Classical and Discrete Functional Analysis with Measure Theory

2022 ◽  
Author(s):  
Martin Buntinas
Keyword(s):  
Functional Analysis ◽  
Quantum Physics ◽  
Measure Theory ◽  
Teaching Experience ◽  
First Year ◽  
Infinite Dimensional ◽  
Pure Mathematics ◽  
Self Study ◽  
Background Material ◽  
One Year

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

scholarly journals Cardiovascular risk factors associated with acute myocardial infarction and stroke in the MADIABETES cohort

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
M. A. Salinero-Fort ◽  
F. J. San Andrés-Rebollo ◽  
J. Cárdenas-Valladolid ◽  
M. Méndez-Bailón ◽  
R. M. Chico-Moraleja ◽  
...  
Keyword(s):  
Atrial Fibrillation ◽  
Blood Pressure ◽  
Antihypertensive Drugs ◽  
Hdl Cholesterol ◽  
First Year ◽  
Backward Elimination ◽  
One Year ◽  
Time Varying Covariates

AbstractWe aimed to develop two models to estimate first AMI and stroke/TIA, respectively, in type 2 diabetes mellitus patients, by applying backward elimination to the following variables: age, sex, duration of diabetes, smoking, BMI, and use of antihyperglycemic drugs, statins, and aspirin. As time-varying covariates, we analyzed blood pressure, albuminuria, lipid profile, HbA1c, retinopathy, neuropathy, and atrial fibrillation (only in stroke/TIA model). Both models were stratified by antihypertensive drugs. We evaluated 2980 patients (52.8% women; 67.3 ± 11.2 years) with 24,159 person-years of follow-up. We recorded 114 cases of AMI and 185 cases of stroke/TIA. The factors that were independently associated with first AMI were age (≥ 75 years vs. < 75 years) (p = 0.019), higher HbA1c (> 64 mmol/mol vs. < 53 mmol/mol) (p = 0.003), HDL-cholesterol (0.90–1.81 mmol/L vs. < 0.90 mmol/L) (p = 0.002), and diastolic blood pressure (65–85 mmHg vs. < 65 mmHg) (p < 0.001). The factors that were independently associated with first stroke/TIA were age (≥ 75 years vs. < 60 years) (p < 0.001), atrial fibrillation (first year after the diagnosis vs. more than one year) (p = 0.001), glomerular filtration rate (per each 15 mL/min/1.73 m2 decrease) (p < 0.001), total cholesterol (3.88–6.46 mmol/L vs. < 3.88 mmol/L) (p < 0.001), triglycerides (per each increment of 1.13 mmol/L) (p = 0.031), albuminuria (p < 0.001), neuropathy (p = 0.01), and retinopathy (p = 0.023).

scholarly journals Mortality in older adults following a fragility fracture: real-world retrospective matched-cohort study in Ontario

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Jacques P. Brown ◽  
Jonathan D. Adachi ◽  
Emil Schemitsch ◽  
Jean-Eric Tarride ◽  
Vivien Brown ◽  
...  
Keyword(s):  
Cohort Study ◽  
Hip Fracture ◽  
Fragility Fracture ◽  
Mortality Risk ◽  
Real World ◽  
First Year ◽  
Matched Cohort ◽  
Matched Cohort Study ◽  
Fracture Cohort ◽  
One Year

