Nonrelativistic Geodesic Motion

We show that any second-order dynamic equationon a configuration space X R ofnonrelativistic time-dependent mechanics can be seen asa geodesic equation with respect to some (nonlinear)connection on the tangent bundle TX X of relativisticvelocities. We compare relativistic and nonrelativisticgeodesic equations, and study the Jacobi vector fieldsalong nonrelativistic geodesics.     

On the regularization of projection methods for solving III-posed problems

Summary In this paper we consider a class of regularization methods for a discretized version of an operator equation (which includes the case that the problem is ill-posed) with approximately given right-hand side. We propose an a priori- as well as an a posteriori parameter choice method which is similar to the discrepancy principle of Ivanov-Morozov. From results on fractional powers of selfadjoint operators we obtain convergence rates, which are (in many cases) the same for both parameter choices.     

Systematic investigations of anthocyanin–metal interactions by Raman spectroscopy

The FT‐Raman spectra of the chloride salts of pelargonidin‐3‐glucoside, cyanidin‐3‐glucoside and delphinidin‐3‐glucoside, their structures at pH 5.0 and their interaction with aluminium and ferric ions are presented for the first time and discussed with regard to their spectroscopic response. Two marker bands at approximately 1510 and 1330/1350 cm⁻¹ and one band at approximately 1330/1350 cm⁻¹ were identified being characteristic for the formation of ferric and aluminium chelates, respectively, of cyanidin‐3‐glucoside and delphinidin‐3‐glucoside. In contrast, pelargonidin‐3‐glucoside, exhibiting one single hydroxyl group in the B‐ring, did not form metal chelates, which could be clearly demonstrated by missing marker bands. The formation of anthocyanin–metal chelates was also verified in model systems containing commercial sugar beet pectin and a pectic polysaccharide fraction isolated thereof, respectively. In addition, the absence of anthocyanin–metal chelates in systems prepared with citrate buffer was confirmed, and the effects of low and high methoxylated citrus pectins on chelate formation were studied. Copyright © 2012 John Wiley & Sons, Ltd.     

Residual {\bar\partial}-cohomology and the complex Radon transform on subvarieties of {\mathbb C P^n}

We show that the complex Radon transform realizes an isomorphism between the quotient-space of residual ${\bar\partial}$ -cohomologies of a locally complete intersection algebraic subvariety in a linearly concave domain of ${{{\mathbb C}}P^n}$ and the space of holomorphic solutions of the associated homogeneous system of differential equations with constant coefficients in the dual domain in ${({{\mathbb C}}P^n)^*}$ .     

Reactions of polystyryllithiums and model lithium carbanions with 9,10‐bis(halomethyl)anthracenes

The direct and nearly quantitative incorporation of 9,10‐anthracenylidene (AN) chromophores into polystyrene occurred via the reaction of polystyryllithium (PSLi) with 9,10‐bis(chloromethyl)anthracene (BCMA) at ?78 °C in tetrahydrofuran (THF)/ hexane containing between 30 and 40 vol % hexane. Although the reaction of PSLi and BCMA or 9,10‐bis(bromomethyl)anthracene (BBMA) in THF at ?78 °C gave nearly quantitative coupling, typically only 30–50% AN incorporation was observed, as determined by ultraviolet–visible spectrometry. Model coupling reactions of 3,3‐dimethyl‐1,1‐diphenyl‐1‐lithiobutane, (1,1,2,2‐tetramethyl)propylcyclopentadienyllithium, 9‐methylfluorenyllithium, and triphenylmethyllithium with BCMA or BBMA at ?78 °C in THF in nearly all cases gave several AN‐containing coupling products. This was consistent with lithium–halogen exchange leading to the linking of multiple AN groups. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3121–3129, 2001     

On the Explicit Reconstruction of a Riemann surface from its Dirichlet–Neumann operator

This article gives a complex analysis lighting on the problem which consists in restoring a bordered connected riemaniann surface from its boundary and its Dirichlet–Neumann operator. The three aspects of this problem, unicity, reconstruction and characterization are approached. Received: May 2005 Revision: October 2005 Accepted: October 2005