Introduction to Functional Analysis.

This is lecture notes for several courses on Functional Analysis at School of Mathematics of University of Leeds. They are based on the notes of Dr. Matt Daws, Prof. Jonathan R. Partington and Dr. David Salinger used in the previous years. Some sections are borrowed from the textbooks, which I used since being a student myself. However all misprints, omissions, and errors are only my responsibility. I am very grateful to Filipa Soares de Almeida, Eric Borgnet, Pasc Gavruta for pointing out some of them. Please let me know if you find more. The notes are available also for download in PDF. The suggested textbooks are [1,6,8,9]. The other nice books with many interesting problems are [3, 7]. Exercises with stars are not a part of mandatory material but are nevertheless worth to hear about. And they are not necessarily difficult, try to solve them! CONTENTS List of Figures 3 Notations and Assumptions 4 Integrability conditions 4 1. Motivating Example: Fourier Series 4 1.1. Fourier series: basic notions 4 1.2. The vibrating string 8 1.3. Historic: Joseph Fourier 10 2. Basics of Linear Spaces 11 2.1. Banach spaces (basic definitions only) 12 2.2. Hilbert spaces 14 2.3. Subspaces 16 2.4. Linear spans 19 3. Orthogonality 20 3.1. Orthogonal System in Hilbert Space 21 3.2. Bessel’s inequality 23 3.3. The Riesz–Fischer theorem 25 3.4. Construction of Orthonormal Sequences 26 3.5. Orthogonal complements 28 4. Fourier Analysis 29 Date: 16th October 2017. 1

Introduction to Functional Analysis. By Angus E. Taylor. Pp. xvi. 423. $12.50. 1958. (John Wiley and Sons)

Attitudes, acceptance and hesitancy among the general population worldwide to receive the COVID-19 vaccines and their contributing factors: A systematic review.

This study aimed to determine the prevalence and investigate the constellations of psychological determinants of the COVID-19 vaccine hesitancy among the Bangladeshi adult population utilizing the health belief model-HBM (perceived susceptibility to and severity of COVID-19, perceived benefits of and barriers to COVID-19 vaccination, and cues to action), the theory of planned behavior-TPB (attitude toward COVID-19 vaccine, subjective norm, perceived behavioral control, and anticipated regret), and the 5C psychological antecedents (confidence, constraints, complacency, calculation, and collective responsibility). We compared the predictability of these theoretical frameworks to see which framework explains the highest variance in COVID-19 vaccine hesitancy. This study adopted a cross-sectional research design. We collected data from a nationally representative sample of 1,497 respondents through both online and face-to-face interviews. We employed multiple linear regression analysis to assess the predictability of each model of COVID-19 vaccine hesitancy. We found a 41.1% prevalence of COVID-19 vaccine hesitancy among our study respondents. After controlling the effects of socio-economic, demographic, and other COVID-19 related covariates, we found that the TPB has the highest predictive power (adjusted R 2 = 0.43), followed by the 5C psychological antecedents of vaccination (adjusted R 2 = 0.32) and the HBM (adjusted R 2 = 0.31) in terms of explaining total variance in the COVID-19 vaccine hesitancy among the adults of Bangladesh. This study provides evidence that theoretical frameworks like the HBM, the TPB, and the 5C psychological antecedents can be used to explore the psychological determinants of vaccine hesitancy, where the TPB has the highest predictability. Our findings can be used to design targeted interventions to reduce vaccine hesitancy and increase vaccine uptake to prevent COVID-19.

/pdf/health-belief-model-theory-of-planned-behavior-or-2lgmp7b7cs.pdf

Health Belief Model, Theory of Planned Behavior, or Psychological Antecedents: What Predicts COVID-19 Vaccine Hesitancy Better Among the Bangladeshi Adults?

Determinants of COVID-19 Vaccine Acceptance among the Adult Population of Bangladesh Using the Health Belief Model and the Theory of Planned Behavior Model

https://www.mdpi.com/2076-393X/9/5/416/pdf

COVID-19 vaccination intent and willingness to pay in Bangladesh: a cross-sectional study

