Fixed point theorems for mappings with convex diminishing diameters on cone metric spaces

In this work, Cantor’s intersection theorem is extended to cone metric spaces and as an application, a fixed point theorem is derived for mappings with locally power diminishing diameters.     

Photophysical Investigations of Carmoisine Interacting with Conventional Cationic Surfactants Under Different pH Conditions

The present study describes the extent of interactions of an efficient food dye, Carmoisine (CAR), with conventional cationic surfactants, hexadecyltrimethylammonium bromide, and ethylhexadecyldimethylammonium bromide (EHDAB). The study was carried out by quantifying the spectral changes of CAR as a function of premicellar to postmicellar surfactant concentrations at various pH conditions. The quantification of CAR molecules entrapped by cationic micellar systems has been estimated with the help of mathematical models. Binding parameters of each surfactant were calculated using differential spectroscopic method. The enhanced solubilization of dye by switching the pH was observed. In support of the electrostatic forces, the larger and more hydrophobic head group favors the promising solubilization of CAR in the outer region of the micellar interior. These findings extend the proficiency of dye molecule as a reporter for sensing electrostatic environment in lipidic membranes and related organized assemblies.     

Study of projectile fragmentation in the reaction (158 A GeV) Pb + Pb using CR-39

The fragmentation of Pb ions at 158 A GeV energy produced in the interaction with Pb target has been studied using a CR-39 track detector. A stack comprising of 64 detectors was prepared such that a target of 1 cm thickness was sandwiched between the sheets of CR-39. The purpose of this exposure geometry was to calibrate CR-39 with respect to relativistic heavy ions as well as to study the fragmentation of Pb ions at 158 A GeV energy. The exposure was carried out at the SPS beam facility of CERN at normal incidence with a fluence of . Two detectors from the exposed stack have been selected for this study: one before and the other after the target material. After etching, the detectors were scanned using an optical microscope and the etched track lengths and the diameters of the track openings were measured manually. Considering that the lengths of tracks provide the best charge resolution for Z>65, we have measured track lengths for a sufficiently large number of fragments to identify individual charge states for 65<Z<83. The total charge-changing cross section has also been determined.     

An application of a fixed point theorem to best simultaneous approximation

Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.     

High throughput synthesis of diverse 2,5-disubstituted indoles using titanium carbenoids bearing boronate functionality

A titanium benzylidene complex bearing a boronate group converted resin-bound esters into enol ethers. Suzuki cross-coupling with aryl iodides followed by cleavage with acid completed the solid-phase synthesis of 2,5-disubstituted N-Boc-indoles. Also reported is the use of tert-butyllithium and 2-isopropoxy-4,4,5,5-tetramethyl-1,3,2-dioxaborolane to convert an aryl bromide into an arylboronate in the presence of a dithiane, with simultaneous reduction of an aryl azide to an amine.     

Simultaneous determination of potassium clavulanate and cefixime in synthetic mixtures by high-performance liquid chromatography

A simple, precise, and sensitive high-performance liquid chromatographic method was developed and validated for the simultaneous determination of potassium clavulanate and cefixime in synthetic mixture form. The analytes were separated on a C18 column by using 0.03 M disodium hydrogen phosphate buffer (pH 6.5)-methanol (84 + 16, v/v) as the mobile phase with detection at 220 nm. The method exhibited high sensitivity and good linearity in the concentration ranges of 12.5-62.5 and 20-100 microg/mL for potassium clavulanate and cefixime, respectively. The total run time for the 2 components was <8 min, and the average recovery was >101.5% with a relative standard deviation of <1.0%. The proposed method was validated according to guidelines of the International Conference on Harmonization by evaluation of linearity, recovery, selectivity, robustness, limits of detection and quantitation, and within- and between-day precision. The results obtained for the synthetic mixture show that the method is highly precise and accurate for the simultaneous determination of potassium clavulanate and cefixime.     

Spectroscopic properties of Dy(3+) ions in NaF-B(2)O(3)-Al(2)O(3) glasses

This paper reports the optical properties of Dy(3+) in sodium fluoroborate glasses of the type XNaF.(89-X)B(2)O(3).10 Al(2)O(3).1Dy(2)O(3) (where X=8, 12, 16, 20 and 24). Judd-Ofelt intensity parameters (Omega(2), Omega(4), Omega(6)) are derived from the absorption spectra. The Judd-Ofelt theory has been applied to interpret the local environment of Dy(3+) ions and bond covalency of RE-O bond. These parameters have been used to calculate radiative transition probabilities (A(rad)), lifetimes (tau(R)) and branching ratios (beta(R)) for the excited level (4)F(9/2). The predicted values of tau(R) are compared with the measured values for (4)F(9/2) level for five glass compositions (Glass (A-E)). The stimulated emission cross-section sigma(lambda(P)) are also evaluated for the (4)F(9/2)-->(6)H(J) (J=11/2, 13/2, and 15/2) transitions.     

Fixed points for generalized contractions and applications to control theory

The concepts of “weak/strong topological contraction” and a generalization of Banach contraction mappings called “p$p$-contraction” are introduced and used to prove fixed point theorems for self-mappings from a topological/metric space into itself satisfying topological contraction/metric p$p$-contraction, respectively. Certain non-linear integral equations defined on C[a,b]$C[a,b]$ satisfying generalized Lipschitzian conditions can easily be solved by applying these theorems. In the sequel, we shall study the possibility of optimally controlling the solution of the ordinary differential equation via dynamic programming.     

Electrospun PDA‐CA Nanofibers toward Hydrophobic Coatings

Nowadays, encapsulated dyes in a polymeric matrix have opened up new perspectives in many applications such as filtration of subatomic particles, composite reinforcement, multifunctional membranes, tissue engineering scaffolds, wound dressing, coatings, medical purposes as well as sensors. In the presented work, we report on electrospinning neat peryelene dianhydride based thermoplastic elastomers. Perylene‐3, 4,9, 10‐tetracarboxylic dianhydride (PDA) is encapsulated into cellulose acetate (CA) electrospun fibers, which was prepared from 12 % cellulose acetate solution, at 20 kV with a distance of 10 cm. The flow rate was 0.2 ml · h^–1. These water repellent nanofibrous coatings are anticipated to serve as hydrophobic coatings. Scanning electron microscope is used to study the properties of the electrospun PDA‐CA nanofibers.     

Structural and Magnetic Properties of Chemically Synthesized Pd-Modified NiFe2O4 Nanoparticles

Magnetic nanoparticles of NiFe₂O₄-Pd composites have been synthesized using a simple, low cost, sol-gel auto-combustion method. As-prepared samples were sintered at 800 ℃ for 6 h in order to develop the crystalline phase. X-ray diffraction confirmed the spinel structure of the ferrite samples. Structural morphology and size of the nanoparticles were evaluated using a field emission scanning electron microscope. Magnetic hysteresis loops were obtained at 300 and 100 K using a physical properties measurement system. The value of saturation magnetization was observed to decrease at the temperatures with the increase of Pd contents up to 5% but then a sudden rise in saturation magnetization was observed for the addition of 10% Pd in NiFe₂O₄.