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We survey mainly recent results on the two most important orthogonality types in normed linear spaces, namely on Birkhoff orthogonality and on isosceles (or James) orthogonality. We lay special emphasis on their fundamental properties, on their differences and connections, and on geometric results and problems inspired by the respective theoretical framework. At the beginning we also present other interesting types of orthogonality. This survey can also be taken as an update of existing related representations. Mathematics Subject Classification (2000). 46B20, 46C15, 52A21.

We consider a forced harmonic oscillator at resonance with a nonlinear perturbation and obtain a sharp condition for the existence of unbounded motions. Such a condition is extended to the case of a semilinear vibrating string.

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This report describes the results of six antimicrobial regimens used for the treatment of brucellosis in an open, randomized study performed over two periods (1980-1983 and 1984-1987). In the first period, rifampicin and doxycycline were used for 4 weeks, trimethoprim-sulfamethoxazole for 6 months, and doxycycline for 6 weeks. During the second period, we used streptomycin for 2 or 3 weeks together with doxycycline for 6 weeks and rifampicin with doxycycline for 6 weeks. Comparison of the results showed the following: (1) no statistically significant findings were revealed when the different regimens were compared and (2) the regimens containing streptomycin yielded statistically more favorable results than those consisting of rifampicin and monotherapy when the patients treated with rifampicin were compared with those taking streptomycin and those receiving single-agent therapy. No significant differences were observed between monotherapeutic regimens and those including rifampicin.