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A Novel Method for Determining Microbial Kinetics

Journal of Life Sciences 2013年第8期7卷 787-790页

作者： Anne M. Talkington Floyd L. Inman III Leonard D. Holmes Sartorius Stedim-Biotechnology Laboratory Biotechnology Research and Training Center University of North Carolina atPembroke Pembroke North Carolina 28372 USA

Understanding microbial growth is essential to any research conducted in the fields of microbiology and biotechnology. Current methods of determining growth characteristics of microbes involve subjective graphical interpretations of linearized logarithmic data. Reducing error in logistical data decreases disparity between graphical and analytical predictions of microbial characteristics. In this study, a method has been developed to calculate the kinetics of microbial characteristics utilizing a modified maclaurin series. Convergence of this series approaches the true kinetic value of microbial characteristics to include specific growth rates. In this research, a modified maclaurin series is used to evaluate microbial kinetics in comparison to graphical determinations.

关键词： Microbial kinetics maclaurin series microbial growth models series convergence.

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Generalized series of Bernoulli Type

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Advances in Pure Mathematics 2023年第9期13卷 537-542页

作者： Thomas Beatty Nicholas Bianco Nicole Legge Department of Mathematics Florida Gulf Coast University Fort Myers FL USA

The problem of evaluating an infinite series whose successive terms are reciprocal squares of the natural numbers was posed without a solution being offered in the middle of the seventeenth century. In the modern era, it is part of the theory of the Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve it by considering other more tractable series which were superficially similar and which he hoped could be algebraically manipulated to yield a solution to the difficult series. This approach was eventually unsuccessful, however, Bernoulli did produce an early monograph on summation of series. It remained for Bernoulli’s student and countryman Leonhard Euler to ultimately determine the sum to be . We characterize a class of series based on generalizing Bernoulli’s original work by adding two additional parameters to the summations. We also develop a recursion formula that allows summation of any member of the class.

关键词： Bernoulli series Convergence Sum Recursion Formula Zeta-Function Sine maclaurin series Infinite Product

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