Abstract Background Recent studies are lacking reports on mortality after non-hip fractures in adults aged > 65. Methods This retrospective, matched-cohort study used de-identified health services data from the publicly funded healthcare system in Ontario, Canada, contained in the ICES Data Repository. Patients aged 66 years and older with an index fragility fracture occurring at any osteoporotic site between 2011 and 2015 were identified from acute hospital admissions, emergency and ambulatory care using International Classification of Diseases (ICD)-10 codes and data were analyzed until 2017. Thus, follow-up ranged from 2 years to 6 years. Patients were excluded if they presented with an index fracture occurring at a non-osteoporotic fracture site, their index fracture was associated with a trauma code, or they experienced a previous fracture within 5 years prior to their index fracture. This fracture cohort was matched 1:1 to controls within a non-fracture cohort by date, sex, age, geography and comorbidities. All-cause mortality risk was assessed. Results The survival probability for up to 6 years post-fracture was significantly reduced for the fracture cohort vs matched non-fracture controls (p < 0.0001; n = 101,773 per cohort), with the sharpest decline occurring within the first-year post-fracture. Crude relative risk of mortality (95% confidence interval) within 1-year post-fracture was 2.47 (2.38–2.56) in women and 3.22 (3.06–3.40) in men. In the fracture vs non-fracture cohort, the absolute mortality risk within one year after a fragility fracture occurring at any site was 12.5% vs 5.1% in women and 19.5% vs 6.0% in men. The absolute mortality risk within one year after a fragility fracture occurring at a non-hip vs hip site was 9.4% vs 21.5% in women and 14.4% vs 32.3% in men. Conclusions In this real-world cohort aged > 65 years, a fragility fracture occurring at any site was associated with reduced survival for up to 6 years post-fracture. The greatest reduction in survival occurred within the first-year post-fracture, where mortality risk more than doubled and deaths were observed in 1 in 11 women and 1 in 7 men following a non-hip fracture and in 1 in 5 women and 1 in 3 men following a hip fracture.

scholarly journals Across the COVID-19 Waves; Assessing Temporal Fluctuations in Perceived Stress, Post-Traumatic Symptoms, Worry, Anxiety and Civic Moral Disengagement over One Year of Pandemic

2021 ◽  
Vol 18 (11) ◽  
pp. 5651
Author(s):  
Alessio Gori ◽  
Eleonora Topino
Keyword(s):  
Perceived Stress ◽  
State Anxiety ◽  
Moral Disengagement ◽  
Online Survey ◽  
Well Being ◽  
First Year ◽  
Effective Interventions ◽  
Post Traumatic ◽  
One Year ◽  
Traumatic Symptoms

This study aimed at investigating the psychological effect of the COVID-19 pandemic in Italy by analysing the trends of perceived stress, post-traumatic symptoms, state anxiety, worry, and civic moral disengagement in four different moments from March 2020 to March 2021. The study involved a total of 1827 Italian participants (30% men and 70% women; Mage = 34.72; SD = 12.40) divided into four groups to which an online survey was administered. The first group completed the survey in March 2020, the second one in August 2020, the third one in November 2020, and the fourth one in March 2021. Results highlighted significant decreases in post-traumatic symptoms and a significant increase in civic moral disengagement over the first year of the COVID-19 pandemic. The levels of perceived stress, worry, and state anxiety remained constant. The correlations between the variables at different times were also explored, as well as gender differences over the year. The COVID-19 emergency has had significant effects on the mental state of the population, with important repercussions for individual and collective well-being during but probably also after the pandemic. This study offers a clear snapshot of the psychological outcomes over one COVID-19 pandemic year, providing important information that may contribute to tailor more effective interventions for mental health.

How well does A-level Mathematics prepare students for the mathematical demands of chemistry degrees?

2016 ◽  
Vol 17 (4) ◽  
pp. 1190-1202 ◽  
Author(s):  
Ellie Darlington ◽  
Jessica Bowyer
Keyword(s):  
First Year ◽  
Chemistry Students ◽  
Undergraduate Chemistry ◽  
Undergraduate Study ◽  
Pure Mathematics ◽  
Entry Requirements ◽  
Good Preparation

332 undergraduate chemistry students were surveyed in order to establish whether they had found A-level Mathematics and/or Further Mathematics to be good preparation for their degree. Perceptions of both subjects were found to be positive, with more than 80% of participants describing Mathematics or Further Mathematics as good preparation. In particular, pure mathematics and mechanics topics were found to be the most useful. Additionally, over 90% of participants who had studied at least AS-level Further Mathematics reported that there was an overlap between the material they encountered at A-level and in the first year of undergraduate study. This indicates that prospective undergraduate chemists would significantly benefit from studying A-level Mathematics, and in particular may benefit from specialising in the study of mechanics, something which will only be possible through the study of Further Mathematics after qualifications are reformed in September 2017. Universities should consequently consider revising their entry requirements or recommendations to applicants.

scholarly journals Topics of Measure Theory on Infinite Dimensional Spaces

Mathematics ◽  
2017 ◽  
Vol 5 (3) ◽  
pp. 44
Author(s):  
José Velhinho
Keyword(s):  
Measure Theory ◽  
Infinite Dimensional

