The formal translation equation for iteration groups of type II

We investigate the translation equation $$F(s+t, x) = F(s, F(t, x)),\quad \quad s,t\in{\mathbb{C}},\qquad\qquad\qquad\qquad({\rm T})$$ in ${\mathbb{C}\left[\kern-0.15em\left[{x}\right]\kern-0.15em\right]}$ , the ring of formal power series over ${\mathbb{C}}$ . Here we restrict ourselves to iteration groups of type II, i.e. to solutions of (T) of the form ${F(s, x) \equiv x + c_k(s)x^k {\rm mod} x^{k + 1}}$ , where k ≥ 2 and c _k ≠ 0 is necessarily an additive function. It is easy to prove that the coefficient functions c _n (s) of $$F(s, x) = x + \sum_{n \ge q k}c_n(s)x^n$$ are polynomials in c _k (s). It is possible to replace this additive function c _k by an indeterminate. In this way we obtain a formal version of the translation equation in the ring ${(\mathbb{C}[y])\left[\kern-0.15em\left[{x}\right]\kern-0.15em\right]}$ . We solve this equation in a completely algebraic way, by deriving formal differential equations or an Aczél–Jabotinsky type equation. This way it is possible to get the structure of the coefficients in great detail which are now polynomials. We prove the universal character (depending on certain parameters, the coefficients of the infinitesimal generator H of an iteration group of type II) of these polynomials. Rewriting the solutions G(y, x) of the formal translation equation in the form ${\sum_{n\geq 0}\phi_n(x)y^n}$ as elements of ${(\mathbb{C}\left[\kern-0.15em\left[{x}\right]\kern-0.15em\right])\left[\kern-0.15em\left[{y}\right]\kern-0.15em\right]}$ , we obtain explicit formulas for ${\phi_n}$ in terms of the derivatives H ^(j)(x) of the generator ${H}$ and also a representation of ${G(y, x)}$ as a Lie–Gröbner series. Eventually, we deduce the canonical form (with respect to conjugation) of the infinitesimal generator ${H}$ as x ^k + hx ^2k-1 and find expansions of the solutions ${G(y, x) = \sum_{r\geq 0} G_r(y, x)h^r}$ of the above mentioned differential equations in powers of the parameter h.     

Hilberts satz Über Flächen Konstanter Negativer Krümmung

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Four-wave mixing in semiconductor laser amplifiers: Applications for optical communication systems

Four-wave mixing in semiconductor laser amplifiers enables various applications in photonic switching including wavelength conversion, space and time switching, optical phase conjugation, and demultiplexing. Switching times faster than 1 ps are possible.     

ON THE ACRIDINE AND THIAZINE DYE SENSITIZED PHOTODYNAMIC INACTIVATION OF LYSOZYME—SINGLET OXYGEN SELF-QUENCHING BY THE SENSITIZERS

Abstract— The quantum yield of the photodynamic inactivation of lysozyme increases in the sequence acridine orange, methylene blue, proflavine and acriflavine (1:5:6:12). At least up to protein concentrations of 0.1 m M , singlet oxygen is exclusively responsible for the inactivation of the enzyme. For methylene blue, acriflavine and proflavine the quantum yields decrease considerably with increasing dye concentrations. From measurements in H₂O and D₂O buffer solutions it was concluded that in the case of methylene blue the effect is mainly caused by the quenching of singlet oxygen [rate constant (3–4) × 10⁸ M ⁻¹ s⁻¹]. For the acridine sensitizers both singlet oxygen and dye triplet quenching processes have to be taken into consideration. It has been found that all sensitizers act as competitive inhibitors of the enzymatic reaction of lysozyme. However, the dye-protein interaction near the active center cannot be responsible for the observed dye self-quenching effect.     

Oxadiazole-metal interface: from isolated molecules to pi-stacking

Derivatives of 2,5-diaryl-1,3,4-oxadiazole are used widely for electron transport in organic light emitting diodes (OLED). This study addresses the structure of 2,5-diphenyl-1,3,4-oxadiazole (PPD) molecules on Cu(111) using scanning tunneling microscopy (STM) and density function theory (DFT): at incomplete coverage, PPD molecules are found horizontally on the surface; once the surface area is insufficient to accommodate all adsorbates in this fashion, a pi-stacked film of vertically arranged molecules is formed. In contrast to bulk PPD, in this film, the molecules are arranged face-to-face at a separation of square root(3a0) = 4.4 A as imposed by the substrate interatomic spacing along the [-2 1 1] direction.     

