Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces

In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393]. Examples to support our new results are given.     

Fluorescent Flavin/PVP-Coated Silver Nanoparticles: Design and Biological Performance

A red-emitting fluorescent Riboflavin (RF)/Polyvinylpyrrolidone (PVP)-coated silver nanoparticles system, λ_em?=?527 nm, Φ?=?0.242, with a diameter of the metallic core of 27.33 nm and a zeta potential of ? 25.05 mV was prepared and investigated regarding its biological activity. We found that PVP has a key role in RF adsorption around the SNPs surface leading to an enhancement of antioxidant properties (～70%), low cytotoxicity (> 90% cell viability, at 50 µL/mL, after 48 h of incubation) as well as to an efficient process of its cellular uptake (～ 60%, after 24 h of incubation) in L929 cells. The results are relevant concerning the involvement of RF and its coenzymes forms in SNPs - based systems, in cellular respiration as well as for future studies as antioxidant marker system on tumoral cells for viewing and monitoring them, by cellular imaging.

     

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.     

Thermal behavior of some new triazole derivative complexes

A series of new complexes with mixed ligands of the type [ML(C₃H₃O₂)₂]·nH₂O (((1) M=Mn, n=1; (2) M=Co(II), n=2; (3) M=Ni(II), n=4; (4) M=Cu(II), n=1.5; (5) M=Zn(II), n=0; L=3-amino-1,2,4-triazole and (C₃H₃O₂)=acrylate anion) were synthesized and characterised by chemical analysis and IR data. In all complexes the 3-amino-1,2,4-triazole acts as bridge while the acrylate acts as bidentate ligand except for complex (5) where it is found as unidentate. The thermal behaviour steps were investigated in nitrogen flow. The thermal transformations are complex processes according to TG and DTG curves including dehydration, acrylate ion and 3-amino-1,2,4-triazole degradation respectively. The final products of decomposition are the most stable metal oxides, except for complex (4) that leads to metallic copper.     

Antioxidant activity of rosemary extracts in solution and embedded in polymeric systems

The rosemary extract was encapsulated in polyethylene or in covalently-based network gels. The covalent gels were obtained by the reaction of isocyanate end-capped polyethylene glycol (PEG) with β-cyclodextrin or glycerol. The 2,2-diphenyl-1-picrylhydrazyl (DPPH) assay was used to evaluate the antioxidant activity (AA) of rosemary extract entrapped in polymeric structures and in ethanol or water solutions. The AA of the rosemary extract was determined using a DPPH radical for samples prepared in ethanol, and a water-soluble derivative, the sulphonated DPPH radical (DPPH-SO₃Na), for the rosemary extract in water. Formulation of the rosemary extract in polymeric gels ensures a rapid release which determines the AA values similar to those in solution.     

Towards a receptor-free immobilization and SERS detection of urinary tract infections causative pathogens

Based on molecular-specific surface-enhanced Raman scattering (SERS) spectroscopy we were able to discriminate between rough and smooth strains of Escherichia coli and Proteus mirabilis bacteria. For this purpose, bacteria have been immobilized through electrostatic forces by inducing a positive charge on the glass slide. This way, SERS spectra on bacterial biomass and also on single bacteria could be recorded in less than 2 h, by using concentrated silver nanoparticles as SERS-active substrate. Single-bacterium SERS spectral fingerprints showed to be sensitive to the presence of the O-antigen at strain level and to the microorganisms growth phase. By using principal component analysis (PCA) on the SERS spectra recorded from E. coli and P. mirabilis, these two uropathogens could be fairly discriminated.     

The Cu- and Zn-complex-catalyzed methanolysis of the chemical warfare nerve agents soman,sarin, and VX

The catalytic methanolysis of the chemical warfare nerve agents soman, sarin, and VX was investigated by using Cu or Zn complexes. Although VX withstood decontamination, the decomposition yield being around 96%, the soman and sarin deposited on different surfaces were almost fully destroyed under ambient conditions. The catalytic tests performed on a wide range of contaminated surfaces confirm the activity of the investigated catalytic systems, these complexes being suitable, from an economical point of view, for use in the formulation of a possible decomposition kit with military or civilian applicability.     

Microfabrication techniques using focused ion beams and emergent applications.

The application of focused ion beam (FIB) machining in several technologies aimed at microstructure fabrication is presented. These emergent applications include the production of micromilling tools for machining of metals and the production of microsurgical tools. An example of the use of microsurgical manipulators in a circulatory system measurement is presented. The steps needed to transform the laboratory fabrication of these tools and manipulators into a routine FIB production process are discussed. The ion milling of three-dimensional cavities by the exact solution of a mathematical model of the FIB deflection is demonstrated. A good agreement between the model calculation and the ion beam control has been obtained for parabolic and cosine cross-section features with planes of symmetry.     

Intercalation of halogen fluorides into graphite

IF₇ intercalates into graphite accompanied by the partial fluorination of the graphite host. The intercalated species was identified as IF₅ by IR and ¹⁹F nmr spectroscopies. Mass spectrometric analyses of the gases evolved from the intercalate showed only IF₅ and fluorocarbons. Iodine pentafluoride intercalates only in the presence of HF, yielding a compound with the stoichiometry C₈IF₅ and no fluorination of the graphite host. Careful elimination of even traces of HF resulted in no intercalation. Evolved gas analysis showed that the only species recovered from the intercalation was IF₅. The remaining interhalogens, ClF₅, ClF₃, BrF₅ and BrF₃ all intercalate into graphite with extensive fluorination of the lattice. In the case of these four compounds, the intercalate proved to be more difficult to characterize, e.g. stoichiometry was often variable, and ¹⁹F nmr yielded resonances that did not agree with any known halogen fluorides. Thermal decomposition of these intercalates showed little or no gas evolution until relatively high temperatures were reached, whereupon Cl₂ or Br₂ was evolved, followed by fluorocarbons.