Geodesic flow on the diffeomorphism group of the circle

We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds.     

Kinetics of enzymatic hydrolysis of sodium carboxymethylcellulose with different degrees of polymerization by cellulase

The reaction cellulase (EC 3.2.1.4)—sodium carboxymethylcellulose (Na-CMC) with different degrees of polymerization (n=140, 640 and 900) was investigated by the use of a modifiedMichaelis-Menten equation, valid for enzymatic hydrolysis of linear homopolymers. TheMichaelis-Menten constant [Km (M)=6.31·10^–2mol/dm³] and the reaction rate constant (k ₊₂=4.07·10^–6s^–1), which correspond to the enzymatic hydrolysis of a single bond in the homopolymer substrates are determined. The free energy ( =101 kJ/mol), which corresponds to the degradation and formation of a single bond in the enzyme—polymer substrate is also estimated. This energy expressed in electronvolt units is =1.39 eV. The ratio between the effective cross section of the reactive substrate bond and the active enzyme center is =1.22.

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Kinetik der enzymkatalysierten Hydrolyse von Natriumcarboxymethylcellulose mit verschiedenem Polymerisationsgrad durch Cellulase

Zusammenfassung Die modifizierte Gleichung nachMichaelis-Menten wird bei der durch Cellulase (EC 3.2.1.4) katalysierten hydrolytischen Spaltung von Natriumcarboxy-methylcellulose (Na-CMC) verschiedenen Polymerisationsgrades (n=140, 640 und 900) angewandt. Es wurde dieMichaelis-Menten-Konstante [Km (M)=6.31·10^–2mol/dm³] und die Reaktionsgeschwindigkeitskonstante (k ₊₂=4.07·10^–6s^–1), die der enzymatischen Hydrolyse einer Einfachbindung im homopolymeren Substrat entspricht, berechnet. Die freie Energie ( =101 kJ/mol), die dem Abbau und der Bildung einer Einfachbindung im Enzym—Polymer-Substrat entspricht, wurde bestimmt. Diese Energie — ausgedrückt in Elektronvolt-Einheiten — beträgt =1.39 eV. Das Verhältnis zwischen den effektiven Querschnitten der reaktiven Substratbindung ( _S ) und des aktiven Enzym-Zentrums ( _E ) beträgt =1.22.

     

Determination of carbon dioxide in gaseous samples by gas diffusion-flow injection

A gas diffusion-flow injection system was developed for the determination of carbon dioxide in gaseous samples. The calibration was based on the use of either gaseous carbon dioxide or aqueous sodium carbonate standards. Gaseous carbon dioxide samples and gaseous or aqueous standards were injected directly into a donor stream of 1.0×10⁻⁴ M H₂SO₄. In the gas diffusion unit, carbon dioxide diffused through a PTFE membrane into an acceptor stream containing a mixed acid/base indicator. The absorbance of the acceptor stream was monitored spectrophotometrically at 554 nm. The calibration plot was linear over the range of 5.00×10² to 1.27×10⁴ μl l⁻¹ with a sample throughput of 28 h⁻¹ and 3.2% R.S.D. ([CO₂]=2.37×10³ μl l⁻¹, n=12). The detection limit was determined as 2.50×10² μl l⁻¹. The flow system was successfully applied to the analysis of several natural gaseous samples and the headspace of milk containers during storage. The flow injection results were found to be statistically indistinguishable at the 95% confidence level from those obtained by gas chromatography using thermal conductivity detection.     

l‐Argininamidium bis­(hydrogen­squarate)

Cations and anions of the title compound {systematic name: 1‐[4‐(amino­carbonyl)butyl]guanidinium bis­(hydrogen­squarate)}, C₆H₁₇N₅O²⁺·2C₄HO₄⁻, are connected into a three‐dimensional network by inter­molecular N—H⋯O hydrogen bonds between the l ‐argininamidium ammonium, amide and guanidinium functions and the hydrogensquarate carbonyl O atoms. The independent hydrogensquarate monoanions are linked into dimers by pairs of O—H⋯O′ hydrogen bonds.     