Stabilization of foams with inorganic colloidal particles

Wet foams are used in many important technologies either as end or intermediate products. However, the thermodynamic instability of wet foams leads to undesired bubble coarsening over time. Foam stability can be drastically improved by using particles instead of surfactants as foam stabilizers, since particles tend to adsorb irreversibly at the air-water interface. Recently, we presented a novel method for the preparation of high-volume particle-stabilized foams which show neither bubble growth nor drainage over more than 4 days. The method is based on the in-situ hydrophobization of initially hydrophilic particles to enable their adsorption on the surface of air bubbles. In-situ hydrophobization is accomplished through the adsorption of short-chain amphiphiles on the particle surface. In this work, we illustrate how this novel method can be applied to particles with various surface chemistries. For that purpose, the functional group of the amphiphilic molecule was tailored according to the surface chemistry of the particles to be used as foam stabilizers. Short-chain carboxylic acids, alkyl gallates, and alkylamines were shown to be appropriate amphiphiles to in-situ hydrophobize the surface of different inorganic particles. Ultrastable wet foams of various chemical compositions were prepared using these amphiphiles. The simplicity and versatility of this approach is expected to aid the formulation of stable wet foams for a variety of applications in materials manufacturing, food, cosmetics, and oil recovery, among others.     

On the Validity of Stokes–Einstein and Stokes–Einstein–Debye Relations in Ionic Liquids and Ionic‐Liquid Mixtures

Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations in the neat ionic liquid (IL) [C₂mim][NTf₂] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)? H bond in the cation C₂mim⁺, and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non‐Gaussian parameter α(t). If α(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.     

Third Generation ATP Sensor with Enzymatic Analyte Recycling

For the first time the direct electron transfer of an enzyme ‐ cellobiose dehydrogenase, CDH ‐ has been coupled with the hexokinase catalyzed competition for glucose in a sensor for ATP. To enhance the signal output for ATP, pyruvate kinase was coimmobilized to recycle ADP by the phosphoenolpyruvate driven reaction. The new sensor overcomes the limit of 1 : 1 stoichiometry of the sequential or competitive conversion of ATP by effective enzymatic recycling of the analyte. The anodic oxidation of the glucose converting CDH proceeds at electrode potentials below 0 mV vs. Ag|AgCl thus potentially interfering substances like ascorbic acid or catecholamines do not influence the measuring signal. The combination of direct electron transfer of CDH with the enzymatic recycling results in an interference‐free and oxygen‐independent measurement of ATP in the lower µmolar concentration range with a lower limit of detection of 63.3 nM (S/N=3).     

Formation of polymeric toroidal-spiral particles

Compared to spherical matrices, particles with well-defined internal structure provide large surface to volume ratio and predictable release kinetics for the encapsulated payloads. We describe self-assembly of polymeric particles, whereby competitive kinetics of viscous sedimentation, diffusion, and cross-linking yield a controllable toroidal-spiral (T-S) structure. Precursor polymeric droplets are splashed through the surface of a less dense, miscible solution, after which viscous forces entrain the surrounding bulk solution into the sedimenting polymer drop to form T-S channels. The intricate structure forms because low interfacial tension between the two miscible solutions is dominated by viscous forces. The biocompatible polymer, poly(ethylene glycol) diacrylate (PEG-DA), is used to demonstrate the solidification of the T-S shapes at various configurational stages by UV-triggered cross-linking. The dimensions of the channels are controlled by Weber number during impact on the surface, and Reynolds number and viscosity ratio during subsequent sedimentation. We anticipate applications of the T-S particle in drug delivery, wherein diffusion through these T-S channels and the polymer matrix would offer parallel release pathways for molecules of different sizes. Polyphosphate, as a model macromolecule, is entrained in T-S particles during their formation. The in vitro release kinetics of polyphosphate from the T-S particles with various channel length and width is reported. In addition, self-assembly of T-S particles occurs in a single step under benign conditions for delicate macromolecules, and appears conducive to scaleup.