Oscillations in three-reaction quadratic mass-action systems

It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the minimum number that is required for oscillation. However, some of our intermediate results are valid in greater generality. One key finding is that an isolated periodic orbit cannot occur in a three-reaction, trimolecular, mass-action system with bimolecular sources. In fact, we characterize all networks in this class that admit a periodic orbit; in every case, all nearby orbits are periodic too. Apart from the well-known Lotka and Ivanova reactions, we identify another network in this class that admits a center. This new network exhibits a vertical Andronov–Hopf bifurcation. Furthermore, we characterize all two-species, three-reaction, bimolecular-sourced networks that admit an Andronov–Hopf bifurcation with mass-action kinetics. These include two families of networks that admit a supercritical Andronov–Hopf bifurcation and hence a stable limit cycle. These networks necessarily have a target complex with a molecularity of at least four, and it turns out that there are exactly four such networks that are tetramolecular.     

Spectral and Photophysical Properties of α-carboline (1-Azacarbazole) in Aqueous Solutions

The absorption and fluorescence spectra of α-carboline, 9H-pyrido[2,3-b]indole, AC, in organic aprotic solvents containing different water proportions and in acid/base aqueous solutions inside and outside the pH range have been examined. In the organic aprotic solvents, the addition of increasing concentrations of water sequentially quenches and shifts to the red the fluorescence spectra of AC. These spectral changes have been rationalized assuming the formation, at the lower water concentrations, of a discrete ground state non-cyclic weakly fluorescent AC hydrate emitting at 376 nm that, upon increasing the water concentrations, evolves to a higher order AC poly hydrate emitting at 397 nm. The changes of the AC absorption spectra in aqueous acid/basic solutions indicate the existence of three ground state prototropic species; the pyridinic protonated cation, C (pK_a?=?4.10?±?0.05), the neutral, N (pK_a?=?14.5?±?0.2), and the pyrrolic deprotonated anion, A. Conversely, the changes of the AC fluorescence spectra in these media indicate the existence of four excited state species emitting at 376 nm, 397 nm, 460 nm and 465 nm. Since the emissions at 376 nm and 397 nm satisfactorily match those of the hydrates observed in the organic-water mixtures, they were consistently assigned to two differently hydrated ground state N species. The remaining emissions at 460 nm and 465 nm have been assigned without ambiguity, on the basis of their excitation spectra, to the C and A species, respectively. The excited-state pK_as of the prototropic species of AC have been estimated by using the Förster-Weller cycle.     

Substrate effect on microstructure and optical performance of sputter‐deposited TiO2 thin films

This study deals with the role of the different substrates on the microstructural, optical and electronical properties of TiO₂ thin films produced by conventional direct current (DC) magnetron sputtering in a mixture of pure argon and oxygen using a Ti metal target with the aid of X–ray diffractometer (XRD), ultra violet spectrometer (UV–vis) and atomic force microscopy (AFM) measurements. Transparent TiO₂ thin films are deposited on Soda lime glass, MgO(100), quartz and sitall substrates. Phase purity, surface morphology, optical and photocatalytic properties of the films are compared with each other. It is found that the amplitude of interference oscillation of the films is in a range of 77‐89%. The transmittance of the film deposited on Soda lime glass is the smallest while the film produced on MgO(100) substrate obtains the maximum transmittance value. The refractive index and optical band gap of the TiO₂ thin films are also inferred from the transmittance spectra. The results show that the film deposited on Soda lime glass has the better optical property while the film produced on MgO(100) substrate exhibits much better photoactivity than the other films because of the large optical energy band gap. As for the XRD results, the film prepared on MgO(100) substrate contains the anatase phase only; on the other hand, the other films contain both anatase and rutile phases. Furthermore, AFM images show that the regular structures are observed on the surface of all the films studied. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reductive transformations of unsaturated azabicyclic nitrolactams

Using different reducing methods unsaturated indolizidine and quinolizidine lactams substituted with a nitro group were transformed into various alkaloid-like derivatives. Hydrogen transfer and palladium catalyzed hydrogenation gave compounds of ketolactam or lactam type meanwhile the nitro group was eliminated. On the other hand, in presence of Raney-nickel catalyst the nitro compounds were reduced to diastereomeric amino derivatives whose stereochemistry was elucidated by NMR spectroscopy. Using sodium bis-dimethoxy-ethoxy-aluminum-hydride (Red-Al) as reducing agent an unexpected tricyclic azetidine was isolated and characterized.     

