques will be used, such as the Gram-Schmidt process and the pivoted-QR process. In addition, concepts such as node density and greedy algorithms will be explored.