A lower bound for systems with double characteristics

We give necessary and sufficient conditions for a lower bound with a gain of 3/2 derivatives (the so-called Weak-Hörmander inequality) for a class of systems with double characteristics.     

Intriguing sets in partial quadrangles

The point‐line geometry known as a partial quadrangle (introduced by Cameron in 1975) has the property that for every point/line non‐incident pair (P, ?), there is at most one line through P concurrent with ?. So in particular, the well‐studied objects known as generalized quadrangles are each partial quadrangles. An intriguing set of a generalized quadrangle is a set of points which induces an equitable partition of size two of the underlying strongly regular graph. We extend the theory of intriguing sets of generalized quadrangles by Bamberg, Law and Penttila to partial quadrangles, which gives insight into the structure of hemisystems and other intriguing sets of generalized quadrangles. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:217‐245, 2011     

On the transfer matrix of a MIMO system

We develop a deterministic ab initio model for the input–output relationship of a multiple‐input multiple‐output (MIMO) wireless channel, starting from the Maxwell equations combined with Ohm's law. The main technical tools are scattering and geometric perturbation theories. The derived relationship can lead us to a deep understanding of how the propagation conditions and the coupling effects between the elements of multiple‐element arrays affect the properties of an MIMO channel, e.g. its capacity and its number of degrees of freedom. Copyright © 2011 John Wiley & Sons, Ltd.     

Rembrandt's Old Woman Praying, 1629/30: A look below the surface using X-ray fluorescence mapping

Rembrandt's painting Old Woman Praying, 1629/30, is the most valuable and exceptional work of art of the Residenzgalerie Salzburg (RGS). It is painted on a gilded copper plate with dimensions of only approximately 15 × 12 cm. The painting probably belongs to a series of three small-scale tronies, all executed on gilded copper plates. This particular picture preparation, which represents a special feature in Rembrandt's work, is quite unusual in the history of art. Previous investigations on the comparable paintings The Laughing Man, 1629/30, in the Mauritshuis, The Hague and the Self Portrait, 1630, in the National Museum, Stockholm showed that the gilding of the copper plate was applied over a lead white ground. To characterize the painting in the RGS, X-ray fluorescence (XRF) mapping was performed in a collaboration between the Research Office Residenzgalerie, Land Salzburg, the XGLab S.R.L, Milan, and the Conservation Science Department of the Kunsthistorische Museum Vienna (KHM). The results indicate a different structure for this painting than that used for The Laughing Man and the Self Portrait. The gilding was applied directly onto the copper plate, but with three areas with the gilding missing. It seems likely that in these sections, the gold was purposely removed to provide a different darker effect. XRF mapping yielded valuable insights into the structure of the painting and its technique as well as the principal pigments used for its composition.     

Synthesis and photoreactions of polyesters containing triazene and cinnamylidene malonyl units

The synthesis and photoreactions of polyesters containing the photolabile triazene group (Ph NN NR₂) as well as photocrosslinkable units based on substituted cinnamylidene malonyl moieties are reported. The polyesters were obtained by reacting a triazene containing difunctional alcohol with different substituted cinnamylidene malonic acid dichlorides. Irradiation at λ > 395 nm enables selective photocrosslinking of the cinnamylidene malonyl ester units via [2+2]π‐cycloaddition without affecting the triazene units. The photocrosslinking reaction of the triazene containing polyesters as well as triazene‐free reference polyesters were investigated by UV and IR spectroscopy. After selective photocrosslinking the irradiated polymers became insoluble and no longer exhibited a T_g below decomposition temperature. The crosslinked triazene containing polyesters show strong absorption at λ = 308 nm and are therefore interesting candidates for applications using XeCl excimer laser ablation. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1903–1910, 2000     

EPR study on ligand-exchange reaction between bis(diethyldiselenocarbamato)copper(II) and some bis(acetylacetonato)copper(II) complexes

