57Fe Mössbauer Spectroscopy Study of LaFe1−x Co x O3 (x=0 and 0.5) Formed by Mechanical Milling

Hyperfine Interactions - Perovskite-related phases of the type LaFe1?x Co x O3 (x=0 and 0.5) have been synthesised by milling techniques. The materials are of smaller particle size and more...     

Differentiation of chiral phosphorus enantiomers by P and H NMR spectroscopy using amino acid derivatives as chemical solvating agents

The ability of commercially available amino acid derivatives, especially Fmoc-Trp(Boc)-OH, to differentiate enantiomers of chiral phosphonates, phosphinates, phosphates, phosphine oxides, and phosphonamidates is demonstrated with (31)P, (13)C, and (1)H NMR spectroscopy. The chiral differentiation provided a rapid and convenient method for measuring the enantiomeric purity of these phosphorus compounds.     

Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity

We consider the nonlinear Schrödinger equation: (1) $${{i\partial u} \mathord{\left/ {\vphantom {{i\partial u} {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} = - \Delta u - \left| u \right|^{{4 \mathord{\left/ {\vphantom {4 N}} \right. \kern-\nulldelimiterspace} N}} uandu\left( {0,.} \right) = \varphi \left( . \right),$$ whereu:[0,T)×? ^N →?. For any given pointsx ₁,x ₂,...,x _k in ? ^N , we construct a solution of Eq. (1),u(t), which blows up in a finite timeT at exactlyx ₁,x ₂,...,x _k . In addition, we describe the precise behavior of the solutionu(t) whent→T, at the blow-up points {x ₁,x ₂,...,x _k } and in ? ^N ?{x ₁,x ₂,...,x _k }.     

Linear equations depending differentiably on a parameter

We investigate operator functionsT(x) inBanach spaces, depending differentiably (meaning of classC orC ) on a parameterx and enjoying a certain regularity property. Iff is a given differentiable function such that the equationT(x)e=f(x) is solvable for eachx then the existence of a functione is proved which belongs to the same differentiability class asf andT, solving the equationT(x)e(x)f(x) identically inx. As an application we extend a result ofJ. Leiterer [9] and give a comprehensive answer to a question posed byJ.L. Taylor in [15] concerning the exactness of certain cochain complexes.