Counting fixed points and rooted closed walks of the singular map x↦xxnx \mapsto x^{x^n} modulo powers of a prime

The "self-power" map $x \mapsto x^x$ modulo $m$ and its generalized form $x \mapsto x^{x^n}$ modulo $m$ are of considerable interest for both theoretical reasons and for potential applications to cryptography. In this paper, we use $p$-adic methods, primarily $p$-adic interpolation, Hensel's lemma, and lifting singular points modulo $p$, to count fixed points and rooted closed walks of equations related to these maps when $m$ is a prime power. In particular, we introduce a new technique for lifting singular solutions of several congruences in several unknowns using the left kernel of the Jacobian matrix.Comment: 18 pages. Version 2 shortens proofs, reduces redundancy, and introduces new technique for counting rooted closed walks. Version 3 updates title to agree with journal publicatio

ILLUMINATING HOPEWELL LEGACY DATA: A CASE STUDY OF MOUND 23 AT HOPEWELL MOUND GROUP

Digital archives present new opportunities for transparency, context and accessibility by digitizing and publishing limitedly accessible collections of archival documents and artifacts. Due to the destructive nature of archaeological inquiry these datasets are the only remaining materials from which archaeologists can make interpretations about past human behavior. The objective of this thesis was to be a case study for the usability of legacy data from Hopewell Mound Group by examining newly accessible data sources through the Ohio Hopewell digital archive (hopewell.unl.edu). The resulting databases for the burial data and artifacts of Hopewell Mound Group’s Mound 23 are a combination of the Field Museum of Natural History artifact catalog, archival field notes, published manuscripts, unpublished manuscripts, excavation reports, and plan maps. In addition, contemporary data sources such as Case and Carr’s (2005: Appendix 6.1) HOPEBIOARCH database and geophysical data from Hopewell Culture National Historic Park were also used in this study. Through the examination of the archival data in conjunction with museum artifact catalogs and contemporary data I was able to glean new details and interpretations of Mound 23 at Hopewell Mound Group. Details regarding burial numbering, burial preparation, and artifact associations which were previously unintelligible from the published data are presented for future study. The databases were also situated within a GIS environment to provide a new level of analysis for comparing burial deposits within Mound 23. Lastly, the materials recovered and compiled through this investigation of Mound 23 were compared to previous mortuary analyses of Hopewell Mound Group’s Mound 25 by Greber and Ruhl (1989) and Case and Carr (2005). Overall, based upon a set of measures outlined by Case and Carr (2005), Mound 23 possessed few individuals of potentially high social status and based upon Case and Carr’s (2005) suite of features demonstrated ceremonial society membership or achieved status. Future analyses should examine the ethnographic record in relation to patterns of mortuary deposits at Hopewell Mound Group. Moreover, more reliable dating of the deposits of mounds 23 and 25 should be undertaken to better elucidate their relationship to one another and expand the analytical capabilities of future research. Advisor: Carolyn Heitma

Jubilation

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ILLUMINATING HOPEWELL LEGACY DATA: A CASE STUDY OF MOUND 23 AT HOPEWELL MOUND GROUP

Digital archives present new opportunities for transparency, context and accessibility by digitizing and publishing limitedly accessible collections of archival documents and artifacts. Due to the destructive nature of archaeological inquiry these datasets are the only remaining materials from which archaeologists can make interpretations about past human behavior. The objective of this thesis was to be a case study for the usability of legacy data from Hopewell Mound Group by examining newly accessible data sources through the Ohio Hopewell digital archive (hopewell.unl.edu). The resulting databases for the burial data and artifacts of Hopewell Mound Group’s Mound 23 are a combination of the Field Museum of Natural History artifact catalog, archival field notes, published manuscripts, unpublished manuscripts, excavation reports, and plan maps. In addition, contemporary data sources such as Case and Carr’s (2005: Appendix 6.1) HOPEBIOARCH database and geophysical data from Hopewell Culture National Historic Park were also used in this study. Through the examination of the archival data in conjunction with museum artifact catalogs and contemporary data I was able to glean new details and interpretations of Mound 23 at Hopewell Mound Group. Details regarding burial numbering, burial preparation, and artifact associations which were previously unintelligible from the published data are presented for future study. The databases were also situated within a GIS environment to provide a new level of analysis for comparing burial deposits within Mound 23. Lastly, the materials recovered and compiled through this investigation of Mound 23 were compared to previous mortuary analyses of Hopewell Mound Group’s Mound 25 by Greber and Ruhl (1989) and Case and Carr (2005). Overall, based upon a set of measures outlined by Case and Carr (2005), Mound 23 possessed few individuals of potentially high social status and based upon Case and Carr’s (2005) suite of features demonstrated ceremonial society membership or achieved status. Future analyses should examine the ethnographic record in relation to patterns of mortuary deposits at Hopewell Mound Group. Moreover, more reliable dating of the deposits of mounds 23 and 25 should be undertaken to better elucidate their relationship to one another and expand the analytical capabilities of future research. Advisor: Carolyn Heitma

