Large Deviations Principle for a Large Class of?One-Dimensional Markov Processes

We study the large deviations principle for one-dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process X _t in ? that is continuous with probability one, under some minimal regularity conditions, is governed by a generalized elliptic operator D _v D _u , where v and u are two strictly increasing functions, v is right-continuous and u is continuous. In this paper, we study large deviations principle for Markov processes whose infinitesimal generator is ??D _v D _u where 0<???1. This result generalizes the classical large deviations results for a large class of one-dimensional ??classical?? stochastic processes. Moreover, we consider reaction-diffusion equations governed by a generalized operator D _v D _u . We apply our results to the problem of wavefront propagation for these type of reaction-diffusion equations.     

Where galaxies really come from

The fundamental paradox of the incompatibility of the observed large-scale uniformity of the Universe with the fact that the age of the Universe is finite is overcome by the introduction of an initial period of superluminal expansion of space, called cosmic inflation. Inflation can also produce the small deviations from uniformity needed for the formation of structures in the Universe such as galaxies. This is achieved by the conjunction of inflation with the quantum vacuum, through the so-called particle production process. This mechanism is explained and linked with Hawking radiation of black holes. The nature of the particles involved is discussed and the case of using massive vector boson fields instead of scalar fields is presented, with emphasis on its distinct observational signatures. Finally, a particular implementation of these ideas is included, which can link the formation of galaxies, the standard model vector bosons and the observed galactic magnetic fields.     

APN permutations on and Costas arrays

We study PN and APN functions over the integers modulo n. We give some construction techniques based on Costas arrays, which allow us to construct APN permutations on where p is a prime. Although PN permutations do not exist, one set of our functions is very close to being a set of PN permutations.     

Rumor spreading on random regular graphs and expanders

Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well‐studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random and transmits the message to it. In this paper we consider random networks where each vertex has degree d ≥ 3, i.e., the underlying graph is drawn uniformly at random from the set of all d ‐regular graphs with n vertices. We show that with probability 1 ‐ o(1) the push model broadcasts the message to all nodes within (1 + o(1))C_d lnn rounds, where Particularly, we can characterize precisely the effect of the node degree to the typical broadcast time of the push model. Moreover, we consider pseudo‐random regular networks, where we assume that the degree of each node is very large. There we show that the broadcast time is (1 + o(1))Clnn with probability 1 ‐ o(1), where \begin{align*}C = \lim_{d\to\infty}C_d = \frac{1}{\ln2} + 1\end{align*}. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Synthesis of 2D Germanane (GeH): a New,Fast, and Facile Approach

Germanane (GeH), a germanium analogue of graphane, has recently attracted considerable interest because its remarkable combination of properties makes it an extremely suitable candidate to be used as 2D material for field effect devices, photovoltaics, and photocatalysis. Up to now, the synthesis of GeH has been conducted by substituting Ca by H in a β‐CaGe₂ layered Zintl phase through topochemical deintercalation in aqueous HCl. This reaction is generally slow and takes place over 6 to 14 days. The new and facile protocol presented here allows to synthesize GeH at room temperature in a significantly shorter time (a few minutes), which renders this method highly attractive for technological applications. The GeH produced with this method is highly pure and has a band gap (E_g) close to 1.4 eV, a lower value than that reported for germanane synthesized using HCl, which is promising for incorporation of GeH in solar cells.     

Accurate Interaction Energies of CO2 with the 20 Naturally Occurring Amino Acids

We have performed a series of highly accurate calculations between CO₂ and the 20 naturally occurring amino acids for the investigation of the attractive noncovalent interactions. Different nucleophilic groups present in the amino acid structures were considered (α-NH₂, COOH, side groups), and the stronger binding sites were identified. A database of accurate reference interactions energies was compiled as computed by explicitly-correlated coupled-cluster singles-and-doubles, together with perturbative triples extrapolated to the complete-basis-set limit. The CCSD(F12)(T)/CBS reference values were used for comparing a variety of popular density functionals with different basis sets. Our results show that most density functionals with the triple-zeta basis set def2-TZVPP align with the CCSD(F12)(T)/CBS reference values, but errors range from 0.1 kcal/mol up to 1.0 kcal/mol.     

Investigation of the incorporation of electrolyte anions in porous anodic Al2O3 films by employing a suitable probe catalytic reaction

