A Vulnerability Parameter of Networks

Mathematical Notes - The vulnerability in a communication network is the measurement of the strength of the network against damage that occurs in nodes or communication links. It is important that...     

On the difference spaces of almost convergent and strongly almost convergent double sequences

In this paper, we study the difference spaces \({\mathcal {F}}(\varDelta )\), \({\mathcal {F}}_0(\varDelta )\), \({\mathcal {[F]}}(\varDelta )\) and \({\mathcal {[F]}}_0(\varDelta )\) of double sequences obtained as the domain of four-dimensional backward difference matrix \(\varDelta \) in the spaces \({\mathcal {F}}\), \({\mathcal {F}}_{0}\), \({\mathcal {[F]}}\) and \({\mathcal {[F]}}_{0}\) of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We examine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces.

     

Computational estimates of thermochemistry and pKa values of cyclopropenyl imine superbases

The thermochemical properties of superbase species derived from cyclopropeneimine are estimated by computations on systems of isodesmic reactions. Proton affinities, gas phase basicities, and pK_a values are well represented by computations incorporating G4 and CBS‐QB3 schemes augmented for large systems by DFT calculations with functionals M06‐2X and ωB97DX in the cc‐pVTZ Dunning basis. Our calculations show that relative base strengths in gas are enhanced by alkyl substitution, either by methyl groups or larger species. For acetonitrile solution, alkyl substitution seems to weaken the base. © 2013 Wiley Periodicals, Inc.     

Palladium(II)‐N‐heterocyclic carbene complexes: synthesis,characterization and catalytic application

N‐Heterocyclic carbenes (NHCs) are of great importance and are powerful ligands for transition metals. A new series of sterically hindered benzimidazole‐based NHC ligands (LHX) ( 2a , 2b , 2c , 2d , 2e , 2f ), silver–NHC complexes ( 3a , 3b , 3c , 3d , 3e , 3f ) and palladium–NHC complexes ( 4a , 4b , 4c , 4d , 4e , 4f ) have been synthesized and characterized using appropriate spectroscopic techniques. Studies have focused on the development of a more efficient catalytic system for the Suzuki coupling reaction of aryl chlorides. Catalytic performance of Pd–NHC complexes and in situ prepared Pd(OAc)₂/LHX catalysts has been investigated for the Suzuki cross‐coupling reaction under mild reaction conditions in aqueous N,N‐dimethylformamide (DMF). These complexes smoothly catalyzed the Suzuki–Miyaura reactions of electron‐rich and electron‐poor aryl chlorides. Copyright © 2014 John Wiley & Sons, Ltd.     

Statistical Extensions of Some Classical Tauberian Theorems for Cesàro Summability of Triple Sequences

Some growth conditions of the resolvent function of a Banach space operator are investigated using higher order Cesàro means. More precisely, Abel and Nevanlinna estimates are obtained under the condition of boundedness of some weighted Cesàro averages. Also, certains results related to the (strong or uniform) convergence of Cesàro means are mentioned.     

Interaction in the TlSe-Pr2Se3 system

The interaction of components in the TlSe-Pr₂Se₃ system was studied by differential thermal, X-ray powder diffraction, and microstructural analyses and also by microhardness and density measurements. The state diagram of this system was constructed. It was found that the section TlSe-Pr₂Se₃ is a quasi-binary section of the Tl-Pr-Se ternary system. In the TlSe-Pr₂Se₃ system at the component ratio 1: 1, a new chemical compound, TlPr₂Se₄, forms, which melts congruently at 1295°C. In the system based on TlSe, solid solutions form until 3.5 mol % Pr₂Se₃, and in the system based on Pr₂Se₃, solid solutions occur until 2.5 mol % TlSe.     

A novel amperometric hydrogen peroxide biosensor based on pyrrole-PAMAM dendrimer modified gold electrode

Horseradish peroxidase (HRP) was immobilized into an electrochemically prepared copolymer of pyrrole–PAMAM (PAMAM; polyamidoamine) dendrimers for the construction of amperometric hydrogen peroxide biosensor. First, second, and third generation amidoamine–pyrrole dendrons having branched amine periphery and focal pyrrole functionality were synthesized via divergent pathway. Pyrrole dendrimers were covalently attached onto the electrode surface and polymerized by electrochemical copolymerization with pyrrole monomer. The synthesized dendrimers and copolymers have been characterized by FTIR-ATR and NMR. These copolymers have been utilized as conducting films for amperometric hydrogen peroxide sensing. The HRP retains its bioactivity after immobilization into the dendronized pyrrole-copolymers. Amperometric response was measured as a function of concentration of hydrogen peroxide, at fixed potential of +0.35 V vs. Ag/AgCl in a phosphate buffered saline (pH 7.5). The effect of pH and temperature of the medium, storage, and reusability properties were investigated. The results indicate an efficient immobilization of enzyme onto the PAMAM type dendrimer modified surface containing pyrrole monomer, which leads to high enzyme loading, and increased lifetime stability of the electrode.