A result of suzuki type in partial G-metric spaces

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.     

On dimension of the Schur multiplier of nilpotent Lie algebras

Let L be an n-dimensional non-abelian nilpotent Lie algebra and $ s(L) = \frac{1} {2}(n - 1)(n - 2) + 1 - \dim M(L) $ s(L) = \frac{1} {2}(n - 1)(n - 2) + 1 - \dim M(L) where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2.     

Synthesis and application of modified poly (styrene‐alt‐maleic anhydride) networks as a nano chelating resin for uptake of heavy metal ions

A chelating resin based on modified poly (styrene‐alt‐maleic anhydride) with 3‐aminobenzoic acid was synthesized. This modified resin was further reacted by 1,2‐diaminoethane or 1,3‐diaminopropane in the presence of ultrasonic irradiation to prepare tridimensional chelating resin for the removal of heavy metal ions from aqueous solutions. The adsorption behavior of Fe(II), Cu(II), Zn(II) and Pb(II) ions was investigated by synthesized chelating resins in various pH. Among the synthesized resins, CSMA‐AB1 and CSMA‐AB2 demonstrated a high affinity for the selected metal ions compared to SMA‐AB, and the order of removal percentage changes as follow: Fe(II) > Cu(II) > Zn(II) > Pb(II). The adsorption of all metal ions in acidic medium was moderate, and it was favored at the pH value of 6 and 7. Also, the prepared resins were examined for removal of metal ions from industrial wastewater and were shown to have a very efficient adsorption in the case of Cu(II), Fe(II) and Pb(II); however, the adsorption of Zn(II) was lower than others. The resin was characterized by Fourier transform infrared spectroscopy, scanning electron microscopy, X‐ray diffraction analysis and thermogravimetric analysis/derivative thermogravimetry. Copyright © 2012 John Wiley & Sons, Ltd.     

Water-Accelerated Selective Synthesis of 1,2-Disubstituted Benzimidazoles at Room Temperature Catalyzed by Br⊘nsted Acidic Ionic Liquid

An environmentally benign method for the rapid and selective synthesis of 2-aryl-1-arylmethyl-1H-1,3-benzimidazoles by the reaction of o-phenylenediamines and aromatic aldehydes in the presence of 1-methylimidazolium triflouroacetate ([Hmim]TFA) at room temperature under aqueous conditions is described. The ionic liquid is reusable and could be recycled for several runs without any decrease in its efficiency.     

A simple and efficient route for the synthesis of di and tri(bis(indolyl) methanes) as new triarylmethanes

Preparation of di and tri(bis(indolyl) methanes) from di and trialdehydes and indoles in the presence of silica sulfuric acid was described. Reactions proceeded in good to excellent yields in acetonitrile as solvent at room temperature.     

A blind and robust video watermarking based on IWT and new 3D generalized chaotic sine map

In the modern world, high-bandwidth internet access has led to the theft of all types of digital data, including digital video, and their illegal distribution. The digital video watermarking technique was introduced late last century to enforce video copyright protection. In this paper, a robust blind and secure video watermarking method is presented based on integer wavelet transform and the generalized chaotic sine map. In this method, integer wavelet transform is applied to each main frame of the standard video. Basically, watermarking techniques are evaluated based on three concepts of content quality, data resilience and data capacity. Therefore, in order to guarantee the quality of the watermarked video, the watermark is inserted in low-frequency coefficients. An appropriate security level is added to increase the efficiency and functionality by chaotic map to watermark. In addition, the normalized correlation coefficient (NCC) between the main watermark and extraction watermark is used as the main criterion of resistance measurement. The results show that the proposed method is good in terms of both quality and resistance to a variety of attacks, and the NCC values obtained in most cases are 1 or very close to 1.