Background: Silver nanoparticles (AgNPs) are toxic to microorganisms and can potentially kill multidrug-resistant bacteria. Nanoparticles can be synthesized in many ways, such as physical or chemical methods. Recently, it has been found that plant molecules can perform the same reduction reactions necessary for the production of nanoparticles but in a much more efficient way. Results: Here, green chemistry was employed to synthesize AgNPs using leaf extracts of Cymbopogon citratus. The effects of different parameters such as temperature, pH, and the volume of plant extract were also tested using their absorbance pattern at different wavelengths. The Surface Plasmon Resonance (SPR) changed with the changes in parameters. Changes in temperature from 20 °C to 60 °C have changed the highest absorbance from 0.972 to 3.893 with an SPR of 470 nm. At higher pH (11.1), the particles become highly unstable and have irregular shapes and sizes. The peak shifts to the right at a lower pH level (3.97), indicating a smaller but unstable compound. We have also investigated the effect of the volume of plant extracts on the reaction time. The sample with the highest amount of plant extract showed the most absorbance with a value of 0.963 at λmax, calculated to be 470 nm. The total formation of the AgNPs was observed visually with a color change from yellow to brownish-black. UV-visible spectroscopy was used to monitor the quantitative formation of AgNPs, showing a signature peak in absorbance between 400 and 500 nm. We have estimated the size of the nanoparticles as 47 nm by comparing the experimental data with the theoretical value using Mieplot. The biosynthesized AgNPs showed enhanced antibacterial activity against several multidrug-resistant bacteria, determined based on the minimal inhibitory concentration and zone of inhibition. Conclusion: The findings of this study indicate that an aqueous extract of C. citratus can synthesize AgNPs when silver nitrate is used as a precursor, and AgNPs act as antimicrobial property enhancers, which can be used to treat antibiotic-resistant bacteria. Hence, mass production and green synthesis of AgNPs from C. citratus will be able to increase the overall health of the general population. Moreover, it will enormously reduce the costs for drug development and provide employment options in the remotely located source areas. Finally, our findings will influence further studies in this field to better understand the properties and applications of AgNPs and ultimately contribute to improving planetary health by increasing immunity with high biocompatibility and less drug toxicity.

/pdf/biosynthesis-of-silver-nanoparticles-from-cymbopogon-23yvefon.pdf

Biosynthesis of Silver Nanoparticles from Cymbopogon citratus Leaf Extract and Evaluation of Their Antimicrobial Properties

Gavruta [L. Gavruta, Frames for operators, Appl. Comput. Harmon. Anal. 32 (2012) 139–144] introduced the notion of K-frame and atomic system for an operator K in Hilbert spaces. We extend these not...

Atomic systems for operators

Background: Numerous studies have been conducted to explicate the scope of emotional intelligence in educational success and coping with stress in different academic sectors, but very few have been conducted with dental students. This scoping review aimed to ascertain the role of emotional intelligence in academic performance and stress factors among dental students. Methods: All publications in the English language between 2001 and 2020 were retrieved employing MeSh keywords. Academic resources such as Pubmed, Pubmed Central, EMBASE, Web of Science, EBSCO-Host, Cochrane, PROSPERO, and ARU E-library were comprehensively searched for empirical research. One thousand, three hundred and fifty-nine papers were screened according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) standards for inclusion and exclusion criteria. These publications were then evaluated further by deleting duplicates, examining full-text articles, and conducting an abstract assessment. This review included a critical appraisal of 24 articles. Results: The narrative analysis method was applied to evaluate the data retrieved from publications regarding EI, academic performance, and stress factors. The review found that EI had a greater impact on the educational success of dental students throughout their clinical years. Moreover, EI may be a key tool in coping with stress and negative emotions. Higher EI scores were shown to be associated with better performance in organizational and leadership abilities, which are important for career advancement. Conclusion: The review suggested including EI training in the dental curriculum. Furthermore, EI should be used as a selection criterion for admission to dental education.

/pdf/exploring-the-association-between-emotional-intelligence-and-1e2dsj76.pdf

Exploring the Association between Emotional Intelligence and Academic Performance and Stress Factors among Dental Students: A Scoping Review

Oral health is essential in general health and well-being to maintain overall quality of life [...].

/pdf/oral-healthcare-during-pregnancy-its-importance-and-3s7q2asu.pdf

Shah Jahan

Papers

COVID-19 vaccination intent and willingness to pay in Bangladesh: a cross-sectional study

Biosynthesis of Silver Nanoparticles from Cymbopogon citratus Leaf Extract and Evaluation of Their Antimicrobial Properties

Atomic systems for operators

Exploring the Association between Emotional Intelligence and Academic Performance and Stress Factors among Dental Students: A Scoping Review

Oral Healthcare during Pregnancy: Its Importance and Challenges in Lower-Middle-Income Countries (LMICs)