Fixed point theorems in metric spaces

In this paper, we establish two general theorems for equivalence between the Meir–Keeler type contractive conditions and the contractive definitions involving gauge functions. One of these theorems is an extension of a recent result of Lim (On characterization of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120).     

Computational study on the ring distortions of 1,4-dicyanobenzene in the gas phase and in the crystal

A molecular mechanics software enhanced to perform empirical energy calculations on crystals (KESSHOU) was further developed to handle intermolecular electrostatic interactions as well. The packing of the molecules of 1,4-dicyanobenzene and 1,4-diisocyanobenzene in the crystal was studied. The role of the van der Waals and the electrostatic interactions in the balance of nonbonded atom-atom interactions is analyzed. The packing forces are dominated by van der Waals forces. The electrostatic interactions have higher stabilizing contribution for the dicyano isomer than for the diisocyano form. The dependence of the results on the size of the crystal, the molecular mechanics force field (MM2 vs MM3), and the dielectric constant are also assessed. Ab initio MP2/6–311G** geometries of the isolated molecules are in accordance with the observed benzene ring distortions determined by electron diffraction.     

Chemical properties of <Emphasis Type="Italic">N</Emphasis>-polyfluoroethylimidazole and -pyrrole derivatives

Bromination, acylation, nitration, and metallation of imidazole and pyrrole derivatives containing the difluoromethylene fragment at the N atom were studied. 1-(1,1,2,2-Tetrafluoroethyl)pyrrole, 1-(1,1,2,2-tetrafluoroethyl)imidazole, and 1-(2-chloro-1,1,2-trifluoroethyl)imidazole were used as substrates. 1-Alkyl-3-(1,1,2,2-tetrafluoroethyl)- and 1-alkyl-3-(2-chloro-1,1,2-trifluoroethyl)imidazolium iodides were obtained. These can be used as intermediates for preparation of new ionic liquids of the imidazole series and 1-alkyl-3-polyfluoroethylimidazole-2-thiones.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 781–787, March, 2005.     

Influence of Gamma Irradiation on Different Phytochemical Constituents of Dried Rose Hip (Rosa canina L.) Fruits

Gamma irradiation is efficiently applied to many foods, but nevertheless there is a distinct lack of information about the changes of macro- and micronutrients (e.g., carbohydrates, lipids, organic acids, and phenolics) in dried rose hip (RH) fruits. Therefore, in this study, for the first time, the effect of gamma irradiation (10 and 25 kGy) on RH constituents is investigated. Different analytical techniques (GC-FID, HPLC-UV, HPSEC-RID, IR-FT, and SEM) are employed to examine this effect. The irradiation treatment (10 kGy) increased the glucose content by 30% and released cellobiose from RH fruits, thus revealing cellulose destruction. The extractability of total uronic acids increased from 51% (control) to 70.5% (25 kGy-irradiated), resulting in a higher pectin yield (10.8% < 12.8% < 13.4%) and molecular heterogeneity. Moreover, de-esterification was not a major effect of the irradiation-induced degradation of pectin. The sample exposure to the highest dose did not change the content of total carotenoids, β-carotene, and (un)saturated fatty acids, but it affected the tocopherols levels. Gamma rays had a negligible effect on the phenolic constituents and did not affect ORAC and HORAC antioxidant activity. In conclusion, it can be compromised that the exposition of dried RH is safe and can be successfully applied to decontaminate fruits without affecting their nutritional value and biological activity.     

Computational studies on pseudorotaxanes by molecular dynamics and free energy perturbation simulations

A computational scheme that comprises the utilization of the AMBER force field with RESP charges and an explicit solvent model for acetonitrile proved to be useful for studying the structures and energetics of pseudorotaxanes of benzidine and 4,4'-biphenol with cyclobis(paraquat-p-phenylene). The scheme can be further utilized for modeling [2]rotaxanes.     

