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Scientiae Baccalaureus was a scientific journal, mostly mathematics, published in Rolla, Missouri, USA in 1890-1891. Largely forgotten today, it nevertheless had the distinction of being the first to publish English translations of the principal works of Lobachevsky and Bolyai on non-Euclidean geometry. This paper provides a brief overview of Scientiae Baccalaureus and some of the people associated with it.
We give a sufficient condition for a family of pseudoresolvents in a Banach algebra to be trivially zero. As an important consequence, we provide an alternate proof of the classical result that the spectrum of any linear bounded operator on a Banach space is nonempty. The proofs are elementary, requiring only a basic knowledge of real and complex analysis.
The representation of the regular functions by power sets of polynomials of the single complex variable $z$ in Faber regions is the subject of the present work. Different kinds of order and type of these sets are investigated.