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.

     

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.     

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 DFT Study on Estrone – TNT Interaction

Trinitrotoluene, known as TNT, is a widely used powerful explosive. It is a poisonous material, which injures almost all cells, especially those of liver, bone marrow, and kidney. Estrone is a sex hormone having an electron rich aromatic (phenolic) ring that is capable of forming a π complex with molecules containing an electron deficient π system. This study has focused on investigating the tendency of the complex formation of TNT with estrone. It has been thought that the formation of estrone‐TNT π complex might take place in a human body exposed to acute or prolong period of this hazardous chemical and consequently estrone activities might be impaired. The complex formation reaction was investigated mainly using DFT method with B3LYP/6‐31G(d, p) basis set in gas phase. The existence of π interaction between estrone and TNT was demonstrated by computational spectroscopic analyses (UV/Vis, IR, and ¹H NMR techniques). The frontier molecular orbital (HOMO and LUMO) analyses have shown that the considered π complex is very resistant to oxidation with respect to its components, estrone and TNT.     

Complexation and transport of amino acid esters and their salts with synthesised chiral novel aza crown ether derivatives

The syntheses of four aza-15-crown-5 ethers bearing phenyl and phenoxymethyl moieties attached to a stereogenic centre on the crown ring were achieved. Macrocycles have exhibited strong binding ability (K_a = 5364–12,969 M^? 1) and modest enantiomeric discrimination towards the enantiomers of amino acid methyl ester salts by UV titration method in CHCl₃ at 25°C. Computer modelling results supported experimental data providing a detailed understanding of the molecular recognition mode between hosts and guests and the likely binding sites involved. Macrocycles were used for chiral discrimination of amino acids in their zwitterionic forms or as potassium and sodium salts in transport experiments across a bulk chloroform membrane with satisfactory selectivity.     

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.     

Palladium(II) complexes bearing N‐alkylpiperidoimidazolin‐2‐ylidene derivatives: Effect of alkyl chain length of ligands on catalytic activity

A series of piperidoimidazolinium salts which differ in the chain lengths (butyl, octyl, dodecyl, octadecyl) and their Pd–N‐heterocyclic carbene complexes with pyridine were synthesized and characterized using elemental analysis and spectroscopic methods. The effects of these ligands on catalyst activation and the performance of the complexes were studied in Suzuki–Miyaura reactions of arylboronic acid with aryl chlorides. The complex with the ligand having the longest chain length was found to be most active. The results demonstrated that the length of the alkyl chain of the piperidoimidazolin‐2‐ylidene controlled the dispersion and composition of the nanoparticles and it affected the catalytic activity. The impact of alkyl chain length of piperidoimidazolin‐2‐ylidene on the Suzuki–Miyaura reactions of arylboronic acid with aryl halides was systematically investigated.     

A Fractal Representation of the Complex Clifford Algebra Equivalent to the Fock Representation

We construct a representation of the infinite dimensional complex Clifford algebra on the Hilbert space of square-integrable complex-valued functions on the Cantor set, which we show to be equivalent to the classical Fock representation.