Simulation of a crossover from the precipitation wave to moving Liesegang pattern formation

Model simulations to investigate the precipitation wave phenomenon and a crossover from the precipitation wave to moving Liesegang patterns were performed. The chemical scheme contains four chemical species via the interaction of precipitation and redissolution (complex formation), in which the precipitation reaction term was based on Ostwald's supersaturation theory. In this article, for the first time, all the features and behaviors of the heterogeneous traveling waves are reproduced, which were observed experimentally in the work of Zrínyi et al. (Zrínyi, et al. J. Phys. Chem. 1991, 95, 1618.). The detailed investigation of the pattern formation showed three possible states of the system, which depend on the initial concentration of the inner and outer electrolytes, respectively. These are the precipitation wave (single moving precipitation band), the moving Liesegang pattern (moving precipitation bands), and the state where these two patterns coexist.     

An investigation of enhanced secondary ion emission under Au n + (n=1–7) bombardment

We investigate the mechanism of the nonlinear secondary ion yield enhancement using Au(n)+ (n = 1, 2, 3, 5, 7) primary ions bombarding thin films of Irganox 1010, DL-phenylalanine and polystyrene on Si, Al, and Ag substrates. The largest differences in secondary ion yields are found using Au+, Au2+, and Au3+ primary ion beams. A smaller increase in secondary ion yield is observed using Au5+ and Au7+ primary ions. The yield enhancement is found to be larger on Si than on Al, while the ion yield is smaller using an Au+ beam on Si than on Al. Using Au(n)+ ion structures obtained from Density Functional Theory, we demonstrate that the secondary yield enhancement is not simply due to an increase in energy per area deposited into the surface (energy deposition density). Instead, based on simple mechanical arguments and molecular dynamics results from Medvedeva et al, we suggest a mechanism for nonlinear secondary ion yield enhancement wherein the action of multiple concerted Au impacts leads to efficient energy transfer to substrate atoms in the near surface region and an increase in the number of secondary ions ejected from the surface. Such concerted impacts involve one, two, or three Au atoms, which explains well the large nonlinear yield enhancements observed going from Au+ to Au2+ to Au3+ primary ions. This model is also able to explain the observed substrate effect. For an Au+ ion passing through the more open Si surface, it contacts fewer substrate atoms than in the more dense Al surface. Less energy is deposited in the Si surface region by the Au+ primary ion and the secondary ion yield will be lower for adsorbates on Si than on Al. In the case of Au(n)+ the greater density of Al leads to earlier break-up of the primary ion and a consequent reduction in energy transfer to the near-surface region when compared with Si. This results in higher secondary ion yields and yield enhancements on silicon than aluminum substrates.     

Copper(II) interaction with unstructured prion domain outside the octarepeat region: speciation, stability, and binding details of copper(II) complexes with PrP106-126 peptides

Copper(II) complexes of the neurotoxic peptide fragments of human and chicken prion proteins were studied by potentiometric, UV-vis, CD, and EPR spectroscopic and ESI-MS methods. The peptides included the terminally blocked native and scrambled sequences of HuPrP106-126 (HuPrPAc106-126NH2 and ScrHuPrPAc106-126NH2) and also the nona- and tetrapeptide fragments of both the human and chicken prion proteins (HuPrPAc106-114NH2, ChPrPAc119-127NH2, HuPrPAc109-112NH2, and ChPrPAc122-125NH2). The histidyl imidazole-N donor atoms were found to be the major copper(II) binding sites of all peptides; 3N and 4N complexes containing additional 2 and 3 deprotonated amide-N donors, respectively, are the major species in the physiological pH range. The complex formation processes for nona- and tetrapeptides are very similar, supporting the fact that successive deprotonation and metal ion coordination of amide functions go toward the N-termini in the form of joined six- and five-membered chelates. As a consequence, the peptide sequences investigated here, related to the neurotoxic region of the human PrP106-126 sequence, show a higher metal-binding affinity than the octarepeat fragments. In the case of the HuPrP peptide sequences, a weak pH-dependent binding of the Met109 residue was also detected in the 3N-coordinated complexes.     

Absolutely convergent Fourier series, classical function classes and Paley’s theorem

This is a survey paper on the recent progress in the study of the continuity and smoothness properties of a function f with absolutely convergent Fourier series. We give best possible sufficient conditions in terms of the Fourier coefficients of f which ensure the belonging of f either to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes Zyg(α) and zyg(α) for some 0 < α ≤ 2. We also discuss the termwise differentiation of Fourier series. Our theorems generalize those by R. P. Boas Jr., J. Németh and R. E. A. C. Paley, and a number of them are first published in this paper or proved in a simpler way.     

Atomic force microscopy investigation of electrochemically produced carbon nanotubes

Carbon nanostructures have been synthesized in NaCl-MgCl₂ and in NaCl-CaCl₂ salt melts and the extracted material was investigated by tapping-mode atomic force microscopy (TM-AFM) and scanning electron microscopy. Some interesting new nanostructures were found and investigated as torus-shaped carbon structures with a ring diameter of 300-400 nm and 10-15 nm height. These tori are closely related to the wrapped SWNT rings described recently. They are probably formed during the electrolysis. A chain-like structure was also revealed.     

Schreier loops

We study systematically the natural generalization of Schreier’s extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.     

Absolute convergence of multiple Fourier series revisited

In a recent paper [4], Gogoladze and Meskhia generalized the classical results of Bernstein, Szász, Zygmund and others related to absolute convergence of single trigonometric Fourier series. Our aim is to extend these results from single to multiple Fourier series. To this effect, we introduce the notions of multiplicative moduli of continuity and that of smoothness. Multiplicative Lipschitz classes of functions in several variables, and functions of bounded s-variation in the sense of Vitali are also considered.