Stability of a generalized trigonometric functional equation

The stability of the functional equation F(x+y)−G(x−y)=2H(x)K(y) over the domain of an abelian group G and the range of the complex field is investigated. Several related results extending a number of previously known ones, such as the ones dealing with the sine functional equation, the d’Alembert functional equation and Wilson functional equation, are derived as direct consequences. Applying the main result to the setting of Banach algebra, it is shown that if their operators satisfy a functional inequality and are subject to certain natural requirements, then these operators must be solutions of some well-known functional equations.     

Segregation of controlled and failed heads using an integration of noise amplitudes in a limited range of harmonic frequency

In this report, two new testing parameters; applied-field integrated noise amplitude (AFINA) and no-field integrated noise amplitude (NFINA) are proposed. The AFINA is characterized by using a fast Fourier transform (FFT) technique to summarize noise amplitudes in a range of 2–20 kHz harmonic frequency whilst the NFINA is characterized by gathering noise amplitudes with no external field. It is clearly seen that noisy and good heads can be successfully separated and found that the AFINA of controlled heads will be normally be less than 10 mV whereas that of failed heads will be more than 10 mV. The statistic results show a 95% confidential interval which is acceptable in manufacturing.