Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients

It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada–Watanabe theorem (Yamada and Watanabe, 1971, [31,32]) and the Feller test for explosions (Feller, 1951, 1954), there exists a unique stationary distribution with respect to the Markov semigroup of transition probabilities. We consider systems on a restricted domain $D$ of the phase space $\mathbb{R}$ and study the rate of convergence to the stationary distribution. Using a geometrical approach that uses the so called free energy function on the density function space, we prove that the density functions, which are solutions of the Fokker–Planck equation, converge to the stationary density function exponentially under the Kullback–Leibler divergence, thus also in the total variation norm. The results show that there is a relation between the Bakry–Émery curvature dimension condition and the dissipativity condition of the transformed system under the Fisher–Lamperti transformation. Several applications are discussed, including the Cox–Ingersoll–Ross model and the Ait-Sahalia model in finance and the Wright–Fisher model in population genetics.     

Nanocrystallization of an amorphous Fe<Subscript>80</Subscript>B<Subscript>20</Subscript> alloy during severe plastic deformation

The structural evolution of an amorphous Fe₈₀B₂₀ alloy subjected to severe plastic deformation at room temperature or at 200°C was studied. Deformation leads to the formation of α-Fe nanocrystals in an amorphous phase. After room-temperature deformation, nanocrystals are localized in shear bands. After deformation at 200°C, the nanocrystal distribution over the alloy is more uniform. Possible causes of the crystallization of the amorphous phase during severe plastic deformation are discussed.     

Effect of adenine on bacterial translocation using technetium-99m labeled E. coli in an intestinal obstruction model in rats

This study aims to investigate effects of adenine on bacterial translocation (BT) using ^99mTc-labeled E. coli in an intestinal obstruction rat model. In the study twenty-one rats were used. The rats were divided into three groups according to different feeding patterns. The control group (CG) was fed with a standard chow diet for 7 days. Group A1 and group A2 were fed with adenine supplemented chow diet for 7 days. At the end of the feeding period, after all groups was submitted intestinal obstruction. ^99mTc-E. coli was injected into the rats’ terminal ileum under anesthetic. The rats were sacrificed under aseptic conditions at 24th h after the surgery. The uptake of ^99mTc-E. coli was determined in organs such as the liver, mesenteric lymph nodes, spleen and ileum. Group A1 and group A2 results show that the uptake of ^99mTc-E. coli decreased in the blood and organs comparing to the CG. As a result, it was observed that adenine reduced the level of BT when compared with CG. The beneficial effect of adenine on BT in intestinal obstruction was observed. However, further studies are needed to more clearly assess how this benefit can be achieved.     

Comparison and optimisation of biodiesel production from <Emphasis Type="Italic">Jatropha curcas</Emphasis> oil using supercritical methyl acetate and methanol

In this study, biodiesel has been successfully produced by transesterification using non-catalytic supercritical methanol and methyl acetate. The variables studied, such as reaction time, reaction temperature and molar ratio of methanol or methyl acetate to oil, were optimised to obtain the optimum yield of fatty acid methyl ester (FAME). Subsequently, the results for both reactions were analysed and compared via Response Surface Methodology (RSM) analysis. The mathematical models for both reactions were found to be adequate to predict the optimum yield of biodiesel. The results from the optimisation studies showed that a yield of 89.4 % was achieved for the reaction with supercritical methanol within the reaction time of 27 min, reaction temperature of 358°C, and methanol-to-oil molar ratio of 44. For the reaction in the presence of supercritical methyl acetate, the optimum conditions were found to be: reaction time of 32 min, reaction temperature of 400°C, and methyl acetate-to-oil molar ratio of 50 to achieve 71.9 % biodiesel yield. The differences in the behaviour of methanol and methyl acetate in the transesterification reaction are largely due to the difference in reactivity and mutual solubility of Jatropha curcas oil and methanol/methyl acetate.     

A Nucleophilic Addition of Acetone Enolate to (<Emphasis Type="Italic">E</Emphasis>)-Alkyloxindolylideneacetates

Summary. The reaction of (E)-(2-oxo-1,2-dihydroindol-3-ylidene)acetic acid esters with dry acetone at 70°C in presence of aluminum oxide as a catalyst led to the formation of an addition product as a mixture of two isomers. When the same reaction was carried out in presence of morpholine as a base, the unexpected spiro-product was obtained beside the two isomers. Methylation of the latter with methyl iodide in acetone in presence of anhydrous potassium carbonate yielded the corresponding methylated products, whereas methylation of the starting material by the same procedure gave an N-methylated product and the unexpected dispiro-compound. The reaction mechanisms are considered and the structural assignments of the new compounds are based on the chemical and spectroscopic evidences. The structure of the dispiro-product was derived by X-ray analysis.     

