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

Palladium(II) Complexes with Anionic N‑Heterocyclic Carbene–Borate Ligands as Catalysts for the Amination of Aryl Halides

A series of (allyl)­palladium­(II) complexes of anionic N-heterocyclic carbenes that contain a weakly coordinating borate moiety (WCA-NHC) were prepared by deprotonation of the carbene IPr with <i>n</i>-butyllithium in the 4-position, which was followed by addition of B­(C₆F₅)₃ and reaction of the resulting lithium carbene–borate with [(η³-allyl)­Pd­(μ-Cl)]₂ (allyl = 2-propenyl, 2-butenyl, 2-methyl-2-propenyl, 1-phenyl-2-propenyl). In polar solvents such as tetrahydrofuran, chloropalladate complexes of the type [Li­(THF)₃]­[(WCA-NHC)­PdCl­(η³-allyl)] were formed, whereas the reactions in toluene afforded neutral complexes of the type [(WCA-NHC)­Pd­(η³-allyl)], which exhibit an intramolecular interaction with the N-aryl groups of the carbene ligands. The allyl-palladium complexes were employed as catalysts for the Buchwald–Hartwig amination of various aryl halides with morpholine

Additional file 2: Table S1. of Association between Taenia solium infection and HIV/AIDS in northern Tanzania: a matched cross sectional-study

Clinical data, data on hygiene and eating habits, medication, family history and diagnostic data of TSOL+ individuals (n = 10) of the initially recruited study population. (DOC 74 kb

Additional file 1: of Association between Taenia solium infection and HIV/AIDS in northern Tanzania: a matched cross sectional-study

Multilingual abstracts in the six official working languages of the United Nations. (PDF 837 kb

Additional file 1: Table S1. of Epidemiology of taeniosis/cysticercosis in Europe, a systematic review: Western Europe

PRISMA 2009 Checklist. (DOC 64 kb