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

Risk factors for obstetric brachial plexus palsy among neonates delivered by vacuum extraction.

OBJECTIVE: The risk of obstetric brachial plexus palsy (OBPP) is increased in infants delivered instrumentally. The aim of this study was to identify risk factors for OBPP and to evaluate the association between possible risk factors linked to the duration of the vacuum extraction procedure and the subsequent risk. METHODS: A population-based retrospective design was adopted. Using a national registry of operative vaginal deliveries linked to the Medical Birth Registry in Sweden, we evaluated by univariate and multiple logistic regression analyses the risk factors for OBPP in 13,716 women delivered by vacuum extraction. The variables assessed in the multiple logistic regression analysis were shoulder dystocia, fetal birth weight of 3,999 g or greater, fundal pressure, number of tractions, vacuum application time, parity, vacuum silicone cup, epidural anesthesia, and fetal head at the level of the ischial spines at vacuum application time. RESULTS: Obstetric brachial plexus palsy was recorded in 153 (1.1%) infants. The following variables increased significantly the risk of OBPP in the newborn: shoulder dystocia (odds ratio 16.0; 95% confidence interval 8.9-28.7), fetal birth weight of 3,999 g or greater (7.1; 4.8-10.5), and administration of fundal pressure (1.6; 1.1-2.3). The probability of the risk of OBPP in vacuum-assisted deliveries increased in relation to vacuum extraction time (minutes). CONCLUSION: Shoulder dystocia in the setting of vacuum extraction is a prominent risk factor for OBPP in the newborn. The risk of OBPP increases with the time required for vacuum extraction. LEVEL OF EVIDENCE: II-3

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

PRISMA 2009 Checklist. (DOC 64 kb