Numération et repérage temporel en inuktitut du Nunavik

Although the Inuit numeration system has no structural limits, its actual use is limited to concrete situations where the quantities involved are small. In Inuktitut (Inuit dialects of the Canadian Eastern Arctic), this system has traditionally had very little use in measuring the passage of time. As a result of contact with Westerners, the situation has partially changed, as shown by the expression of the days of the week and the time of the day. This article presents the essential data relevant to the dialect of Nunavik (Arctic Quebec).

On one sum associated with Fibonacci numeration system

We obtain the asymptotic formula for the sum $S(X)=\sum_{n<X}\varepsilon(n)\varepsilon(n+1)$, where $\varepsilon(n)$ takes the value +1 or -1 depending on the parity of the expansion of the sum of the digits n in the Fibonacci numeration system.

Checkmate to Bioethics?

Bioethics, as the first cousin of philosophy, suffers from what philosopher Hegel told us during his lifetime, “When philosophy paints lights and shadows, an aspect of life has grown old, and cannot be rejuvenated, but only understood. Minerva’s owl takes flight only during sundown”. The problem is how to fight an invisible opponent. What to do when your opponent enters your body and kills you from the inside? This pandemic has taken away out trust in the “Other,” even if they are our parents or children, since it turns a simple act of love —a kiss or a hug— into a deadly weapon. No one, not the richest nor the poorest country, was prepared for this. The covid-19 pandemic has put the world in check and proposes a new planetary order. Bioethics must take its most reflective streak, understand the phenomenon, and draw lessons from this heartbreaking experience so that we do not make the same mistakes again that are costing us so many bitter tears and deaths. I will present in this editorial some points that may help us to continue the debate and possibly reach agreements on how to advance in a post-COVID-19 world. Readers will find too and editorial note on our journals' numeration system. In the name of the editorial board of Revista Latinoamericana de Bioética and my own, we dedicate this issue to the heroes of this pandemic, the health professionals (doctors, nurses, para- medics, to name just a few) who have risked their lives for the most vulnerable and feeble, those who have suffered the agony of this utterly heartless coronavirus disease.

BETA CANTOR SERIES EXPANSION AND ADMISSIBLE SEQUENCES

We introduce a numeration system, called the <em>beta Cantor series expansion</em>, that generalizes the classical positive and negative beta expansions by allowing non-integer bases in the Q-Cantor series expansion. In particular, we show that for a fix $\gamma \in \mathbb{R}$ and a sequence $B=\{\beta_i\}$ of real number bases, every element of the interval $x \in [\gamma,\gamma+1)$ has a <em>beta Cantor series expansion</em> with respect to B where the digits are integers in some alphabet $\mathcal{A}(B)$. We give a criterion in determining whether an integer sequence is admissible when $B$ satisfies some condition. We provide a description of the reference strings, namely the expansion of $\gamma$ and $\gamma+1$, used in the admissibility criterion.

Multidimensional Numbers and Semantic Numeration Systems:Theoretical Foundation and Application

In this article, we present a new class of numeration systems, namely Semantic Numeration Systems. The methodological background and theoretical foundations of such systems are considered. The concepts of abstract entity, entanglement and valence of abstract entities, and the topology of the numeration system are introduced. The proposed classification of semantic numeration systems allows to choose the numeration system depending on the problem being solved. Examples of the use of a two-dimensional number system for image compression problems and computation of a two-dimensional convolution are given.