Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group H ( G,E[p] ) does not vanish, and investigate the analogous question for E[p] when i > 1. We include an application to the verification of certain cases of the Birch a...

At 25.0 °C the specific rates of solvolysis for allyl and vinyl chloroformates have been determined in a wide mix of pure and aqueous organic mixtures. In all the solvents studied, vinyl chloroformate was found to react significantly faster than allyl chloroformate. Multiple correlation analyses of these rates are completed using the extended (two-term) Grunwald-Winstein equation with incorpora...

The solvolyses of 4-fluorophenyl chlorothionoformate (1) are studied in fifteen binary aqueous organic mixtures of widely varying nucleophilicity and ionizing power values. The specific rates of solvolyses of 1 are plotted against the specific rates of solvolysis observed for phenyl chloroformate (2) and deviations from the line-of-best-fit are observed in some of the highly ionizing aqueous fl...

Becker, P.T., Grunwald, P.C., & Brazy, J.E. (1999). Motor organization in very low birth weight infants during caregiving: Effects of a developmental intervention. Journal of Developmental and Behavioral Pediatrics, 20(5), 344 – 352. A study of very low birth weight (VLBW) infants demonstrated that using an individualized, developmentally supportive approach to handling the newborn rather than ...

The "parent" tertiary alkyl chloroformate, tert-butyl chloroformate, is unstable, but the tert-butyl chlorothioformate (1) is of increased stability and a kinetic investigation of the solvolyses is presented. Analyses in terms of the simple and extended Grunwald-Winstein equations are carried out. The original one-term equation satisfactorily correlates the data with a sensitivity towards chang...

Given a field K with finitely many valuations; does there exist an extension of K which at these valuations has a prescribed local behavior? The Grunwald-Wang theorem answers this question in the case of abelian field extensions. Originally developed for algebraic number fields in the context of class field theory, it has turned out that it is valid quite generally, for arbitrary multi-valued f...

• Connections in Rn . We have by now defined a number of different notions of differentiation: the differential of maps between manifolds, the exterior derivative of differential forms, and the Lie derivative. To begin to see the need for a new notion of differentiation (which will turn out to be the most fundamental and will apply to general tensor fields) consider first the problem of definin...

In Europe G6PD deficiency is encountered most frequently in Sardinia and Greece but may also be found in other Mediterranean countries (Sansone, Piga, and Segni, 1958; Szeinberg, Asher, and Sheba, 1958), including Yugoslavia (Fraser, Grunwald, and Stamatoyannopoulos, 1966). The occurrence of haemolytic anaemia after ingestion of fava beans in Yugoslavia was first reported as a clinical finding ...

We survey recent results on the structure of the range of the derivative of a smooth mapping f between two Banach spaces X and Y . We recall some necessary conditions and some sufficient conditions on a subsetA of (X ,Y) for the existence of a Fréchet differentiable mapping f from X into Y so that f ′(X)= A. Whenever f is only assumed Gâteaux differentiable, new phenomena appear: for instance, ...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...