An isometry theorem for quadratic differentials on Riemann surfaces of finite genus

Assume both and are Riemann surfaces which are subsets of compact Riemann surfaces and respectively, and that the set has infinitely many points. We show that the only surjective complex linear isometries between the spaces of integrable holomorphic quadratic differentials on and are the ones induced by conformal homeomorphisms and complex constants of modulus 1. It follows that every biholomorphic map from the Teichmüller space of onto the Teichmüller space of is induced by some quasiconformal map of onto . Consequently we can find an uncountable set of Riemann surfaces whose Teichmüller spaces are not biholomorphically equivalent.

     

Optimization of cubic GaN/AlGaN quantum cascade structures for negative refraction in the THz spectral range

In this work we theoretically investigate a possibility to use cubic nitride based multi-layer periodic nanostructure as a semiconductor metamaterial. The structure design is based on an active region of a quantum cascade laser optimized to achieve optical gain in the Terahertz (THz) spectral range. In particular, we test the GaN/AlGaN quantum well configurations, which should exhibit important advantages compared to GaAs-based structures, namely room temperature operation without the assistance of magnetic field and lower doping densities. Our numerical rate-equations model is solved self-consistently and it takes into account electron-longitudinal optical phonon scattering between all the relevant states among the adjacent periods of the structure. A global optimization routine, specifically genetic algorithm is then used to generate new gain-optimized structures. This work confirms the advantages of cubic GaN designs over GaAs ones, namely feasibility of negative refraction at room temperature without the assistance of magnetic field while keeping the doping densities of the same order of magnitude.     

Redox driven conductance changes for resistive memory

The relationship between bias-induced redox reactions and resistance switching is considered for memory devices containing TiO₂ or a conducting polymer in “molecular heterojunctions” consisting of thin (2–25 nm) films of covalently bonded molecules, polymers, and oxides. Raman spectroscopy was used to monitor changes in the oxidation state of polythiophene in Au/P3HT/SiO₂/Au devices, and it was possible to directly determine the formation and stability of the conducting polaron state of P3HT by applied bias pulses [P3HT = poly(3-hexyl thiophene)]. Polaron formation was strongly dependent on junction composition, particularly on the interfaces between the polymer, oxide, and electrodes. In all cases, trace water was required for polaron formation, leading to the proposal that water reduction acts as a redox counter-reaction to polymer oxidation. Polaron stability was longest for the case of a direct contact between Au and SiO₂, implying that catalytic water reduction at the Au surface generated hydroxide ions which stabilized the cationic polaron. The spectroscopic information about the dependence of polaron stability on device composition will be useful for designing and monitoring resistive switching memory based on conducting polymers, with or without TiO₂ present.     

An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös

For any fixed finite interval [a, b] on the real line, an arbitrary natural numberr and σ>0, we describe the extremal function to the problem $\left\| {f^{(k)} } \right\|L_p \left[ {a,b} \right]^{ \to \sup } \left( {1 \leqslant k \leqslant r - 1, 1 \leqslant p< \infty } \right)$ over all functionsf ∈W _∞ ^r such that |f ^(r)(x)| ≤σ, |f(x)|≤1 on (?∞, ∞). Similarly, we solve the problem, raised by Paul Erdös, of characterizing the trigonometric polynomial of fixed uniform norm whose graph has maximal arc length over [a, b].     

Pulsradiolytische Untersuchungen der Reaktion des e aq − mit halogenierten aromatischen Verbindungen

Kinetic pulse radiolysis experiments (1 s pulse duration) on the reaction of e _aq ^– with halogenated aromatic compounds (fluoro-, chloro-, bromobenzene, benzylchloride and phenethylchloride were carried out in order to check the existence and to investigate the fate of an electron adduct. The measured absorption spectra, being identical with those previously observed for the phenyl and benzyl radical, and thepH dependence of the formation of the H-adducts, indicating no protonation of an intermediateRX ^–, can be explained simply by quantitative elimination of the halide. No evidence for the existence of an electron adduct as an intermediate could be obtained under the applied experimental conditions.

