Fixed points of non-Newtonian contraction mappings on non-Newtonian metric spaces

The study of non-Newtonian calculi was started in 1972 by Grossman and Katz. These calculi provide an alternative to the classical calculus and they include the geometric, anageometric and bigeometric calculi, etc. Recently, Çakmak and Ba?ar (2002) have studied the concept of non-Newtonian metric. Also they have given the triangle and Minkowski’s inequalities in the sense of non-Newtonian calculus. In this paper, we introduce a fixed point theory by defining some topological structures of the relevant non-Newtonian metric space.     

Site-specific interactions of Cu(II) with alpha and beta-synuclein: bridging the molecular gap between metal binding and aggregation

The aggregation of alpha-synuclein (AS) is a critical step in the etiology of Parkinson's disease (PD) and other neurodegenerative synucleinopathies. Protein-metal interactions play a critical role in AS aggregation and might represent the link between the pathological processes of protein aggregation and oxidative damage. Our previous studies established a hierarchy in AS-metal ion interactions, where Cu(II) binds specifically to the protein and triggers its aggregation under conditions that might be relevant for the development of PD. In this work, we have addressed unresolved structural details related to the binding specificity of Cu(II) through the design of site-directed and domain-truncated mutants of AS and by the characterization of the metal-binding features of its natural homologue beta-synuclein (BS). The structural properties of the Cu(II) complexes were determined by the combined application of nuclear magnetic resonance, electron paramagnetic resonance, UV-vis, circular dichroism spectroscopy, and matrix-assisted laser desorption ionization mass spectrometry (MALDI MS). Two independent, noninteracting copper-binding sites with significantly different affinities for the metal ion were detected in the N-terminal regions of AS and BS. MALDI MS provided unique evidence for the direct involvement of Met1 as the primary anchoring residue for Cu(II) in both proteins. Comparative spectroscopic analysis of the two proteins allowed us to deconvolute the Cu(II) binding modes and unequivocally assign the higher-affinity site to the N-terminal amino group of Met1 and the lower-affinity site to the imidazol ring of the sole His residue. Through the use of competitive chelators, the affinity of the first equivalent of bound Cu(II) was accurately determined to be in the submicromolar range for both AS and BS. Our results prove that Cu(II) binding in the C-terminal region of synucleins represents a nonspecific, very low affinity process. These new insights into the bioinorganic chemistry of PD are central to an understanding of the role of Cu(II) in the fibrillization process of AS and have implications for the molecular mechanism by which BS might inhibit AS amyloid assembly.     

Core-shell nanoparticles: characterization and study of their use for the encapsulation of hydrophobic fluorescent dyes

Core-shell nanocapsules intended to be used as drug scavengers were prepared using a surfactant mixture containing octadecyltrimethoxysilane (OTMS) as a reactive amphiphile, to form spherical templates. A siloxane shell was grown on the surface of the templates by reacting tetramethoxysilane (TMOS) with the silanol groups obtained after the hydrolysis and condensation of OTMS. Dynamic light scattering (DLS) showed that particles with diameters in the range of 100-200 nm were obtained, with core and shell sizes controlled by varying component compositions. Atomic force microscopy (AFM) was used to study the effect of the silica coating of the templates on their robustness after deposition on a substrate. Subsequently, we present studies on the encapsulation of two hydrophobic fluorescent dyes, which are sensors of polarity and rigidity. Steady-state fluorescence spectroscopy was used to examine the fluorescence response of the dyes before and after shell growth. Changes in the emission of the encapsulated dyes were related to changes in the polarity and rigidity of the microenvironment where the dyes were located and correlated to the AFM results. Finally, dye-free core-shell particles were used to sequester the dyes from aqueous suspensions. Fluorescence of the sequestered species was compared to the dye-loaded particles to determine the final fate of the fluorophores in the nanoparticles.     

Effect of the presence of strong and weak electrolytes on the existence of uniaxial and biaxial nematic phases in lyotropic mixtures

The lyotropic mixture of potassium laurate/decanol/water presenting only the uniaxial nematic calamitic phase was doped with one strong (potassium chloride, KCl) and 11 weak electrolytes with phenyl-rings (DL-mandelic acid, benzoic acid, DL-phenyllactic acid, phenylacetic acid, phenol and phenylmethanol) and with cyclohexyl-ring (RS-hexahydromandelic acid, cyclohexanecarboxylic acid, cyclohexaneacetic acid, cyclohexanol and cyclohexylmethanol), separately. We also chose two nonpolar dopant molecules, benzene and cyclohexane, for the comparison of them with weak electrolytes, since they are located in the hydrocarbon core of the micelle. The nematic phase sequences, in particular the presence of the biaxial nematic phase, were investigated as a function of the dopant molar concentration and temperature. The laser conoscopy and small-angle X-ray scattering techniques were used to characterise the different nematic phases. Weak electrolytes having –COOH group as polar part were found to be very effective in stabilising the three nematic phases (two uniaxial and a biaxial). Guest molecules with only the –OH group did not show any effect on the stabilisation of other nematic phases. The experimental results are interpreted considering the screening effect of the hydrophilic parts of the dopants on the repulsion between the polar heads of the main amphiphilic molecules at micelle surfaces. This process favours the increase of the more flat micellar surfaces of micelles, which triggers the orientational fluctuations responsible for the biaxial and discotic nematic phases.     

