Generalised divisor sums of binary forms over number fields

Estimating averages of Dirichlet convolutions $1 \ast \chi$, for some real Dirichlet character $\chi$ of fixed modulus, over the sparse set of values of binary forms defined over $\mathbb{Z}$ has been the focus of extensive investigations in recent years, with spectacular applications to Manin's conjecture for Ch\^atelet surfaces. We introduce a far-reaching generalization of this problem, in particular replacing $\chi$ by Jacobi symbols with both arguments having varying size, possibly tending to infinity. The main results of this paper provide asymptotic estimates and lower bounds of the expected order of magnitude for the corresponding averages. All of this is performed over arbitrary number fields by adapting a technique of Daniel specific to $1\ast 1$. This is the first time that divisor sums over values of binary forms are asymptotically evaluated over any number field other than $\mathbb{Q}$. Our work is a key step in the proof, given in subsequent work, of the lower bound predicted by Manin's conjecture for all del Pezzo surfaces over all number fields, under mild assumptions on the Picard number

Case notes and clinicians : Galen's commentary on the Hippocratic epidemics in the Arabic tradition

Galen’s Commentaries on the Hippocratic Epidemics constitute one of the most detailed studies of Hippocratic medicine from Antiquity. The Arabic translation of the Commentaries by Ḥunayn ibn Isḥāq (d. c. 873) is of crucial importance because it preserves large sections now lost in Greek, and because it helped to establish an Arabic clinical literature. The present contribution investigate the translation of this seminal work into Syriac and Arabic. It provides a first survey of the manuscript tradition, and explores how physicians in the medieval Muslim world drew on it both to teach medicine to students, and to develop a framework for their own clinical research

From Convergence to Compromise: Understanding the Interplay of Digital Transformation and Mergers on Data Breach Risks in Local and Cross-Border Mergers

In today\u27s digital age, the potential risks and challenges associated with digital transformation (DT) and cybersecurity have received limited research attention. This dissertation consists of three interconnected studies that aim to address this gap. The first study employs paradox theory to demonstrate that DT initiatives can increase a firm\u27s susceptibility to data breaches. Using a unique dataset spanning 10 years and involving 3604 brands, our analysis reveals that DT efforts in mobile and digital marketing are associated with a higher incidence of data breaches. However, firms can mitigate this impact by enhancing their innovative capacities. These findings contribute to a better understanding of the complex relationship between DT, data breaches, and innovation. Our second investigation, rooted in complexity theory and matching theory, examines the impact of mergers and acquisitions (M&As) on the frequency of data breaches. By analyzing 18 years of data from 5072 US firms, we find that M&As increase the likelihood of data breaches, particularly when the merging firms operate in different business domains. Furthermore, we observe that M&As that receive more media attention are more prone to data breaches, while those involving a more vulnerable target firm have fewer breaches. In our third study, guided by Institutional theory, we explore the relationship between cross-border mergers and acquisitions (CBMA) and data breaches. Our findings indicate that CBMAs, especially those accompanied by significant media publicity and involving firms from divergent institutional contexts, heighten the risk of data breaches. Overall, these studies provide valuable insights for firms aiming to mitigate data breach risks during their digital transformation (DT) efforts and M&A activities. They emphasize the importance of adopting a balanced communication strategy and considering the security implications of strategic actions. Moreover, our findings contribute to the academic discourse in information systems by illuminating the intricate interplay between DT, M&As, and data breaches

Equilibrium states of generalised singular value potentials and applications to affine iterated function systems

We completely describe the equilibrium states of a class of potentials over the full shift which includes Falconer's singular value function for affine iterated function systems with invertible affinities. We show that the number of distinct ergodic equilibrium states of such a potential is bounded by a number depending only on the dimension, answering a question of A. K\"aenm\"aki. We prove that all such equilibrium states are fully supported and satisfy a Gibbs inequality with respect to a suitable subadditive potential. We apply these results to demonstrate that the affinity dimension of an iterated function system with invertible affinities is always strictly reduced when any one of the maps is removed, resolving a folklore open problem in the dimension theory of self-affine fractals. We deduce a natural criterion under which the Hausdorff dimension of the attractor has the same strict reduction property.Comment: 33 pages, 2 figures. V2: Minor changes. This is the final version, accepted for publication in GAF

μὴ διακρίνων τ̀ο σω̑υα (Mē diakrinōn to sōma (romanized form)

The purpose of this paper is to explore the meaning of Paul\u27s expression μὴ διακρίνων τ̀ο σω̑υα in 1 Cor.11:29. The basic task is exegetical, but the concern which promted the research is the pragmatic concern of meaning in use. This paper will, therefore, begin with a careful study to determine, as best as is possible, what Paul meant when he wrote the words in question. It will conclude with an analysis and evaluation of past and present application of 1 Cor. 11:29 and its context