Determination of selected trace elements in marine biota samples with the application of fast temperature programs and solid sampling continuous source high resolution atomic absorption spectroscopy: method validation

Analytical procedure for the determination of As, Cd, Cu, Ni, Co and Cr in marine biota samples using solid sampling high-resolution continuum source atomic absorption spectrometry (HR CS AAS) and accelerated fast temperature programmes has been developed. Calibration technique based on the use of solid certified reference materials similar to the nature of the analysed sample and statistics of regression analysis were applied. A validation approach in line with the requirements of ISO 17025 standard and Eurachem guidelines was followed. Accordingly, blanks, selectivity, calibration, linearity, working range, trueness, repeatability and reproducibility, limits of detection and quantification and expanded uncertainty for all investigated elements were assessed. The major contributors to the combined uncertainty of the analyte mass fractions were found to be the homogeneity of the samples and the microbalance precision. Traceability to the SI system of units of the obtained with the proposed analytical procedure results was also demonstrated. The potential of the proposed analytical procedure based on solid sampling HR CS AAS technique was demonstrated by direct analysis of marine reference biota samples. Overall, the use of solid sampling HR CS AAS permits obtaining significant advantages for the determination of selected trace elements in marine biota samples, such as straightforward calibration, a high sample throughput, sufficient precision, a suitable limit of detection and reduced risk of analyte loss and contamination.     

Circular Dichroism of Some 2-(Phenylmethyl)pyridine Derivatives

The absolute configuration of the 2-(phenylmethyl)pyridine derivatives 1 – 9 had been established by X-ray diffraction and chemical correlation. Their CD spectra have been studied in different solvents for the free and protonated forms. It has now been found that, from the sign of the strong CD couplet between 270 and 220 nm, which was observable for all these compounds besides 7 and 9 , their absolute configuration can be determined much quicker.     

Stereochemical applications of potential energy calculations : Part V. Conformational studies of some 1,1,2-trisubstituted ethanes by the molecular mechanics method (MM2)

The conformational distribution of some 1,1,2-trisubstituted ethanes was studied by the molecular mechanics method. An overall satisfactory correlation with experimental data is obtained, especially when these refer to experimental conditions excluding possible dimerization.     

New general convergence theory for iterative processes and its applications to Newton–Kantorovich type theorems

Let T:D⊂X→X$T:D\subset X\to X$ be an iteration function in a complete metric space X$X$. In this paper we present some new general complete convergence theorems for the Picard iteration _xn+1=T_xn$x_{n+1}=T{x}_n$ with order of convergence at least r≥1$r\ge 1$. Each of these theorems contains a priori and a posteriori error estimates as well as some other estimates. A central role in the new theory is played by the notions of a function of initial conditions   of T$T$ and a convergence function   of T$T$. We study the convergence of the Picard iteration associated to T$T$ with respect to a function of initial conditions E:D→X$E:D\to X$. The initial conditions in our convergence results utilize only information at the starting point _x0$x_0$. More precisely, the initial conditions are given in the form E(_x0)∈J$E\left(x_0\right)\in J$, where J$J$ is an interval on _R+${\mathbb{R}}_{+}$ containing 0. The new convergence theory is applied to the Newton iteration in Banach spaces. We establish three complete ω$\omega$-versions of the famous semilocal Newton–Kantorovich theorem as well as a complete version of the famous semilocal α$\alpha$-theorem of Smale for analytic functions.     

CO coordination at XNi4 clusters with impurities X = H, C, O. A density functional study

We report a computational investigation of CO adsorption on small nickel clusters that contain single impurity atoms H, C, or O. At bare Ni 4 and clusters with H or O impurity, the most stable coordination of the probe molecule is on top of a Ni atom which interacts with the impurity. The CNi 4 cluster is an exception where 3-fold coordination of CO was determined to be more stable than that on top, however, by 4 kJ/mol only. Our results suggest that the heteroatoms X (X = H, C, O) affect only weakly the reactivity of the cluster with respect to CO; the binding energy of CO in the most stable complexes (CO)XNi 4 increases at most by 10% compared to the value for bare Ni 4, 194 kJ/mol. The impurity induces a small decrease of the CO infrared frequency shift for on-top coordinated CO, compared to Ni 4, because of partial oxidation of the metal moiety. A notable difference is predicted for clusters that contain a C impurity because of the different preferred coordination mode which results in a strong CO frequency red shift of approximately 300 cm (-1). The calculated characteristic CO frequency shifts may be helpful in identifying experimentally clusters with impurity atoms.