Sobolev mappings with integrable dilatations

We show that each quasi-light mapping f in the Sobolev space W ¹ⁿ (, R ⁿ ) satisfying ¦Df(x)¦ ⁿ K(x, f)J(x, f) for almost every x and for some KL ^r (), r>n-1, is open and discrete. The assumption that f be quasilight can be dropped if, in addition, it is required that f W ^1p (, R ⁿ ) for some p > = n + 1/ (n-2). More generally, we consider mappings in the John Ball classes Axxx _p,q (), and give conditions that guarantee their discreteness and openness.     

Charging and discharging at the nanoscale: Fermi level equilibration of metallic nanoparticles

The redox properties of metallic nanoparticles are discussed, in particular the relationships between excess charge, size and the Fermi level of the electrons. The redox potentials are derived using simple electrostatic models to provide a straightforward understanding of the basic phenomena. The different techniques used to measure the variation of Fermi level are presented. Finally, redox aspects of processes such as toxicity, electrochromicity and surface plasmon spectroscopy are discussed.     

The quaternary complex Hadamard matrices of orders 10, 12, and 14

A complete classification of quaternary complex Hadamard matrices of orders 10, 12 and 14 is given, and a new parametrization scheme for obtaining new examples of affine parametric families of complex Hadamard matrices is provided. On the one hand, it is proven that all 10×10 and 12×12 quaternary complex Hadamard matrices belong to some parametric family, but on the other hand, it is shown by exhibiting an isolated 14×14 matrix that there cannot be a general method for introducing parameters into these types of matrices.     

The RTAM electronic bibliography,version 17.0, on relativistic theory of atoms and molecules

The RTAM bibliography is freely available at rtam.csc.fi and the Version 17.0 of August 22, 2013 now contains 16,566 items from the year 1916–2013. “Production works” were systematically covered until 1999. Since the year 2000, mainly methodological papers were included. The methods and principles behind RTAM are described. © 2013 Wiley Periodicals, Inc.     

Mappings of finite distortion: Formation of cusps III

We give sharp integrability conditions on the distortion of a planar homeomorphism that maps a standard cusp onto the unit disk.     

Mappings of Finite Distortion: Generalized Hausdorff Dimension Distortion

We study how planar Sobolev homeomorphisms distort sets of Hausdorff dimension strictly less than two. We measure the image size by means of a generalized Hausdorff measure. As an application, we obtain a sharp generalized dimension distortion estimate for mappings of exponentially integrable distortion.     

Quantification of triacylglycerol regioisomers by ultra‐high‐performance liquid chromatography and ammonia negative ion atmospheric pressure chemical ionization tandem mass spectrometry

The regioisomer composition of triacylglycerols (TAGs) in various vegetable oils was determined with a new liquid chromatography/tandem mass spectrometry (LC/MS/MS method). A direct inlet ammonia negative ion chemical ionization (NICI) MS/MS method was improved by adapting it to LC negative ion (NI) atmospheric pressure chemical ionization (APCI) MS/MS system using ammonia as nebulizer gas. The method is based on the preferential formation of [M–H–RCOOH–100]^? ions during collision‐induced dissociation by loss of sn‐1/3 fatty acids from [M–H]^? ions. Calibration curves were created from nine reference TAGs: Ala/L/L, Gla/L/L, L/L/O, L/O/O, P/O/O, P/P/O, Po/Po/V, Po/Po/O, and C/O/O. The calibration curves were used to quantify the regioisomer compositions of selected TAGs in rapeseed oil, sunflower seed oil, palm oil, black currant seed oil, and sea buckthorn pulp oil. The method discriminates the different regioisomers and the results obtained by this method were in good agreement with previous results. This proves that this new method can be used for the determination of regiospecific distribution of fatty acids in TAGs. Copyright © 2009 John Wiley & Sons, Ltd.     

Mappings of Finite Distortion: Decay of the Jacobian

We establish the sharp degree of integrability for the reciprocal of the Jacobian determinant of an open and discrete mapping with finite, p-integrable distortion.