Estimação e diagnóstico em modelos multivariados para dados censurados

Orientadores: Víctor Hugo Lachos Dávila, Luis Mauricio Castro CeperoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Em alguns ensaios clínicos da síndrome da imunodeficiência adquirida (AIDS), as medições dos ácidos ribonucleicos do vírus da imunodeficiência humana (HIV-1) são coletadas periodicamente ao longo do tempo e muitas vezes estão sujeitas a limites de detecção inferiores ou superiores, dependendo dos ensaios de quantificação que foram utilizados. Assim, estas respostas podem ser censuradas à esquerda ou à direita. Na prática, dados longitudinais provenientes de estudos de acompanhamento do HIV, podem ser modelados utilizando modelos lineares e não-lineares de efeitos mistos censurados e também modelos de regressão censurados com estruturas de correlação específicas sobre os erros. Uma complicação adicional surge quando duas ou mais variáveis respostas são coletadas de forma irregular e repetidamente em cada sujeito durante um certo período de tempo. Os modelos lineares multivariados de efeitos mistos com respostas censuradas são ferramentas bastante utilizadas para análise conjunta de mais de uma série de respostas de dados longitudinais. Nesta tese desenvolvemos métodos inferenciais para lidar com dados censurados com estrutura longitudinal sob uma perspectiva clássica. Como resultado, conclusões importantes foram obtidas a partir da análise dos modelos propostosAbstract: In some acquired immunodeficiency syndrome (AIDS) clinical trials, the human immunodeficiency virus-1 ribonucleic acid measurements are collected irregularly over time and are often subject to some upper and lower detection limits, depending on the quantification assays. Hence, these responses are either left- or right-censored. In practice, longitudinal data coming from those follow-up studies can be modelled using censored linear and nonlinear mixed-effects models and also censored regression models with a specific correlation structures on the error terms. A complication arises when more than one series of responses are repeatedly collected on each subject at irregularly occasions over a period of time. The multivariate censored linear mixed model is a frequently used tool for a joint analysis of more than one series of longitudinal data. In this thesis we develop a series of essays in which different models and techniques to deal with censored data are applied. As result, we had several works to carry out censored dataDoutoradoEstatisticaDoutora em Estatística2011/22063-9, 2015/05385-3FAPES

Navigation and flight director guidance for the NASA/FAA helicopter MLS curved approach flight test program

The navigation and flight director guidance systems implemented in the NASA/FAA helicopter microwave landing system (MLS) curved approach flight test program is described. Flight test were conducted at the U.S. Navy's Crows Landing facility, using the NASA Ames UH-lH helicopter equipped with the V/STOLAND avionics system. The purpose of these tests was to investigate the feasibility of flying complex, curved and descending approaches to a landing using MLS flight director guidance. A description of the navigation aids used, the avionics system, cockpit instrumentation and on-board navigation equipment used for the flight test is provided. Three generic reference flight paths were developed and flown during the test. They were as follows: U-Turn, S-turn and Straight-In flight profiles. These profiles and their geometries are described in detail. A 3-cue flight director was implemented on the helicopter. A description of the formulation and implementation of the flight director laws is also presented. Performance data and analysis is presented for one pilot conducting the flight director approaches

Drawing and dramatization in forensic settings:external and internal prompts in children's and adults' eyewitness testimony

This thesis explored the effects of drawing and dramatization as well as the intersection between temperament, symbolic skills, language ability, mood, and various interview methods (drawing, dramatization, verbal-only) in children’s and adults’ verbal recall of a salient event. Studies One and Two examined whether drawing and dramatization facilitate 3- to 6- year olds’ verbal recall, after delays of one day, two weeks, and six months. Study Three looked the content of the drawings the children produced and how it changes over time. Study Four investigated whether drawings (own drawing or another’s drawing) can act as memory aids for a video event after a two-week delay. Study Five explored the effects of drawing on adults’ memory of a live event, after an immediate, a two-week, and a three-month delay. In all studies, measures of internal characteristics were taken, and their intersection with different interview methods was examined. The findings suggest that drawing while narrating enhances children’s recall about objects within a two-week time frame. Drawing does not have an effect on adults’ recall. Children consistently depict the more general features of an event, whereas information regarding ‘the perpetrator’ and ‘victim’ dissipates from drawings as time elapses. Drawings per se may not act as memory cues for a past event, as children may use them to identify the depicted features rather than link back to the event. Importantly, the intersection between different interview methods and children’s and adults’ individual differences may affect their reports. Temperamental traits, language skills, and symbolic ability interrelate with a verbal-only, a drawing, and a dramatization interview to either facilitate or compromise verbal reports. Given these findings, forensic officials are advised to take eyewitnesses’ individual characteristics into account and try to adapt investigative interviews to their needs, to facilitate their eyewitness testimony

A workbook to develop library skills in the junior high school

Thesis (Ed.M.)--Boston Universit