A new method has been developed capable of describing the incorporation of electrolyte anions along the pore wall surface and across both the barrier layer and the pore wall oxide after the establishment of the steady state of growth of porous anodic Al₂O₃ where other methods cannot be applied to obtain reliable results. The knowledge of the nature/composition of anodic oxides as regards the incorporation of species like electrolyte anions is of specific importance for both the understanding of the electrochemical mechanism of oxide production and growth and the scientific and technological applications of porous anodic Al₂O₃ films. The method consists of the selection and use of a suitable catalytic probe reaction on porous anodic oxides at thicknesses varying from a value near zero up to the maximum limiting thickness and the treatment of the experimental reaction rate results by a properly developed mathematical formalism. This method was employed in anodic Al₂O₃ films prepared in H₂SO₄ anodizing electrolyte at a constant bath temperature and different current densities using as a probe reaction the decomposition of HCOOH on these oxides, which is almost exclusively a dehydration reaction, at relatively high reaction temperatures, 350 °C and 390 °C, where the effect of other species except SO₄ ²⁻ incorporated in the oxide on the reaction rate is eliminated. It has been shown that the fraction of the intercrystallite surfaces occupied by SO₄ ²⁻ follows a parabola-like distribution. It has a significant value at the pore base surface, depending on the current density, then it passes through a maximum along the pore wall surface and across both the barrier layer and the pore walls near the pore bases at positions depending on the current density and then becomes almost zero at the mouths of the pores of the oxide with the maximum limiting thickness and at both the Al₂O₃/Al interface and cell boundaries. The maximum value of the surface coverage is almost independent of the current density and is always near 1, showing an almost complete saturation of intercrystalline surfaces at these positions. The above distribution of surface coverage predicts a qualitatively similar distribution of the SO₄ ²⁻ bulk concentration across both the barrier layer and pore wall oxide around the pore bases. The method may be improved and developed further either for a more detailed investigation of the above films or to investigate films prepared in other pore-forming electrolytes. Received: 30 July 1998 / Accepted: 30 September 1998     

Travelling wave ion mobility mass spectrometry studies of protein structure: biological significance and comparison with X-ray crystallography and nuclear magnetic resonance spectroscopy measurements

The three-dimensional conformation of a protein is central to its biological function. The characterisation of aspects of three-dimensional protein structure by mass spectrometry is an area of much interest as the gas-phase conformation, in many instances, can be related to that of the solution phase. Travelling wave ion mobility mass spectrometry (TWIMS) was used to investigate the biological significance of gas-phase protein structure. Protein standards were analysed by TWIMS under denaturing and near-physiological solvent conditions and cross-sections estimated for the charge states observed. Estimates of collision cross-sections were obtained with reference to known standards with published cross-sections. Estimated cross-sections were compared with values from published X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy structures. The cross-section measured by ion mobility mass spectrometry varies with charge state, allowing the unfolding transition of proteins in the gas phase to be studied. Cross-sections estimated experimentally for proteins studied, for charge states most indicative of native structure, are in good agreement with measurements calculated from published X-ray and NMR structures. The relative stability of gas-phase structures has been investigated, for the proteins studied, based on their change in cross-section with increase in charge. These results illustrate that the TWIMS approach can provide data on three-dimensional protein structures of biological relevance.     

Determination of spiroxamine residues in grapes, must, and wine by gas chromatography/ion trap-mass spectrometry

Analytical methodology was developed and validated for the determination of spiroxamine residues in grapes, must, and wine by gas chromatography/ion trap-mass spectrometry (GC/IT-MS). Two extraction procedures were used: the first involved grapes, must, and wine extraction with alkaline cyclohexane-dichloromethane (9 + 1, v/v) solution, and the second grape extraction with acetone, dichloromethane, and petroleum ether. In both procedures, the extract was centrifuged, evaporated to dryness, and reconstituted in cyclohexane or 2,2,4-trimethylpentane-toluene (9 + 1, v/v), respectively. Spiroxamine diastereomers A and B were determined by GC/IT-MS, and a matrix effect was observed in the case of grapes but not in must and wine. Recovery of spiroxamine from fortified samples at 0.02 to 5.0 mg/kg ranged from 78-102% for grapes and must, with relative standard deviation (RSD) <13%; for red and white wines, recoveries ranged from 90 to 101% with RSD <9%. The limit of quantification was 0.02 mg/kg for grapes, must, and wine or 0.10 mg/kg for grapes, depending on the extraction procedure used.     

Determination of carbendazim,thiabendazole, and<Emphasis Type="Italic"> o-</Emphasis>phenylphenol residues in lemons by HPLC following sample clean-up by ion-pairing

An efficient analytical method is presented involving effective sample clean-up with solid-phase extraction and HPLC-UV analysis for the simultaneous determination of carbendazim, thiabendazole, and o-phenylphenol residues in lemons. Sample preparation involves extraction with acetonitrile acidified with trifluoroacetic acid and an ethyl acetate/petroleum ether mixture. Purification of the crude extract was carried out with liquid–liquid partitioning after addition of an aqueous ammonia solution. Final clean-up was performed on polymeric reversed-phase cartridges pretreated with sodium dodecyl sulfate. Chromatographic analysis was performed on a reversed-phase HPLC column isocratically eluted with an acetonitrile/water/ammonia mixture and UV detection at 254 nm. The chromatographic method is repeatable, reproducible, and sensitive. Fungicide recoveries from lemon samples fortified at levels of 5 and 1 mg kg^–1 were 81–85% for carbendazim, 96–98% for thiabendazole, and 81–106% for o-phenylphenol with coefficients of variation of 2.5–7.4%. Detection limits for carbendazim, thiabendazole, and o-phenylphenol in lemons were 0.21, 0.27, and 0.51 mg kg^–1, respectively.