A novel approach to fractional calculus: utilizing fractional integrals and derivatives of the Dirac delta function

While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants of integration in their results. An elimination of constants of integration opens the door to an operator that reconciles all known fractional derivatives and shows surprising results in areas unobserved before, including the appearance of the Riemann Zeta Function and fractional Laplace and Fourier Transforms. A new class of functions, known as Zero Functions and closely related to the Dirac Delta Function, are necessary for one to perform elementary operations of functions without using constants. The operator also allows for a generalization of the Volterra integral equation, and provides a method of solving for Riemann's "complimentary" function introduced during his research on fractional derivatives

Distribution of answers of medical doctors to the knowledge questions on toxoplasmosis.

<p>The seventeen answers that were considered correct are highlighted with bold font.</p

Proportion of medical doctors scoring a high knowledge score in the questionnaire surveying knowledge on toxoplasmosis in Nigeria, by their background information.

<p>Proportion of medical doctors scoring a high knowledge score in the questionnaire surveying knowledge on toxoplasmosis in Nigeria, by their background information.</p

Multivariable logistic regression model for predicting having seen a case of clinical toxoplasmosis among medical doctors in Nigeria.

<p>Multivariable logistic regression model for predicting having seen a case of clinical toxoplasmosis among medical doctors in Nigeria.</p

The final multivariable logistic regression model predicting <i>Toxoplasma gondii</i> seropositivity in 1121 domestic cats of eight breeds.

<p>The final multivariable logistic regression model predicting <i>Toxoplasma gondii</i> seropositivity in 1121 domestic cats of eight breeds.</p

An exemplar of how an MA research project unlocked leadership and management potential in a secondary/ HEI partnership

This paper provides a summary of a completed research project from an MA Education: Leadership and Management thesis on a whole school assessment strategy. It shows how Leadership and Management potential has been successfully unlocked through the research process, and at various levels across the secondary school. This was a partner school that had a two year cohort undertaking an Education Masters programme with a specific Leadership and Management angle. The individuals co-writing the paper and presenting are the (now graduated) student, who is a Curriculum Lead, and has subsequently gone on to be selected as a Specialist Leader in Education (an SLE) and her thesis supervisor, who raises issues found in her own doctoral research process. The paper traces the recent journey of systems leadership, and looks at how SLE roles are being used as an alternative path to traditional forms of school leadership. The paper concludes by suggesting that more research is needed to record the impact of SLE roles. Introduction This paper provides a summary of a completed research project from an MA Education: Leadership and Management thesis on a whole school assessment strategy. It shows how Leadership and Management potential has been successfully unlocked through the research process, and at various levels across the secondary school, and into a wider area of the city beyond. The former student presenting (who is an Assistant Head from this September), used her research process across her school, then in her SLE role brought the process to various School Improvement Inspectors and processes. This has led to changes in the City’s schools, and a wider awareness of the impact that assessment strategies can have across the City’s borders into the County beyond. This small scale individual research is put into a wider context here using some of the themes from the research inside the MA supervisor’s own doctoral research process Role of postgraduate study The role of postgraduate study in education has been long recognised with the TDA funding Masters programmes for teachers in the last decade, and more recently Teach First having an integrated Masters programme. O’Grady and Cottle (2015) write about the journey of postgraduate study in Education and conclude that ‘the outcome can be rewarding and transformational for students as their confidence rises, their academic relationships are shaped and their practice emerges in creative and innovative ways’ (O’Grady and Cottle, 2015: 10). This paper highlights a particular case of where this process has taken place

<i>Toxoplasma gondii</i> ELISA results including those that tested positive (POS) and those that tested positive or yielded a grey zone result twice (POS+GREY) in the general population, children, veterinarians, animal caretakers, and hunters in Estonia.

<p><i>Toxoplasma gondii</i> ELISA results including those that tested positive (POS) and those that tested positive or yielded a grey zone result twice (POS+GREY) in the general population, children, veterinarians, animal caretakers, and hunters in Estonia.</p

The disease burden of congenital toxoplasmosis in Denmark, 2014

<div><p>Background</p><p>Congenital toxoplasmosis (CT) causes a substantial disease burden worldwide. The aim of this study was to estimate the disease burden of CT in Denmark, a developed country with free public healthcare and nationwide data available.</p><p>Methods</p><p>Using data primarily from two public health surveillance programmes conducted between 1992 and 2007, we estimated the incidence, occurrence of sequelae, mortality and the burden of disease in terms of disability-adjusted life years (DALYs) of CT in Denmark in 2014.</p><p>Findings</p><p>We estimated that 14 children were born with CT in 2014, of which six will have developed sequelae by the age of 12. CT resulted in a total disease burden of 123 DALYs (95% uncertainty interval [UI], 100–148), of which 78 (95% UI, 64–94) were due to foetal loss and 2 (95% UI, 1–3) were due to neonatal death; the remaining burden was due to moderate to severe life-long sequelae. A comparison of the estimated incidence of CT with the number of reported CT cases in 2008–2014 indicated that for each reported CT case, at least five other CT cases could be expected to have occurred and gone unreported.</p><p>Interpretation</p><p>Early onset, severity, and life-long duration of sequelae have a major effect on the disease burden of CT. Our data suggest that CT is under-diagnosed or under-reported in Denmark. The estimated disease burden and public health impact in Denmark is lower than in other European countries, highlighting the need for country-specific studies.</p></div

Parameters used to estimate the incidence of congenital toxoplasmosis (CT) and selected associated health outcomes.

<p>Parameters used to estimate the incidence of congenital toxoplasmosis (CT) and selected associated health outcomes.</p

Number of estimated (1) and registered (2) cases of congenital toxoplasmosis (CT) in Denmark in the period of 2008–2014.

<p>Number of estimated (1) and registered (2) cases of congenital toxoplasmosis (CT) in Denmark in the period of 2008–2014.</p