The Igusa Local Zeta Function Associated with the Singular Cases of the Determinant and the Pfaffian

AbstractThis paper describes the theory of the Igusa local zeta function associated with a polynomialf(x) with coefficients in ap-adic local fieldK. Results are given in two cases wheref(x) is the determinant of a Hermitian matrix of degreemwith coefficients in: (1) a ramified quadratic extension ofK; and (2) the unique quaternion division algebra overK

Comparison of Norpac temperature sections with average BT sections along the same tracks

The NORPAC ATLAS (NORPAC Comm., 1960), now in press, contains horizontal and vertical charts of oceanographic data collected on the NORPAC Expedition, the first multi-nation synoptic survey of the North Pacific Ocean. Vertical BT temperature sections, included in the NORPAC ATLAS, were prepared by the author...

Alien Registration- Robinson, Margaret M. (Portland, Cumberland County)

https://digitalmaine.com/alien_docs/24271/thumbnail.jp

Working it out for yourself: how young people use strategies and resources to reshape or reinvent identities which they experience as problematic and/or limiting in their progress towards adulthood

Abstract Adulthood is not a destination. Youth research has shown how ‘becoming adult’ is an active relational process of identity change which, in the post-millennium world, is highly individualised. Young people’s choices, however, are contingent on their life circumstances and what they consider, for them, to be ‘plausible’ (Skeggs, 2004) or within reach. In this study I set out to explore ways in which young people exercise agency, especially in situations that offer fewer options and thinner resources that they can call upon. My concern is to uncover the strategies and resources they use to reshape or reinvent identities that they find get in the way of subjectively feeling ‘adult’ and being recognised as such by others. Rather than recruiting participants already ‘marked’ by the systems of education, youth justice or public care, I met young people through volunteering in three youth work projects. I was thus able to engage young people from 13-19 years with markedly different social experiences and characteristics. I approached the analysis of varied data gathered from narrative interviews, creative activities and ethnographic observation with theoretical tools including, but not limited to, Bourdieu's concepts of field, capital and habitus, generating insights into developing femininities, masculinities, ethnicities and friendships. Researching across three sites also enabled me to examine how young people access youth work as a resource in and of itself and as a means of bridging to further resources, whether practical or for use in their ‘identity-work’. ‘Relationships of trust’ with youth work organisations and practitioners can especially benefit young people where these are otherwise absent from their lives. However, the findings suggest that young people in many different circumstances for diverse reasons value youth-friendly space and the relative equality that characterises youth work relationships. This adds weight to arguments for expanding both universal open access provision and flexible delivery of targeted provision

Affiliative interactions between adult male and immature savanna chimpanzees (Pan troglodytes verus)

Social interactions between adult male and immature chimpanzees ( Pan troglodytes) have been understudied compared to those between mothers and their offspring. This study\u27s aim was to gain a better understanding of such relationships among a population of wild West African chimpanzees (P. t. verus). Although overall rates of affiliation between adult males and immatures were low, low-ranking males engaged in such interactions significantly more than higher ranking males. Additionally, males tended to favor the offspring of certain females, although this difference was not statistically significant. It has been suggested that male care in many primate species may serve as a mating strategy. Unlike higher ranking males who engage in displays, low-ranking males may increase their \u27attractiveness\u27 to females by demonstrating their abilities as care-givers. This hypothesis may explain the findings of the current study; low-ranking chimpanzee males may direct affiliative behavior towards infants and juveniles to gain reproductive benefits