On the Orthogonal Stability of the Pexiderized Quadratic Equation

The Hyers--Ulam stability of the conditional quadratic functional equation of Pexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\perp y is established where \perp is a symmetric orthogonality in the sense of Ratz and f is odd.Comment: 10 pages, Latex; Changed conten

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

The qualitative electrochemical determination of clarithromycin and spectroscopic detection of its structural changes at gold electrode

The aim of the present study was the qualitative determination of the pure clarithromycin using a gold electrode in neutral electrolyte by cyclic linear sweep voltammetry. It was shown that in the range of -1.2 V to 1.0 V vs. SCE in 0.05 M NaHCO3, a gold electrode is successfully employed for the qualitative determination of clarithromycin by detection of the reproductive four anodic and one cathodic peaks. After the potentiostatic measurements at the potential values corresponded to current peaks, the bulk electrolyte was analyzed by FTIR spectroscopy to show the changes in molecular structure of clarithromycin. FTIR analysis of the bulk electrolyte after 4 h of holding the potential at -0.61 V vs. SCE (cathodic peak) showed the apparent changes in clarithromycin molecule structure: in the ester bond of the lactone and in ethers and acetal bonds

The electrochemical behavior of commercial clarithromycin and spectroscopic detection of its structural changes

The aim of the present study was to examine the behavior of commercial clarithromycin, Clathrocyn (R), comparing to the results previously obtained using pure clarithromycin under the same experimental conditions. The study was performed by cyclic linear sweep voltammetry and the bulk of electrolyte was analyzed by FTIR spectroscopy and HPLC. At gold electrode, in the range of -1.2 V to 1.0 V vs. SCE in 0.05 M NaHCO3, the electrochemical determination of pure clarithromycin was previously defined by four anodic and one cathodic reproductive peaks, and commercial clarithromycin is defined by reproductive one anodic peak which appears from 0.60 to 0.80 V vs. SCE. Previously, FTIR analysis of the bulk electrolyte showed the apparent changes in pure clarithromycin molecule structure: in the ester bond of the lactone and in ethers and acetal bonds. FTIR analysis of the bulk electrolyte also showed changes in the molecule structure in commercial-tablets form of clarithromycin: indicating disappearance of lactone structure and changes of carbonyl group at position 9