The paper is a study on the formation and properties of mixed-chelate copper(II) complexes, in which one ligand is strongly covalently bound diselenocarbamate (dsc), and the other belongs to a series of differently substituted acetylacetonates (acac), all forming weak covalent bonds. Thenoyltrifluoro- and trifluoro- substituted acetylacetonates only partly form mixed-chelate complexes, stable in toluene, benzene or dichloromethane, but gradually decomposing in chloroform or carbontetrachloride by analogy with Cu(Et(2)dsc)(2) behavior in these solvents. Hexafluoro-acetylacetonato copper(II) completely turns into a mixed-chelate Cu(dsc)(hfacac), which remains unchanged for more than 8 months of monitoring in all solvents used. The stability of Cu(dsc)(hfacac) is attributed to the reduced remaining negative charge on selenium atom embarrassing the formation of weak D-A complex with haloalkanes. The obtained EPR parameters suggest significant lowering of the contribution of the 4s AO of copper(II) in the mixed-chelate complexes. It is shown that Cu(acac)(2) does not react with Cu(Et(2)dsc)(2).     

Living polymerization and block copolymerization of alpha-olefins by an amine bis(phenolate) titanium catalyst

An amine bis(phenolate) dibenzyl titanium complex having a methoxy donor on a side arm leads, upon activation with tris(pentafluorophenyl)borane, to unique living properties in alpha-olefin polymerization: exceptionally high molecular weight poly(1-hexene) is obtained in a living fashion at room temperature, living polymerization of 1-hexene is obtained above room temperature, and block copolymerization of 1-hexene and 1-octene at room temperature is described as well.     

Hydrogen-bonded networks in ethanol proton wires: IR spectra of (EtOH)qH+-Ln clusters (L = Ar/N2, q < or = 4, n < or = 5)

Isolated and microsolvated protonated ethanol clusters, (EtOH)qH+-Ln with L = Ar and N2, are characterized by infrared photodissociation (IRPD) spectroscopy in the 3 microm range and quantum chemical calculations. For comparison, also the spectrum of the protonated methanol dimer, (MeOH)2H+, is presented. The IRPD spectra carry the signature of H-bonded (EtOH)qH+ chain structures, in which the excess proton is either strongly localized on one or (nearly) equally shared between two EtOH molecules, corresponding to Eigen-type ion cores (EtOH2+ for q = 1, 3) or Zundel-type ion cores (EtOH-H+-HOEt for q = 2, 4), respectively. In contrast to neutral (EtOH)q clusters, no cyclic (EtOH)qH+ isomers are detected in the size range investigated (q < or = 4), indicative of the substantial impact of the excess proton on the properties of the H-bonded ethanol network. The acidity of the two terminal OH groups in the (EtOH)qH+ chains decreases with the length of the chain (q). Comparison between (ROH)qH+ with R = CH3 and C2H5 shows that the acidity of the terminal O-H groups increases with the length of the aliphatic rest (R). The most stable (EtOH)qH+-Ln clusters with n < or = 2 feature intermolecular H-bonds between the inert ligands and the two available terminal OH groups of the (EtOH)qH+ chain. Asymmetric microsolvation of (EtOH)qH+ with q = 2 and 4 promotes a switch from Zundel-type to Eigen-type cores, demonstrating that the fundamental structural motif of the (EtOH)qH+ proton wire sensitively depends on the environment. The strength of the H-bonds between L and (EtOH)qH+ is shown to provide a rather sensitive probe of the acidity of the terminal OH groups.     

Phenyliodine(III) bis(trifluoroacetate) (PIFA)-promoted synthesis of Bodipy dimers displaying unusual redox properties

Phenyliodine(III) bis(trifluoroacetate) (PIFA) in conjunction with a Lewis acid promotes C-C coupling of Bodipy monomers leading to mixtures of various oligomers. When a single position is blocked with an iodo or phenyl group, formation of the dimer is favored. These dimers display two successive oxidation and two reduction waves separated on average by 260 and 130 mV, respectively, corresponding to each Bodipy subunit.