Random graphons and a weak Positivstellensatz for graphs

In an earlier article, the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2‐variable real functions called graphons, random graph models satisfying certain consistency conditions, and normalized, multiplicative and reflection positive graph parameters. In this article we show that each of these structures has a related, relaxed version, which are also equivalent. Using this, we describe a further structure equivalent to graph limits, namely probability measures on countable graphs that are ergodic with respect to the group of permutations of the nodes. As an application, we prove an analogue of the Positivstellensatz for graphs: we show that every linear inequality between subgraph densities that holds asymptotically for all graphs has a formal proof in the following sense: it can be approximated arbitrarily well by another valid inequality that is a “sum of squares” in the algebra of partially labeled graphs. © 2011 Wiley Periodicals, Inc. J Graph Theory     

Application of the Systems Chemistry Approach on the Ammonolysis of 1-Ethoxycarbonyl- and 1-Phenoxycarbonyl-3-(2-thienyl)oxindoles. A Method to Predict Reactivity

The routine prediction of the reactivity of a complex, multifunctional molecule is a challenging and time-consuming procedure. In the last step of the synthesis of the well-known drug substance tenidap, a nonexpected difference was observed between the reactivities of two closely related carbamate moieties, the N-ethoxycarbonyl and the N-phenoxycarbonyl group. A detailed kinetic study, necessitating a significant computational effort, is described in the present paper for this reaction step. On the other hand, the systems chemistry concept, by analyzing the details of the electronic structure and the connections between functional groups in a fast and simple way, is also able to answer this question using various "-icity" parameters (aromaticity, carbonylicity, olefinicity). The complete systems chemistry approach involves all these conjugativicity parameters, while its further simplified version is based on only one key parameter, which is carbonylicity in the present case. The above methods were compared in terms of their predictive power. The results show that the systems chemistry concept, even its one-parameter version, is applicable for the characterization of this challenging reactivity issue.     

Microscopic Shape of Shocks in a Domain Growth Model

Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g., the inviscid Burgers equation for the simple exclusion process. The physical solutions of these partial differential equations develop discontinuities, called shocks. The microscopic structure of these shocks is of much interest and far from being well understood. We introduce a domain growth model in which we find a stationary (in time) product measure for the model, as seen from a defect tracer or second class particle, traveling with the shock. We also show that under some natural assumptions valid for a wider class of domain growth models, no other model has stationary product measure as seen from the moving defect tracer.     

Non-Equilibrium Polymerization of Cross-β Amyloid Peptides for Temporal Control of Electronic Properties

Hydrophobic collapse plays crucial roles in protein functions, from accessing the complex three-dimensional structures of native enzymes to the dynamic polymerization of non-equilibrium microtubules. However, hydrophobic collapse can also lead to the thermodynamically downhill aggregation of aberrant proteins, which has interestingly led to the development of a unique class of soft nanomaterials. There remain critical gaps in the understanding of the mechanisms of how hydrophobic collapse can regulate such aggregation. Demonstrated herein is a methodology for non-equilibrium amyloid polymerization through mutations of the core sequence of Aβ peptides by a thermodynamically activated moiety. An out of equilibrium state is realized because of the negative feedback from the transiently formed cross-β amyloid networks. Such non-equilibrium amyloid nanostructures were utilized to access temporal control over its electronic properties.     

TLC Method for Quantitation of Methylenedioxyphenylacetone and its Derivative Formed in a Resin-Added Bioreduction Process

JPC – Journal of Planar Chromatography – Modern TLC -