Teething Symptoms in the First Year of Life and Associated Factors: A Cohort Study

2010 ◽  
Vol 34 (3) ◽  
pp. 201-206 ◽  
Author(s):  
Carlos Alberto Feldens ◽  
Italo Medeiros Faraco Junior ◽  
Andréia Bertani Ottoni ◽  
Eliane Gerson Feldens ◽  
Márcia Regina Vítolo
Keyword(s):  
Associated Factors ◽  
Primary Outcome ◽  
First Year ◽  
Structured Interviews ◽  
Self Medication ◽  
Nuclear Families ◽  
Dental Examination ◽  
Pediatric Dentists ◽  
One Year ◽  
First Year Of Life

Objective: To investigate the occurrence and management of teething symptoms during the first year of life and associated factors. Study design: 500 children were recruited at birth. Research assessments including structured interviews, anthropometric measurements and dental examination were carried out after birth, at 6 months and at one-year of age. The primary outcome of this study was defined as the occurrence of one or more teething symptoms within the first year of life, as reported by the mother. Results: Teething symptoms were reported in 73% of the children analyzed (273/375). The symptoms most frequently reported were irritability (40.5%), fever (38.9%), diarrhoea (36.0%) and itching (33.6%). Dentists had little influence on the management of symptoms and self-medication to relieve them was a common practice. The risk of reporting teething symptoms was higher for children from nuclear families (p=0.040) and for children from families with higher income (p=0.040). Conclusions: Teething symptoms were highly reported in this population. Pediatric dentists should be accessible and provide adequate orientation when symptoms can be managed at home or immediate referral to health services when more serious diseases are suspected.

Partnership in Post-Adoption Services Evaluating the First Year of a Complementary Contract

1997 ◽  
Vol 21 (3) ◽  
pp. 50-56 ◽  
Author(s):  
Alan Burnell ◽  
Adrian Briggs
Keyword(s):  
Social Services ◽  
Comprehensive Assessment ◽  
First Year ◽  
Service Users ◽  
Adoptive Families ◽  
Treatment Services ◽  
Assessment And Treatment ◽  
One Year ◽  
Families With Children ◽  
Consultation Services

In the autumn 1995 edition of Adoption & Fostering, Alan Burnell and Adrian Briggs described the origins and objectives of a novel complementary contract between East Sussex Social Services and the Post-Adoption Centre (PAC), aimed at providing post-adoption counselling and consultation services to all those involved in adoption in the county. The same authors now evaluate the operation of the contract, one year on. After filling in some background they assess its achievements so far, with particular regard to the extra support to service users and staff, and reducing the risk of disruption. The article concludes that the first year of the contract has demonstrated the need for comprehensive assessment and treatment services for adoptive families with children experiencing attachment difficulties.

ADENOVIRUS COMPLEMENT-FIXING ANTIBODY TITERS FROM BIRTH THROUGH THE FIRST YEAR OF LIFE

PEDIATRICS ◽  
1963 ◽  
Vol 32 (4) ◽  
pp. 497-500
Author(s):  
Rosa Lee Nemir ◽  
Donna O'Hare ◽  
Stanley Goldstein ◽  
Charles B. Hilton
Keyword(s):  
Cytopathic Effect ◽  
Gradual Increase ◽  
Newborn Infants ◽  
First Year ◽  
Placental Barrier ◽  
Culture Studies ◽  
Antibody Titers ◽  
Level 1 ◽  
One Year ◽  
First Year Of Life

Complement fixing antibody titers to the adenoviruses were determined in 251 newborn infants, using cord blood. Approximately 95% of these were found to have CF titers of 1:16 or over, the majority (75%) were 1:32 or more. Material from the pharyngeal and rectal swabs of these infants on tissue culture studies (542) on HeLa and amnion cells showed no cytopathic effect in oven 96% of these infants. A longitudinal study of 114 of these infants was made at 3 months intervals; 67 have been observed for one year. At 3 months, only 12% still showed CF antibody titers, and these were chiefly at a low level, 1:16. At the subsequent 3-month interval observations, a gradual rise in CF antibodies were found. At one year of age, approximately 37% had titers of 1:32 on over. The findings of this report support the statement that CF antibodies to adenovirus pass the placental barrier. There is a gradual increase in the percentage of infants with positive CF antibodies after 3 months.

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