Synthesis,characterization and non-linear optical properties of two mononuclear Cu(II) complexes of 2,6-bis(1-butylbenzimidazol-2-yl)pyridine

Two copper(II) complexes, [Cu(L)(N₃)₂]·MeOH and [Cu(L)(NCS)₂]·MeOH, were prepared and characterized by spectroscopic, analytical, and quantum chemical studies, where L is 2,6-bis(1-butylbenzimidazol-2-yl)pyridine. X-ray quality crystals of [Cu(L)(N₃)₂]·MeOH were obtained by slow evaporation of MeOH solution of the complex. Molecular structure of [Cu(L)(N₃)₂]·MeOH was determined by X-ray crystallography. The asymmetric unit contains one [Cu(L)(N₃)₂] and one MeOH molecule. Cu(II) in [Cu(L)(N₃)₂]·MeOH is five-coordinate, bonded to five nitrogens (three from L and two from two azide anions). Coordination geometry around Cu(II) center is distorted square-pyramidal with τ value of 0.065. Optimized geometries, IR spectra, and non-linear optical properties of the complexes were obtained by computational studies based on density functional theory (DFT) with M062X method. NLO properties of these complexes were investigated computationally and both complexes exhibit better NLO properties than urea.     

Pd(II) complexes of novel phosphine ligands: Synthesis,characterization, and catalytic activities on Heck reaction

Novel phosphine oxides, (((3-methylpyridin-2-yl)amino)methyl)diphenylphosphine oxide (1) and diphenyl((pyrazin-2-ylamino)methyl)phosphine oxide (2), were synthesized and characterized. Phosphines ligands (3 and 4) were obtained by the reduction of 1 and 2 with AlH₃, monitored by ³¹P NMR spectroscopy. Pd(II) complexes of 3 and 4 were synthesized and characterized (5 and 6). The catalytic activity of 5 and 6 was tested on the reaction of styrene with both activated and deactivated aryl bromides in air. The results of the catalytic experiments were discussed through DFT calculations.     

Electron density topological properties are useful to assess the difference between hydrogen and dihydrogen complexes

B3LYP/6-31++G(d,p) and MP2/6-31++G(d,p) calculations for a series of hydrogen- and dihydrogen-bonded systems have been carried out in order to analyze the topology of the electron density and the energy densities at the respective energy-optimized bond critical points. Even though there are no significant differences when these properties are represented as a function of the dimerization energy, they can be separated into two well-defined sets if those properties are correlated with intermolecular distances. When analyzing the dependence of various properties with equilibrium bond lengths, the specific trends of dihydrogen bond systems consist of (a) lower electron density at the bond critical point, and (b) lower concentration/depletion of that density which can be translated in a different behavior for the Laplacian components. Furthermore, the sets of molecules form two different plots which allow for a valuable classification between hydrogen- and dihydrogen-bonded systems.     

TG,DTA and X-ray thermodiffraction study of wall paintings from the fifteenth century

Journal of Thermal Analysis and Calorimetry - In this work, it is reported that thermal analysis techniques such as TG, DTA and X-ray thermodiffraction, performed in air or nitrogen atmosphere, are...     

Structural Formulas for Orthogonal Matrix Polynomials Satisfying Second-Order Differential Equations,II

We develop structural formulas satisfied by some families of orthogonal matrix polynomials of size 2 × 2 satisfying second-order differential equations with polynomial coefficients. We consider here three one-parametric families of weight matrices, namely,

Amperometric Lactate Biosensor Based on Carbon Paste Electrode Modified with Benzo[c]cinnoline and Multiwalled Carbon Nanotubes

Amperometric lactate biosensor based on a carbon paste electrode modified with benzo[c]cinnoline and multiwalled carbon nanotubes is reported. Incorporation of benzo[c]cinnoline acting as a mediator and multiwalled carbon nanotubes providing a conduction pathway to accelerate electron transfer due to their excellent conductivity into carbon paste matrix resulted in a high performance lactate biosensor. The resulting biosensor exhibited a fast response, high selectivity, good repeatability and storage stability. Under the optimal conditions, the enzyme electrode showed the detection limit of 7.0×10^?8 M with a linear range of 2.0×10^?7 M–1.1×10^?4 M. The usefulness of the biosensor was demonstrated in serum samples.