Common fixed points of two maps in cone metric spaces

We prove the existence of points of coincidence and common fixed points of a pair of self-mappings satisfying a generalized contractive condition in cone metric spaces. Our results generalize several well-known recent and classical results.      

Geometry of crumpled paper

We measure the geometry of a crumpled sheet of paper with laser-aided topography and discuss its statistical properties. The curvature of an elastoplastic fold scales linearly with applied force. The curvature distribution follows an exponential form with regions of high curvature localized along ridges. The measured ridge length distribution is consistent with a hierarchical model for ridge breaking during crumpling. A large fraction of the ridges are observed to terminate without bifurcating, and the ridge network connectedness is not as complete as anticipated. The self-affinity of the surface is characterized by a Hurst exponent of 0.71+/-0.01 in contrast with previous results.     

Thermal Degradation Studies of Complexes of a Derivative of Phenhomazine (Dibenzo[b,f][1:5]diazocine‐6:12‐Dione (PHZD)) by Thermoanalytical Techniques

Some of the bis‐complexes of a derivative of phenhomazine (dibenzo[b,f][1:5]diazocine‐6:12‐dione; PHZD) with Ni(II), Cu(II), Co(II), Cd(II), Zn(II) and Hg(II) of the general formula M(PHZD)₂X₂ [where X = C1, Br and I], were prepared and identified. These complexes have been characterised on the basis of elemental analysis, and spectroscopic, magnetic and conductance data. The thermal mode of decomposition and thermal stability of these complexes was investigated on the basis of the respective thermal curves in a static air atmosphere. The thermoanalytical investigations indicate that these complexes undergo two‐step changes as temperature is raised, except for Cd(II) and Hg(II) complexes, with the formation of metal oxides as end product. The degradation mechanism of the complexes has also been proposed.     

Biosynthesis of TiO2 nanoparticles and their superior antibacterial effect against human nosocomial bacterial pathogens

Research on Chemical Intermediates - Antibacterial titanium dioxide nanoparticles (TiO2NPs) were biologically synthesized by microwave irradiation of Cissus quadrangularis extract followed by...     

Molecular Structure of (1-Benzyl-4-phenyl-1H-1,2,3-triazol-5-yl)(4-bromophenyl) methanone: A Combined Experimental and Theoretical Study

One-pot three component reaction was used to synthesize 1,4,5-trisubstituted 1,2,3-triazole(A) from the corresponding acid chloride, benzyl azide and 1-copper(I) phenylethyne. The molecular structure was determined by single-crystal X-ray analysis. The compound crystallizes in the orthorhombic space group Pbca, a = 14.9815(14), b = 9.6496(10), c = 25.528(2) A, Z = 8. Furthermore, crystal packing demonstrated a molecular wall-like structure based on supramolecular chains of A, stabilized by CH···O, CH···Br, N···C and CH···π interactions. Molecular geometry in the ground state has been determined by density functional theory(DFT) by B3LYP/6-311G* basis set and compared with the experimental data. The computed vibrational frequencies are compared with the experimental FT-IR data and frontier molecular orbital analyses were performed at the same level of theory. Theoretical parameters are in good agreement with the corresponding X-ray diffraction values.     

Study of H-bonded assemblies of the solvates of anthracene derivatives: guest effect on the crystal symmetry and spectroscopic properties

Two solvates of title compound 1-acetyl-3-naphthyl-5-(9-anthryl)-2-pyrazoline solvate(ANNP) (1a) with chloroform (1b) and acetic acid (1c) and a single crystal of another title compound 1-acetyl-3-(4-chloro)phenyl-5-(9-anthryl)-2-pyrazoline (ACAP) (2a) and its adduct with phenol (2b) were afforded via solution growth technique. The structure of these solids were confirmed and verified by multiple techniques such as single crystal X-ray diffraction (SCXRD) analysis, PXRD, DSC/TGA and Infrared spectroscopy. Structural analysis indicates that guest inclusion results not only in stronger hydrogen bonds, but also in a larger number of favourable C–H?π interactions between ANNP/ACAP molecules. The solvates show symmetry reduction guest effect comparing with the guest free molecules of ANNP and ACAP. Moreover, characteristic changes have been observed in the Infrared bands of the solvates owing to the formation of hydrogen bonds between host–guest.     

A Model on the Mn^2＋ Luminescence Band Redshift with Mn（Ⅱ） Doping and Aggregation within CdS＇Mn Microwires ＊

We report the microphoto-luminescence band redshifts with individual and multi-Mn（Ⅱ） ion emissions within CdS microwires. The localized exciton magnetic polaxons （LEMPs） corresponding to the d-d optical transitions of Mn（Ⅱ） account for this shift. This LEMP emission from the double-, three- and four-Mn（Ⅱ） ions with ferromag- netic coupling after photoexeitation can happen in diluted magnetic semiconductors, except for the individual Mn（Ⅱ） doping. In addition, a simple spin-exchange polaronic model is established to account for these emission peaks well. Through this model, we can verify the local geometry of the Mn（Ⅱ） ions in CdS microwires.     

UV-Visible Spectrometric Study and Micellar Enhanced Ultrafiltration of Alizarin Red S Dye

Ultraviolet spectrometric study of alizarin red S (ARS) showed the substantial change in dye spectra by cationic CTAB as compared to anionic SDS and nonionic TX-100 surfactant. High spectral change by CTAB confirms the anionic nature of ARS dye and thus ARS-CTAB complex formation takes place due to electrostatic force of attraction. A little spectral change by SDS is the result of similarly charged repulsive forces that overcome weak hydrophobic-hydrophobic interaction between dye and surfactant micelles. TX-100 exhibited moderate spectral effect responsive to weak hydrophobic-hydrophobic interaction alone. MEUF study of ARS dye justified the spectral changes and dye rejection percentage (R) decreases in the following order: cationic > nonionic > anionic surfactant. Permeate flux (J) slightly decreases in presence of CTAB and it remains virtually constant for both SDS and TX-100. Addition of copper salt (i.e., CuCl₂) in dye-CTAB complex solution, favors rejection (%) removing dye and copper simultaneously via micellar enhanced ultrafiltration.     

Single-degree-of-freedom model of displacement in vortex-induced vibrations

In contrast to the approach of coupling a nonlinear oscillator that represents the lift force with the cylinder’s equation of motion to predict the amplitude of vortex-induced vibrations, we propose and show that the displacement can be directly predicted by a nonlinear oscillator without a need for a force model. The advantages of the latter approach include reducing the number of equations and, subsequently, the number of coefficients to be identified to predict displacements associated with vortex-induced vibrations. The implemented single-equation model is based on phenomenological representation of different components of the transverse force as required to initiate the vibrations and to limit their amplitude. Three different representations for specific flow and cylinder parameters yielding synchronization for Reynolds numbers between 104 and 114 are considered. The method of multiple scales is combined with data from direct numerical simulations to identify the parameters of the proposed models. The variations in these parameters with the Reynolds number, reduced velocity or force coefficient over the synchronization regime are determined. The predicted steady-state amplitudes are validated against those obtained from high-fidelity numerical simulations. The capability of the proposed models in assessing the performance of linear feedback control strategy in reducing the vibrations amplitude is validated with performance as determined from numerical simulations.