Adsorption of N-Nitrosodiethylamine and N-Nitrosodimethylamine on Activated Carbon: A Pre-Concentration Procedure for Gas Chromatographic Analysis

In this study, a rapid pre-concentration procedure, which employs powdered activated carbon as a clean-up and pre-concentration material, is described for the gas chromatographic analysis of N-nitrosodiethylamine (NDEA) and N-nitrosodimethylamine (NDMA) in aqueous solutions. It was found that powdered activated carbon is suitable for the adsorption of volatile N-nitrosamine compounds from aqueous solutions. Adsorption efficiency with spiked beer samples (alcohol content 5% v/v) was found to be 80.5% (NDMA) and 89.4% (NDEA) and recovery of extraction from activated carbon was calculated as 82.1% (NDMA) and 89.7% (NDEA), respectively. The effect of 100µgmL^–1 of tannic acid on the adsorption was also studied, and no significant effect on the adsorption and extraction of volatile N-nitrosamine compounds was found.     

Di­aqua­bis­(pyridine‐2‐carbox­amide‐κ2N1,O2)­nickel(II) disaccharinate tetrahydrate

In the crystal structure of the title compound, [Ni(C₆H₆N₂O)₂(H₂O)₂](C₇H₄NO₃S)₂·4H₂O or [Ni(pia)₂(H₂O)₂](sac)₂·4H₂O (pia is picolin­amide or pyridine‐2‐carbox­amide, and sac is the saccharinate anion), the Ni²⁺ cation, located on a centre of symmetry, is coordinated by two symmetry‐related aqua ligands together with a pair of symmetry‐related bidentate pia mol­ecules and exhibits a distorted octahedral environment. The unique unligated sac anion in the asymmetric unit resides on a general position and has a single negative charge. The coordinated water mol­ecules link the sac ions to the metal complex via O—H⋯O hydrogen bonds. In addition, the sac ions are linked to the metal complex via intermolecular π–π interactions between the benzene ring of the sac ion and the pyridine ring of a pia ligand. Each uncoordinated water mol­ecule is hydrogen bonded to sac moieties through O—H⋯O and O—H⋯N hydrogen bonds.     

Phase equilibria in the Al-Cu-Fe system at a temperature of 853 K in the aluminum enriched region

The phase equilibria in the Al-Cu-Fe system at 853 K in the aluminum enriched region are studied using the methods of scanning and transmission electron microscopy, X-ray phase analysis, and electron probe microanalysis. An isothermal cross section of the system is constructed. Crystal lattice parameters of the phases based on binary and ternary compounds are determined. Approximant phases are not found to form in the quasicrystalline i-phase region.     

Stable conformations of tripeptides in aqueous solution studied by UV circular dichroism spectroscopy

Determination of the precise solution structure of peptides is of utmost importance to the understanding of protein folding and peptide drugs. Herein, we have measured the UV circular dichroism (UVCD) spectra of tri-alanine dissolved in D(2)O, H(2)O, and glycerol. The results clearly show the coexistence of a polyproline II or 3(1)-helix and a somewhat disordered flat beta-strand conformation, in complete agreement with recent predictions from spectroscopic data (Eker et al. J. Am. Chem. Soc. 2002, 124, 14 330-14 341). A thermodynamic analysis revealed that enthalpic contributions of about 11 and 17 kJ/mol stabilize polyproline II in D(2)O and H(2)O, respectively, but at room temperature they are counterbalanced by entropic contributions, which clearly favor the more disordered beta-strand conformation. It is hypothesized that this delicate balance is the reason for the variety of structural propensities of amino acid residues in the absence of nonlocal interactions. The isotope effect yielding a higher occupation of polyproline II in H(2)O with respect to D(2)O strongly suggests that a hydrogen-bonding network involving the peptide and water molecules in the hydration shell plays a major role in stabilizing this conformation. The equilibrium between polyproline II and beta-strand is practically maintained in glycerol, which suggests that glycerol can substitute water as stabilizing solvent for the polyproline II conformation. We also measured the UVCD spectra of tri-valine and tri-lysine (both at acidic pD) in D(2)O and found them to adopt a flat beta-strand and left-handed turn structure, respectively, in accordance with recent analyses of vibrational spectroscopy data. Generally, the present study adds substantial evidence to the notion that the so-called random coil state of peptides is much more structured than generally assumed.     

Oxidation of cyclohexane catalyzed by metal-ion-exchanged zeolites

The ion-exchange rates and capacities of the zeolite NaY for the Cu(II), Co(II), and Pb(II) metal ions were investigated. Ion-exchange equilibria were achieved in approximately 72 h for all the metal ions. The maximum ion exchange of metal ions into the zeolite was found to be 120 mg Pb(II), 110 mg Cu(II), and 100 mg Co(II) per gram of zeolite NaY. It is observed that the exchange capacity of a zeolite varies with the exchanged metal ion and the amount of metal ions exchanged into zeolite decreases in the sequence Pb(II) > Cu(II) > Co(II). Application of the metal-ion-exchanged zeolites in oxidation of cyclohexane in liquid phase with visible light was examined and it is observed that the order of reactivity of the zeolites for the conversion of cyclohexane to cyclohexanone and cyclohexanol is CuY > CoY > PbY. It is found that conversion increases by increase of the empty active sites of a zeolite and the formation of cyclohexanol is favored initially, but the cyclohexanol is subsequently converted to cyclohexanone.