1,1,1‐Trichloro‐3‐(1‐phenethylamino‐ethylidene)‐ pentane‐2,4‐dione—synthesis,spectroscopic, theoretical and structural elucidation

1,1,1‐Trichloro‐3‐(1‐phenethylamino‐ethylidene)‐pentane‐2,4‐dione is spectroscopically and structurally elucidated by means of linear‐polarized IR spectroscopy (IR‐LD) of oriented solids as a colloidal suspension in nematic liquid crystal. Structural information and IR‐spectroscopic assignment are supported by quantum chemical calculations at MP2 and B3LYP level of theory and 6‐311++G** basis set. The geometry is characterized with an inramolecular hydrogen bond of NH^…O?C with length of 2.526 Å and a NHO angle of 140.5(1)°. The NH? C(CH₃)C?C? C?O(CH₃) fragment is nearly flat with a maximal deviation of total planarity of 10.4°. Copyright © 2007 John Wiley & Sons, Ltd.     

Table-top 50-W laser system for ultra-fast laser ablation

We have built a mode-locked Nd:YVO₄ laser with a very long resonator which produces an average power of 50 W in 13-ps pulses at 1064 nm and was designed for applications in micro-machining, the deposition of optical thin films, and the growth of nano-clusters in the laser-ablated plumes. By operating the laser at very low mode-locking repetition rates (1.5 MHz, 2.6 MHz, and 4.1 MHz), high pulse power is available in a near diffraction limited beam, allowing focused intensities to exceed 10¹² W/cm² and permitting efficient evaporation of difficult materials such as Si. The high power also allows conversion into the second harmonic at 532 nm with an efficiency exceeding 80%. Measurements of the ablation mass in experiments with metals show a 30–100 times increase in the ablation rate compared to the conventional low-repetition-rate ns-range lasers. PACS 79.20.Ds; 81.15.Fg; 81.16.Mk; 42.62.Cf     

Monoclinic and triclinic polymorphs of 2-{5,5-dimethyl-3-[2-(2,4,6-trimethoxyphenyl)vinyl]cyclohex-2-enylidene}malononitrile-solid-state linear-polarized IR-spectroscopy, DFT calculations and vibrational analysis

The linear-dichroic infrared (IR-LD) spectroscopy of oriented solid samples as suspension in nematic liquid crystal have been carried out for experimental IR-band assignment and structural information of 2-{5,5-dimethyl-3-[2-(2,4,6-trimethoxyphenyl)vinyl]cyclohex-2-enylidene} malononitrile polymorphs. The last data have been compared with known crystallographic ones, thus determining the validity of IR-LD spectral conclusions as well as its possibility to determination of Davydov's splitting effect and separation of pairs of maxima corresponding to non-equivalent molecules included in the unit cell of given compound. The experimental structural and spectroscopic data in our case are supported with theoretical DFT ones, obtaining both the electronic structure and vibrational frequencies in gas phase.     

Spectroscopic and structural elucidation of merocyanine dye 2,5-[1-metyl-4-[2-(4-hydroxyphenyl)ethenyl)]piridinium]-hexane tetraphenylborate aggregation processes

Structural and spectroscopic elucidation of merocyanine dye, 2,5-[1-metyl-4-[2-(4-hydroxyphenyl)ethenyl)]piridinium]-hexane tetraphenylborate, is performed in gas and condense phase by means of solution and solid-state conventional and linear-polarized IR-spectroscopy of oriented colloids in nematic liquid crystal suspension, UV-vis and fluorescence methods, HPLC MS/MS tandem and ESI mass spectrometry, (1)H, (13)C and (1)H-(1)H COSY NMR, TGV and DSC methods. Quantum chemical DFT calculations are performed for structural optimization and spectroscopic properties prediction.