Tomás Oliveira e Silva

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This paper presents some results concerning the search for initial values to the so-called 3x+1 problem which give rise either to function iterates that attain a maximum value higher than all function iterates for all smaller initial values, or which have a stopping time higher than those of all smaller initial values. Our computational results suggest that(More)
This paper describes how the even Goldbach conjecture was confirmed to be true for all even numbers not larger than 4 · 1018. Using a result of Ramaré and Saouter, it follows that the odd Goldbach conjecture is true up to 8.37 · 1026. The empirical data collected during this extensive verification effort, viz., counts and first occurrences of so-called(More)
In this report we present a collection of results concerning two families of rational orthonormal functions, one on the unit circle, and another on the imaginary axis. We also describe in detail an interesting link between the two families. Special cases of these rational orthonormal functions include the Laguerre and Kautz orthonormal functions, as well as(More)
Driven by the need to make a more efficient use of communication and computational resources, recently, a strong research effort has been devoted to the study of control systems integrating several controllers, with the goal of selecting the controller that allows to meet the desired quality of control while minimizing resource usage. However, most of the(More)
The problem of optimal control given full state knowledge has been solved many years ago and is very well documented. Nonetheless, in most control settings it is virtually impossible to know the exact state value. To deal with this fact, two concepts were introduced: certainty equivalence and separation principle. In this paper, it is presented a novel(More)