22 research outputs found
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
Aggregated human neurocysticercosis cases as detected by Brain CT scan in eastern and southern Africa (2000–2022).
Aggregated human neurocysticercosis cases as detected by Brain CT scan in eastern and southern Africa (2000–2022).</p
Taeniosis cases reported in Eastern and Southern Africa between 2000–2020.
Taeniosis cases reported in Eastern and Southern Africa between 2000–2020.</p
The distribution of human neurocysticercosis based on imaging data in reviewed studies in Eastern and Southern Africa.
*Proportion based on MRI. (The maps were obtained from an openly available source, Mapchart.net for free. Link: https://www.mapchart.net/terms.html#licensing-maps. Permission has been obtained from the owner).</p
Aggregated human cysticercosis cases identified in Eastern and Southern Africa (2000–2022).
Aggregated human cysticercosis cases identified in Eastern and Southern Africa (2000–2022).</p
Prevalence of human cysticercosis in Eastern and Southern Africa based on serology data in reviewed studies with high variation observed in Madagascar, Rwanda, Tanzania and Zambia.
Prevalence of human cysticercosis in Eastern and Southern Africa based on serology data in reviewed studies with high variation observed in Madagascar, Rwanda, Tanzania and Zambia.</p
Human neurocysticercosis with epilepsy as detected by Brain CT scan in eastern and southern Africa (2000–2022).
Human neurocysticercosis with epilepsy as detected by Brain CT scan in eastern and southern Africa (2000–2022).</p
Prevalence of taeniosis based on copro-Ag ELISA in reviewed studies in Eastern and Southern Africa.
Prevalence of taeniosis based on copro-Ag ELISA in reviewed studies in Eastern and Southern Africa.</p
Aggregated human cysticercosis cases reported in community-based cross-sectional studies in Eastern and Southern Africa between the years 2000 and 2022.
Aggregated human cysticercosis cases reported in community-based cross-sectional studies in Eastern and Southern Africa between the years 2000 and 2022.</p
Diagnostic methods used for aggregated human cysticercosis cases in the included studies for Eastern and Southern Africa.
Diagnostic methods used for aggregated human cysticercosis cases in the included studies for Eastern and Southern Africa.</p