Variable Hardy Spaces

We develop the theory of variable exponent Hardy spaces. Analogous to the classical theory, we give equivalent definitions in terms of maximal operators. We also show that distributions in these spaces have an atomic decomposition including a "finite" decomposition; this decomposition is more like the decomposition for weighted Hardy spaces due to Stromberg and Torchinsky than the classical atomic decomposition. As an application of the atomic decomposition we show that singular integral operators are bounded on variable Hardy spaces with minimal regularity assumptions on the exponent function

A new method to find the potential center of N-body systems

We present a new and fast method to nd the potential center of an N-body distribution. The method uses an iterative algorithm which exploits the fact that the gradient of the potential is null at its center: it uses a smoothing radius to avoid getting trapped in secondary minima. We have tested this method on several random realizations of King models (in which the numerical computation of this center is rather dicult, due to the constant density within their cores), and com- pared its performance and accuracy against a more straightforward, but computer intensive method, based on cartesian meshes of increasing spatial resolution. In all cases, both methods converged to the same center, within the mesh resolution, but the new method is two orders of magnitude faster. We have also tested the method with one astronomical problem: the evolu- tion of a 105 particle King model orbiting around a xed potential that represents our Galaxy. We used a spherical harmonics expansion N-body code, in which the potential center determination is crucial for the correct force computation. We compared this simulation with another one in which a method previously used to determine the expansion center is employed (White 1983). Our routine gives better results in energy conservation and mass loss.Fil: Aguilar, L. A.. Universidad Nacional Autonoma de Mexico. Instituto de Astronomia; MéxicoFil: Cruz, F.. Universidad Nacional Autonoma de Mexico. Instituto de Astronomia; MéxicoFil: Carpintero, Daniel Diego. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Superfluid fraction in disordered bosonic gases

Màster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2022-2023. Tutors: Pietro Massignan, Grigori AstrakharchikIn this work, we study the behaviour of the superfluid fraction f of a bosonic system under the influence of a speckle potential. We start by introducing and defining f, and then we present the lower and upper bounds to f derived by A. Leggett for generic many-body systems. To benchmark our codes, we study first the case of a periodic optical potential, reproducing results that recently appeared in the literature. We continue by describing the particular kind of disordered potential we want to study, and how this is characterized. Finally, we compute the superfluid fraction as a function of the intensity of the disordered potential and the interaction strength between the bosons, and we compare our results to the two bounds in both 1D and 2D

Electric Fall-Out Album Vinyl Cover

An album cover for a playlist containing songs from both the band Fall Out Boy and the band the Electric Mayhem. The album cover depicts original characters dressed in the style and outfits of the Electric Mayhem (Dr. Teeth and Janice) and Fall Out Boy (Patrick Stump and the boy from the cover of American Beauty/American Psycho).https://digitalcommons.kennesaw.edu/illustrationstudents/1026/thumbnail.jp

Insertions Yielding Equivalent Double Occurrence Words

A double occurrence word (DOW) is a word in which every symbol appears exactly twice; two DOWs are equivalent if one is a symbol-to-symbol image of the other. We consider the so called repeat pattern ($\alpha\alpha$) and the return pattern ($\alpha\alpha^R$), with gaps allowed between the $\alpha$'s. These patterns generalize square and palindromic factors of DOWs, respectively. We introduce a notion of inserting repeat/return words into DOWs and study how two distinct insertions into the same word can produce equivalent DOWs. Given a DOW $w$, we characterize the structure of $w$ which allows two distinct insertions to yield equivalent DOWs. This characterization depends on the locations of the insertions and on the length of the inserted repeat/return words and implies that when one inserted word is a repeat word and the other is a return word, then both words must be trivial (i.e., have only one symbol). The characterization also introduces a method to generate families of words recursively

