Obtenção de zeros de funções utilizando Python

Numerical Methods are very important in Engineering because many real problems have complicated mathematical models that are difficult to be solved analytically. Thus, the methods of resolution for several problems that are studied in the discipline of Computational Numerical Methods, as well as in the discipline of Algorithms, are indispensable for the formation of a future Engineer. Among the several numerical methods that exist, the following are the methods for obtaining zeros of functions: Bisection, False Position and Newton-Raphson. The Bisection method consists of defining the range containing a root and, using the arithmetic mean, dividing it until the desired precision is reached. In the case of the False Position method, the weighted arithmetic mean is used to obtain the approximate root. Finally, although Newton-Raphson's method has faster convergence than the others, the drawback of this method is the need to use the derivative of the studied function. Thus, in some cases, this method may be impracticable. In this work, the methods mentioned will be implemented in the Python programming language. In this work, the mentioned methods are implemented in the Python programming language, in order to strengthen programming knowledge in the formation of Engineers, as well as to emphasize the importance of applying numerical methods in practical problems of various engineering areas.

Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series

For a real number $\alpha$ the Hilbert space $\mathscr{D}_\alpha$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$, where $d(n)$ denotes the number of divisors of $n$. We extend a theorem of Seip on the bounded zero sequences of functions in $\mathscr{D}_\alpha$ to the case $\alpha>0$. Generalizations to other weighted spaces of Dirichlet series are also discussed, as are partial results on the zeros of functions in the Hardy spaces of Dirichlet series $\mathscr{H}^p$, for $1\leq p <2$.