Positivity of second order linear recurrent sequences

We give a decision method for the Positivity Problem for second order recurrent sequences: it is decidable whether or not a recurrent sequence defined by u_n=au_n-1+bu_n-2 has only nonnegative terms.     

A time-domain approach to estimating the plucking point of guitar tones obtained with an under-saddle pickup

A method for estimating the plucking point of guitar tones is proposed. The algorithm is based on investigating the time lag between two consecutive pulses arriving at the bridge of the guitar. The signal is detected with an under-saddle pickup attached to the bridge. The method determines the minimum of the autocorrelation function for one period of the signal. The time lag of the minimum can be converted into the distance from the bridge where the string was plucked. The results obtained with the method are good, the error remains smaller than one centimetre, except for a few outliers. The algorithm is easy to implement and can be used to analyse playing styles. The efficiency of the method gives the potential to also use it in real-time computer music applications.     

Electron impact induced fragmentation of dihydro-1,4-oxathiines. 1. 2,3-substituted 5,6-dihydro-1,4-oxathiines

In the electron impact induced fragmentation of 2,3-disubstituted 5,6-dihydro-1,4-oxathiines, the cleavage of the heterocyclic ring proceeds through the retro Diels-Alder type of reaction. The further fragmentation of the resulting radical cation gives rise to substituted carbonyl or thiocarbonyl cations. This fragmentation favours the formation of an ion which, in the electron-deficient carbon-oxygen or carbon-sulphur triple bond, is stabilized by an electron-releasing group. The ring fragmentation was observed to be dependent on the nature of the 3-substituent of the ring when a series of 3-substituted 5,6-dihydro-2-methyl-1,4-oxathiines was investigated.     

Quantum chemical modeling of chiral catalysis. Part 8. On the conformational freedom of the ketone of ketone-borane complexes of oxazaborolidines used as catalysts in the enantioselective reduction of ketones

Standard ab initio molecular orbital methods were employed to study conformational freedom of the ketone of ketone-borane complexes of chiral oxazaborolidines used as catalysts for the enantioselective reduction of ketones (CBS reduction). A formaldehyde-borane complex of 1,3,2-oxazaborolidine was used as a model system. A new conformation was found which was energetically more advantageous than the original one predicted by Corey et al. The new conformation was predicted to be destabilized by bulky substituents at the C-5 of the ring. A new class of potential oxazaborolidine catalysts for the enantioselective reduction of ketones was invented.     

A UV resonance Raman (UVRR) spectroscopic study on the extractable compounds in Scots pine (Pinus sylvestris) wood. Part II. Hydrophilic compounds

Hydrophilic extracts of Scots pine (Pinus sylvestris) heartwood and sapwood and a solid Scots pine knotwood sample were studied by UV resonance Raman spectroscopy (UVRRS). In addition, UVRR spectra of two hydrophilic model compounds (pinosylvin and chrysin) were analysed. UV Raman spectra were collected using 244 and 257 nm excitation wavelengths. The chemical composition of the acetone:water (95:5 v/v) extracts were also determined by gas chromatography. The aromatic and oleophilic structures of pinosylvin and chrysin showed three intense resonance enhanced bands in the spectral region of 1649-1548 cm(-1). Pinosylvin showed also a relatively intense band in the aromatic substitution region at 996 cm(-1). The spectra of the heartwood acetone:water extract showed many bands typical of pinosylvin. In addition, the extract included bands distinctive for resin and fatty acids. The sapwood acetone:water extract showed bands due to oleophilic structures at 1655-1650 cm(-1). The extract probably also contained oligomeric lignans because the UVRR spectra were in parts similar to that of guaiacyl lignin. The characteristic band of pinosylvin (996 cm(-1)) was detected in the UVRR spectrum of the resin rich knotwood. In addition, several other bands typical for wood resin were observed, which indicated that the wood resin in the knotwood was resonance enhanced even more than lignin.     