     

Flow-injection analysis with a small cylindrical wire type electrode

An amperometric detector with a small thin mercury film electrode is described. The device demonstrates advantageous operational characteristics such as small dispersion (D<2) and “memory effect” (me<0.6%), extensive maximum sample frequency (msf −200 samples/h), and high sensitivity. It has been proven useful in flow-injection analysis at a constant potential under hydrodynamic conditions.     

Desmotropy,Polymorphism, and Solid‐State Proton Transfer: Four Solid Forms of an Aromatic o‐Hydroxy Schiff Base

The Schiff base derived from salicylaldehyde and 2‐amino‐3‐hydroxypyridine affords a diversity of solid forms, two polymorphic pairs of the enol‐imino ( D1 a and D1 b ) and keto‐amino ( D2 a and D2 b ) desmotropes. The isolated phases, identified by IR spectroscopy, X‐ray crystallography, and ¹³C cross‐polarization/magnetic angle spinning (CP/MAS) NMR spectroscopy, display essentially planar molecular conformations characterized by strong intramolecular hydrogen bonds of the O? H???N ( D1 ) or N? H???O ( D2 ) type. A change in the position of the proton within this O???H???N system is accompanied by substantially different molecular conformations and, subsequently, by divergent supramolecular architectures. The appearance and interconversion conditions for each of the four phases have been established on the basis of a number of solution and solvent‐free experiments, and evaluated against the results of computational studies. Solid phases readily convert into the most stable form ( D1 a ) upon exposure to methanol vapor, heating, or by mechanical treatment, and these transformations are accompanied by a change in the color of the sample. The course of thermally induced transformations has been monitored in detail by means of temperature‐resolved powder X‐ray diffraction and infrared spectroscopy. Upon dissolution, all forms equilibrate immediately, as confirmed by NMR and UV/Vis spectroscopy in several solvents, with the equilibrium shifted far towards the enol tautomer. This study reveals the significance of peripheral groups in the stabilization of metastable tautomers in the solid state.     

Electrochemical behavior and antioxidant activity of tetradentate Schiff bases and their copper(II) complexes

This study describes the effects of the substituents on electrochemical behavior and antioxidant activity of the six tetradentate Schiff bases, containing ethane-1,2-diamine or propane-1,2-diamine as the amine part and pentane-2,4-dione and/or 1-phenylbutane-1,3-dione as ??-diketone, and corresponding copper(II) complexes. Cyclic voltammograms of these compounds were recorded in dimethylsulfoxide and 0.1?M sodium perchlorate as supporting electrolyte with glassy carbon as working electrode at different scan rates. The voltammograms of Schiff bases alone showed only one irreversible peak. Voltammograms recorded for complexes showed the presence of quasi-reversible processes taking place at the metal center and reversible process at the ligand part. Both steric and inductive effects of substituents and structure of imine bridge of Schiff base ligands as well as complexes were discussed. These effects appear relevant for the antioxidant activity. Antioxidant activity of the investigated compounds expressed as Trolox equivalent antioxidant capacity is also discussed. The electrochemical behavior showed a high correlation with the antioxidant activity for investigated compounds.     

Stability of nanodispersions: a model for kinetics of aggregation of nanoparticles

In the course of aggregation of very small colloid particles (nanoparticles) the overlap of the diffuse layers is practically complete, so that one cannot apply the common DLVO theory. Since nanopoarticles are small compared to the extent of the diffuse layer, the process is considered in the same way as for two interacting ions. Therefore, the Br?nsted concept based on the Transition State Theory was applied. The charge of interacting nanoparticles was calculated by means of the Surface Complexation Model and decrease of effective charge of particles was also taken into account. Numerical simulations were performed using the parameters for hematite and rutile colloid systems. The effect of pH and electrolyte concentration on the stability coefficient of nanosystems was found to be more pronounced but similar to that for regular colloidal systems. The effect markedly depends on the nature of the solid which is characterized by equilibrium constants of surface reactions responsible for surface charge, i.e., by the point of zero charge, while the specificity of counterions is described by their association affinity, i.e., by surface association equilibrium constants. The most pronounced is the particle size effect. It was shown that extremely small particles cannot be stabilized by an electrostatic repulsion barrier. Additionally, at the same mass concentration, nanoparticles aggregate more rapidly than ordinary colloidal particles due to thier higher number concentration.