This paper is an exploration of numerical optimization as it applies to the consumer choice problem. Suggested algorithms are intended to compute solutions to the Marshallian problem, and some can extend to the dual given the suggested modifications. Each method seeks to either weaken the sufficient conditions for optimization, converge to a solution more efficiently, or describe additional properties of the decision space. The purpose of this paper is to explore constrained quasiconvex programming in a less complicated environment by design of Marshallian constraints.

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.

Pelvic Circumferential Compression Devices (PCCDs), an important medical device when caring for patients with pelvic fractures, play a crucial role in the stabilization and reduction of the fracture. During pelvic fracture cases, control of internal bleeding through access to the femoral artery is of utmost importance. Current designs of PCCDs do not allow vital access to this artery and in attempts to gain access, medical professionals and emergency care providers choose to cut into the PCCDs or place them in suboptimal positions with unknown downstream effects. We researched the effects on surface pressure and the overall pressure distribution created by the PCCDs when they are modified or placed incorrectly on the patient. In addition, we investigated the effects of those misuses on pelvic fracture reduction, a key parameter in stabilizing the patient during critical care. We hypothesized that incorrectly placing or modifying the PCCD will result in increased surface pressure and decreased fracture reduction. Our mannequin studies show that for SAM Sling and T-POD, surface pressure increases if a PCCD is incorrectly placed or modified, in support of our hypothesis. However, opposite results occurred for the Pelvic Binder, where the correctly placed PCCD had higher surface pressure when compared to the incorrectly placed or modified PCCD. Additionally, pressure distribution was significantly affected by the modification of the PCCDs. The cadaver lab measurements show that modifying or incorrectly placing the PCCDs significantly limits their ability to reduce the pelvic fracture. These results suggest that while modifying or incorrectly placing PCCDs allows access to the femoral artery, there are potentially dangerous effects to the patient including increased surface pressures and limited fracture reduction.