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.     

Neighbourhood-Perfect Line Graphs

We show that the line graph of any balanced hypergraph is neighbourhood-perfect. This result is a hypergraphic extension of a recent theorem in [GKLM] saying that the line graphs of bipartite graphs are neighbourhood-perfect. The note contains also a graphical extension of the same theorem: the characterization of all graphs with neighbourhood-perfect line graph. The proof relies on a characterization of neighbourhood-perfect graphs among line graphs in terms of forbidden induced subgraphs.     

Some aromatic polyimides based on diamines containing hydrazo group and ether linkages

Three new hydrazo-bridged diamines, 4,4′-bis [4-(4-aminophenyloxy) phenylhydrazyl] biphenyl (BPD-2), 4,4′-bis [4-(4-aminophenyloxy) phenylhydrazyl] biphenyl ether (SPD-2) and 4,4-bis [4-(4-aminophenyloxy) phenyl] hydrazine (APD-2), were synthesized by the reduction of three azo-diols, 4,4′-bis (4-azo-1-hydroxyphenyl) biphenyl (BPD), 4,4′-bis (4-azo-1-hydroxyphenyl) biphenyl ether (SPD) and azo-4-hydroxybenzene (APD), and polymerized with pyromellitic dianhydride (PM), 3,3′,4,4′-benzophenone tetracarboxylic acid dianhydride (BP) and 3,4,9,10-perylenetetracarboxylic acid dianhydride (PR) either by one-step solution polymerization or by two-step procedure which includes ring-opening polyaddition to give poly(amic acid) followed by cyclic dehydration to polyimide. The monomers and polyimides were characterized by their elemental analyses, FTIR and ¹H NMR spectroscopy. Glass transition temperatures of the polymers are quite high (175-310 °C), characteristic of polyimides. The decomposition temperatures for 10% weight loss fall in the range of 280-575 °C in nitrogen. Activation energies of pyrolysis for each of the polymers calculated from Horowitz and Metzger's method are also high (52.54-95.28 kJ mol⁻¹). The inherent viscosities of the polyimides at a concentration of 0.5 g/dl in DMF range from 0.94 to 1.93 dl/g.     

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.     

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.