Non-Decreasing Sequences

Non-decreasing sequences are a generalization of binary covering arrays, which has made research on non-decreasing sequences important in both math and computer science. A non-decreasing sequence of subsets of a finite set S of size s, {S1, S2,.... St}, length t, and strength d, is a sequence of non-empty subsets where the union of any d previous subsets in the sequence does not contain any subsequent subset. The goal of this research is to find properties of these non-decreasing sequences as the variables d, s, and t change. We also explored methods for creating a maximum length for a non-decreasing sequence given d and s. Through our research, we discovered and proved basic properties of these non-decreasing sequences. In addition to this, we can describe a method we used while trying to find the maximum length of a sequence. In the future, research can be conducted to find an exact formula that will generate a maximum length sequence given a non-decreasing sequence of strength d

Constructing a class of topological solitons in magnetohydrodynamics

We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$ respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for $n_t \in \mathbb{Z}^+$ and $n_p=1$ these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity and estimate the soliton lifetime in such a medium as a function of the toroidal winding number.Comment: 5 pages, 3 figure

Simulations of two-planet systems through all phases of stellar evolution: implications for the instability boundary and white dwarf pollution

Exoplanets have been observed at many stages of their host star's life, including the main sequence (MS), subgiant and red giant branch stages. Also, polluted white dwarfs (WDs) likely represent dynamically active systems at late times. Here, we perform 3-body simulations which include realistic post-MS stellar mass loss and span the entire lifetime of exosystems with two massive planets, from the endpoint of formation to several Gyr into the WD phase of the host star. We find that both MS and WD systems experience ejections and star-planet collisions (Lagrange instability) even if the planet-planet separation well-exceeds the analytical orbit-crossing (Hill instability) boundary. Consequently, MS-stable planets do not need to be closely-packed to experience instability during the WD phase. This instability may pollute the WD directly through collisions, or, more likely, indirectly through increased scattering of smaller bodies such as asteroids or comets. Our simulations show that this instability occurs predominately between tens of Myr to a few Gyrs of WD cooling.Comment: Accepted for publication in MNRAS; 24 pages, 19 figure

Examining the Legacy of Transgenerational Trauma and its Effects on Contemporary African American Adults in Parenting and Caregiver Roles to African American Adolescents

The system of institutional enslavement in North America has produced myriad effects on the contemporary African American community via the transmission of individual, familial, and collective trauma across generations (Carter, 2015; DeGruy, 2005; Weingarten, 2004). This research explored the roles of parent and caregiver within this cultural group in an effort to determine how past traumas have influenced the lived experiences and world view of African Americans in these roles. While research on certain historically marginalized cultural and religious groups is plentiful, there is a clear lacuna of scholarly investigation into the African American experience, particularly as it relates to the roles of parent and caregiver. Parenting is among the most significant of human endeavors. The impact of parenting and care-giving on future generations is immeasurable; it is the apex of humanity. A great majority of the world’s cultures and religions place unequaled value on parenting as well as acting in the place of parents, as in the case of caregivers. These roles are even considered sacred within many groups. For these reasons, this aspect of the African American lived experience was examined in this research. The inquiry examined and presented various theories in order to offer a comprehensive background related to this topic. Transgenerational trauma theory provided the foundation for this research, along with cultural trauma and historical trauma theories. Supplemental investigations of self-determination theory, critical race theory, racial/ethnic identity development theory/nigrescence, race-based trauma theory, post traumatic slave syndrome, and acculturative stress theory also were incorporated in an effort to provide a comprehensive perspective. After analyzing the emergent themes resulting from the data collection process, findings suggested that several factors contributed to African American parenting styles, traditions, and perceptions. Among the most ubiquitous were fear, control, punishment, and separation. Fear has been used to take and maintain control over certain populations within American culture. Often, these more prevalent themes implicated the American criminal justice system as a key factor of oppression. Not only has it had the power to mete out punishment, but also to disenfranchise people, affect economic status, and instigate separation within families and from society. Historically, these same tactics have been used against African Americans and have maintained the cycle of transgenerational trauma symptoms to the extent that they have become embedded in the culture via the parenting relationship. These exploratory research findings have suggested multiple factors that affect how parenting and care-giving are viewed in the contemporary African American community. This inquiry aimed to encapsulate how past collective traumas have been integrated into the lived experiences of African Americans and to illuminate the effects of the transferred trauma. The current research indicated that trauma effects have been transmitted via familial and cultural means, which have become manifest in the parent and caregiver relationships in various forms that can be better understood within a transgenerational context. Notably, risk and protective factors were identified as well as commonly incorporated coping mechanisms within the African American community regarding parenting philosophies and behaviors

Criminality of women in the 18th century in the South West of England

Chapter 1: Debates and Developments in the fields of Crime History and Women's History: Frameworks, Methodolozies and Consolidation. This chapter falls into three sections. The first outlines some key issues in Crime History. The second examines the development of women's history and discusses the introduction of gender into Crime History. It is argued that the new issues that have arisen from the joining of these two disciplines have enhanced the development of Crime History. The third section discusses women's history and the study of crime and gender in the early modem period, the source material used and methodology employed in this thesis. Chapter 2: Economy and Socie!y in the South West of England: The Female Experience This chapter provides the social and economic background to the study of eighteenth-century female criminality in this region. It argues that the region constituted a pastoral rural economy; and it is within this context that the recorded criminal activities of women should be seen. The discussion develops, using the work of scholars who have examined this area of women's history, into an account of the roles and lifecycles of eighteenth-century women in these communities. Chapter 3: Female Theft in the South West This chapter falls into two distinct sections. The first is a broad examination of all recorded female property offencesi n the period. The study assessestr ends over -ivtime, using material from the Assizes Gaol Book and the Quarter Sessions Indictments. It discusses relationships between levels of prosecution and food prices and periods of war. It also seeks to identify possible reasons which types of goods were commonly recorded as stolen and discusses any trends for the prosecution of these thefts over time. The second part of the chapter is a detailed examination of the detection and prosecution of theft during the period. An emphasis has been placed on the importance of the sorts of goods stolen, as well as how they were stolen and, consequently, the type of offender most vulnerable of detection and prosecution. The section moves to focus on clothing theft and its relationship to trading networks in the eighteenth century. It places the examination of this networking within the context of the eighteenth-century clothing trade. Chapter 4: Offences Against the Person The first section of Chapter 4 concentrates on the record of assault and disorder found in the quarter sessions rolls and the assizes gaol books. It is argued that the increased use of recognizances to prosecute demonstrates the flexibility of the eighteenth-century criminal justice system. Also discussed in the section, are how assaults may be linked to other offences such as theft and how some assaults constituted unofficial punishments by communities. Although avoiding making too broad a statement about assault and disorder, it seeks to demonstrate that some cases could be representative of womenýs interests in both the public and private sphere. The second section of Chapter 4 discusses the record of homicide and infanticide for the western circuit assizes between 1735 and 1785. The section examines homicide, which seemed to predominantly occur within the familial setting. This includes the specific homicide offence of petty treason. The discussion moves on to examine infanticide, by far the most prominent female homicide offence recorded. The circumstances surrounding each case and the consequences of its discovery are examined. It is argued that a stereotyped narrative of the infanticidal woman dictated the prosecution and conviction rates of the offence