Photoinduced electron transfer in Langmuir-Blodgett monolayers of porphyrin-fullerene dyads

A series of electron donor-acceptor (DA) dyads, composed of a porphyrin donor and a fullerene acceptor covalently linked with two molecular chains, were used to fabricate solid molecular films with the Langmuir-Blodgett (LB) technique. By means of the LB technique, the DA molecules can be oriented perpendicular to the plane of the substrate. In DHD6ee and its zinc derivative hydrophilic groups are attached to the phenyl moieties in the porphyrin end of the molecule; while in the other three dyads, TBD6a, TBD6hp, and TBD4hp, the hydrophilic groups are in the fullerene end of the molecule. This makes it possible to alternate the orientation of the molecules in two opposite directions with respect to the air-water interface and to fabricate molecular assemblies in which the direction of the primary photoinduced vectorial electron transfer can be controlled both by the deposition direction of the LB monolayer and by the selection of the used DA molecule. This was proved by the time-resolved Maxwell displacement charge measurements. The spectroscopic properties of the DA films were studied with the steady-state absorption and fluorescence methods. In addition, the time correlated single photon counting technique was used to determine the fluorescence properties of the dyad films.     

Quantum mechanical investigation of effects in formation of carbonyl and thiocarbonyl cations. Part I. Fragmentation reactions of 1,2-hemithiodione radical cations

In order to study decomposition reactions of ionic oxygen and sulphur-containing compounds, such as hemithiodione radical cations, a quantum chemical investigation of the formation of formyl, thioformyl, acyl and thioacyl cations and radicals was performed. Calculations were carried out mainly at the 6–31G^* level involving complete geometry optimizations. In the ionization of aldehydes and thioaldehydes, no important energy differences were found between the oxygen and sulphur analogues studied. A stepwise generation of formyl and thioformyl cations from formaldehyde and thioformaldehyde, by hydrogen atom abstraction followed by expulsion of unpaired electrons from the resulting radicals, showed the radicalization of formaldehyde to be only 12.6 kJ mol^?1 more favoured than that of thioformaldehyde. The electron expulsion from formyl radical was 23.8 kJ mol^?1 more favoured than that from thioformyl radical. Substitution of hydrogens of formyl and thioformyl groups by methyls lowered the total formation energies of carbonyl and thiocarbonyl cations 119.2 and 96.2 kJ mol^?1. The formation energy difference between acyl and thioacyl cations was also very small.     

Environmental protection of inkjet-printed Ag conductors

Electrically conductive silver nanoparticle ink patterns were fabricated using the inkjet printing method. Two different polymer films were used as the substrate materials. The patterns were exposed to humidity and salt fog and the electrical performance (sheet resistance and RF performance) as well as mechanical endurance (adhesion) were measured before and after the environmental tests. The electrical properties of the printed structures remained good in all the measurable samples. The adhesion between the ink and a substrate material appeared to be a greater challenge in harsh environments. Protection capabilities of one dip coated and one hot laminated barrier materials were evaluated during the environmental tests. The results showed that there is a need for environmental protection in printed electronics. Especially the laminated barrier films can offer a potential solution for shielding printed electronics in harsh environments as they can provide good mechanical protection, and can easily be integrated in roll-to-roll process.     

A UV resonance Raman (UVRR) spectroscopic study on the extractable compounds of Scots pine (Pinus sylvestris) wood. Part I: lipophilic compounds

The wood resin in Scots pine (Pinus sylvestris) stemwood and branch wood were studied using UV resonance Raman (UVRR) spectroscopy. UVRR spectra of the sapwood and heartwood hexane extracts, solid wood samples and model compounds (six resin acids, three fatty acids, a fatty acid ester, sitosterol and sitosterol acetate) were collected using excitation wavelengths of 229, 244 and 257 nm. In addition, visible Raman spectra of the fatty and resin acids were recorded. Resin compositions of heartwood and sapwood hexane extracts were determined using gas chromatography. Raman signals of both conjugated and isolated double bonds of all the model compounds were resonance enhanced by UV excitation. The oleophilic structures showed strong bands in the region of 1660-1630 cm(-1). Distinct structures were enhanced depending on the excitation wavelength. The UVRR spectra of the hexane extracts showed characteristic bands for resin and fatty acids. It was possible to identify certain resin acids from the spectra. UV Raman spectra collected from the solid wood samples containing wood resin showed a band at approximately 1650 cm(-1) due to unsaturated resin components. The Raman signals from extractives in the resin rich branch wood sample gave even more strongly enhanced signals than the aromatic lignin.