The Spectrum of a Linearized 2D Euler Operator

We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two-dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier modes. We prove that the essential spectrum coincides with the imaginary axis, and give an estimate from above for the number of isolated nonimaginary eigenvalues. In addition, we prove that the spectral mapping theorem holds for the group generated by the linearized 2D Euler operator.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

V4S9Br4: a novel high-spin vanadium cluster thiobromide with square-planar metal core

The novel vanadium thiobromide, V4S9Br4, with a square-planar metal cluster core was synthesized and characterized by single-crystal X-ray diffraction, measurements of magnetic properties and the heat capacity, and DFT calculations of the electronic structure. At the room temperature, the compound displays paramagnetic properties with an independent spin on each V atom and with a weak exchange constant (J approximately 10 cm(-1)). The paramagnetic state is transformed into a low-spin state (AF-type ordering) at low temperatures. This change is accompanied by a heat-capacity anomaly. The observed magnetic and heat-capacity anomalies can be explained by the thermal excitation of electrons on the closely spaced molecular energy levels in the presence of the Jahn-Teller effect.     

Interaction between Ti-gel and silver, copper, as well as nickel compounds under ultrasound irradiation

Ag-TiO₂, Cu-TiO₂ and Ni-TiO₂ were prepared by sonication. The interactions of Ti-gel with silver, copper and nickel ions under ultrasound irradiation are very different, although these ions can be dispersed very well in titania. The results of EDXA and XRD analysis indicate that Ti-gel does not react with AgCl and crystallizes unaffectedly to form rutile. M(OH)₂ (M = Cu and Ni), on the other hand, favors polycondensation with Ti-gel and affects the crystallization of Ti-gel. CuO favors stabilization of the anatase phase. Ni²⁺ ions tend to incorporate more easily into titania than Cu²⁺ ions do when the samples are calcined. TEM, and BET were also used to characterize the samples.     

Synthesis and anion binding properties of 2,5-diamidothiophene polypyrrole Schiff base macrocycles

[reaction: see text] Two easy-to-synthesize polypyrrolic 2,5-diamidothiophene Schiff base macrocycles are reported, along with their anion binding properties as determined via UV-vis spectroscopic titrations carried out in dichloroethane. There is a striking difference between the interactions with anions of the two macrocycles, a finding ascribed to differences in their rigidity. For example, the more flexible dipyrromethane-derived macrocycle displays a 1.2:1 hydrogen sulfate versus nitrate selectivity, while its more rigid bipyrrole-derived congener shows a 7.4:1 selectivity in favor to hydrogen sulfate.     

Photodissociation dynamics of pyridine

Photodissociation of pyridine, 2,6-d2-pyridine, and d5-pyridine at 193 and 248 nm was investigated separately using multimass ion imaging techniques. Six dissociation channels were observed at 193 nm, including C5NH5 --> C5NH4 + H (10%) and five ring opening dissociation channels, C5NH5 --> C4H4 + HCN, C5NH5 --> C3H3 + C2NH2, C5NH5 --> C2H4 +C3NH, C5NH5 --> C4NH2 + CH3 (14%), and C5NH5 --> C2H2 + C3NH3. Extensive H and D atom exchanges of 2,6-d2-pyridine prior to dissociation were observed. Photofragment translational energy distributions and dissociation rates indicate that dissociation occurs in the ground electronic state after internal conversion. The dissociation rate of pyridine excited by 248-nm photons was too slow to be measured, and the upper limit of the dissociation rate was estimated to be 2x10(3) s(-1). Comparisons with potential energies obtained from ab initio calculations and dissociation rates obtained from the Rice-Ramsperger-Kassel-Marcus theory have been made.     

Luminol Oxidation by Hydrogen Peroxide Catalyzed by Tobacco Anionic Peroxidase: Steady-State Luminescent and Transient Kinetic Studies

The properties of a newly isolated anionic tobacco peroxidase from transgenic tobacco plants overexpressing the enzyme have been studied with respect to the chemiluminescent reaction of luminol oxidation. These were compared to the properties of horseradish peroxidase in the cooxidation of luminol and p -iodophenol, the enhanced chemiluminescence reaction. The pH, luminol and hydrogen peroxide concentrations were optimized for maximum sensitivity using the tobacco enzyme. The detection limit for the latter under the optimal conditions (2.5 m M luminol, 2 m M hydrogen peroxide, 100 m M Naborate buffer, pH 9.3) was about 0.1 p M , which is at least five times lower than that for horseradish peroxidase in enhanced chemiluminescence with p -iodophenol. The rate constants for the elementary steps of the enzyme-catalyzed reaction have been determined: k ₁= 4.9 × 10⁶ M ⁻¹ s¹, k ₂= 7.3 × 10⁶ M ⁻¹ s⁻¹, k ³= 2.1 × 10⁶ M ⁻¹ s⁻¹ (pH 9.3). The similarity of these rate constants is unusual for plant peroxidases. The high catalytic activity of tobacco peroxidase in the luminescent reaction is explained by the high reactivity of its Compound II toward luminol and the high stability of the holoenzyme with respect to heme dissociation. This seems to be a unique property of this particular enzyme among other plant peroxidases.     

Relaxation dynamics in glycerol-water mixtures: I. Glycerol-rich mixtures

We discuss the relaxation dynamics of glycerol-water mixtures, as studied by dielectric spectroscopy in the frequency range from 1 Hz to 250 MHz and at temperatures between 173 and 323 K. The experimental results obtained for the glycerol-rich mixtures suggest that the main dielectric relaxation process, as well as the so-called high-frequency "excess wing" (EW) and dc conductivity, follow the same temperature dependence. This result indicates that all of these processes are induced by the same molecular origin. A new phenomenological function is proposed to describe the whole dielectric spectrum in the covered frequency range, and some possible mechanisms of dielectric behaviors through the dc conductivity, the main relaxation process, and the EW are discussed.