Sintomas neuropsiquiátricos e declínio cognitivo

Introdução: Os sintomas Neuropsiquiátricos (SNP) são manifestações comuns que afectam quase todas as pessoas que sofrem da doença de Alzheimer. O objectivo principal deste trabalho passa por relatar a prevalência dos diferentes SNP, utilizando uma prova especifica para esse efeito, o Neuropsychiatric Inventory – Questionnaire (NPI-Q), numa amostra de idosos recolhida junto da população geral, em instituições que recebem idosos (em diferentes valências) do Concelho de Coimbra. É igualmente nosso objectivo verificar se existe uma associação significativa entre o declínio cognitivo, avaliado através de uma prova de rastreio cognitivo, o Mini Mental State Examination (MMSE) junto do idoso e a gravidade (atribuída) dos SNP e o grau de perturbação causado pelos mesmos aos cuidadores informais dos idosos. Ao explorar esta associação e eventual papel preditivo da gravidade e grau de perturbação dos SNP para o declínio cognitivo, consideramos potenciais associações entre os SNP e o declínio e diferentes variáveis sociodemográficas, a sintomatologia depressiva e ansiosa. Importará controlar estas variáveis nas análises preditivas, no caso de encontrarmos associações estatisticamente significativas. Pretendemos, igualmente, controlar o eventual papel da simulação (teste Rey-15 Item Test/Rey 15), caso se encontre presente neste estudo. Metodologia: A amostra incluiu 52 idosos (média de idades, M = 80,1; Desvio-padrão, DP = 6,89; variação = 66 - 93) sob resposta social em diferentes instituições do Concelho de Coimbra que aceitaram responder voluntariamente (ou cujos familiares/cuidadores concederam o respectivo consentimento) a uma bateria de testes (incluindo algumas questões sociodemográficas, o MMSE, o Geriatric Anxiety Inventory/GAI a Geriatric Depression Scale/GDS, o Rey-15 e o NPI-Q. Resultados: A maioria dos sujeitos não sofria de declínio cognitivo (65%; n = 34), verificando-se, em oposição a outros estudos, que as percentagens de sujeitos com SNP eram inferiores. Os SNP mais prevalentes foram a Ansiedade (34,6%; n = 18) e a Irritabilidade (34,6%; n = 18). Verificou-se não existirem associações estatisticamente significativas entre a gravidade dos sintomas (NPI-Q) e grau de perturbação dos mesmos (NPI-Q), de acordo com os cuidadores informais, e a presença de declínio cognitivo nos idosos (MMSE). Também não se verificaram associações estatisticamente significativas entre a gravidade dos sintomas (NPI-Q) e grau de perturbação dos mesmos (NPI-Q), de acordo com os cuidadores informais e as variáveis sociodemográficas. Não foram encontradas associações entre a sintomatologia depressiva e ansiosa avaliada junto dos idosos e a gravidade dos SNP e grau de perturbação associado de acordo com os seus cuidadores informais. Conclusão/Discussão: Ao contrário do que poderia ser esperado, não se encontrou uma associação entre o declínio cognitivo, avaliado junto dos idosos, e a presença de SNP de acordo com os cuidadores informais. Vários motivos se podem associar a este resultado não significativo, como o facto da nossa amostra apresentar uma percentagem reduzida de idosos com declínio cognitivo, o tamanho reduzido da nossa amostra ou até mesmo o facto dos SNP terem sido avaliados por auxiliares da instituição que podem não possuir a formação necessária para os avaliar. Um dado igualmente relevante foi a ausência de associações significativas entre as medidas dos SNP e a sintomatologia depressiva/ansiosa e algumas variáveis sociodemográficas. Importa, em estudos futuros, com uma amostra maior, verificar se este padrão de resultados se mantém e, eventualmente, comparar os resultados obtidos depois do NPI-Q ser respondido por clínicos, familiares e auxiliares dos idosos. / Introduction: Neuropsychiatric symptoms (NPS) are common manifestations that afflict almost all Alzheimer’s disease patients. The main goal of this work was to present the prevalence of different NPS, using a specific test, the Neuropsychiatric Inventory – Questionnaire (NPI-Q), in a sample of elderly from the general population, under social answer in different institutions from Coimbra Council. Moreover, we want to verify if there is a significant association between the cognitive decline, assessed with a cognitive screening test, the Mini Mental State Examination (MMSE) administered to the elderly and the (attributed) severity of the NPS and distress caused by the symptoms, assessed by the informal caregiver of the elderly. While exploring this association and the potential predictive role of the severity and distress caused by the NPS to the cognitive decline, we also considered the potential associations between the NPS and the decline, different sociodemographic variables and depressive/anxious symptoms. It will be important to control these variables, if significant associations are found. We also wish to control the potential role of simulation (assessed by the Rey-15 Item Test/Rey 15), if we found that it is present in our sample. Methodology: Our sample comprises 52 elderly (mean age, M = 80,1; Standard deviation, SD = 6,89; range = 66 - 93) under social answer in different institutions from Coimbra Council who accepted to fill in voluntarily a test battery or whose relatives/caregivers gave consent, including some sociodemographic questions, the MMSE, the Geriatric Anxiety Inventory/GAI, the Geriatric Depression Scale/GDS, the Rey-15 and NPI-Q. Results: It was possible to verify that most of the subjects did not suffer from cognitive decline (65%; n = 34). We also verified, in opposition to other studies, that the percentage of elderly with NPS was lower, with the most prevalent being anxiety (34,6%; n = 18) and irritability (34,6%; n = 18). There were no statistically significant associations between symptoms severity (NPI-Q) and distress caused by them (NPI-Q), according to the informal caregivers and the presence of cognitive decline in the elderly (MMSE). Moreover, there were no significant associations between symptoms severity and associated distress (NPI-Q) and the sociodemographic variables of the study. There were no associations between depressive and anxious symptoms in the elderly and the symptoms severity and associated distress (NPI-Q) assessed by the informal caregivers. Conclusion/Discussion: Contrary to what would be expected, we did not find an association between cognitive decline in the elderly and the presence of NPS according to the informal caregivers. Several reasons can explain this non significant result, like the fact that our sample presents a low percentage of elderly with cognitive decline, the reduced sample size our even the fact that NPS were assessed by the assistant workers of the institutions that might no possess the necessary knowledge to assess them. Other relevant result was the absence of significant associations between the NPS measures and depressive/anxious symptoms and some demographic variables. In future studies, with a larger sample it will be important to verify if these patterns of results are maintained and, eventually, it would be interesting to compare the results found after the NPI-Q has been answered by clinicians, family members and institution’s assistants

The marginal utility of money: A modern Marshallian approach to consumer choice

We reformulate neoclassical consumer choice by focusing on lamda, the marginal utility of money. As the opportunity cost of current expenditure, lamda is approximated by the slope of the indirect utility function of the continuation. We argue that lamda can largely supplant the role of an arbitrary budget constraint in partial equilibrium analysis. The result is a better grounded, more flexible and more intuitive approach to consumer choice.budget constraint, separability, value for money