How inefficient can a sort algorithm be?
We find large lower bounds for a certain family of algorithms, and prove that such bounds are limited only by natural computability arguments.
cs.DS↗
arXiv subjects
Miguel A. Lerma
Publications and source records attributed to Miguel A. Lerma.
Distribution of Powers Modulo 1 and Related Topics
This is a review of several results related to distribution of powers and combination of powers modulo 1. We include a proof that given a sequence of real numbers $θ_n$, it is possible to get an $α$ (given $λ\ne 0$), or a $λ$ (given $α> 1$) such that $λα^n$ is close to $θ_n$ modulo 1. We also prove that in a number field, if a combination of powers $λ_1 α_1^n + \cdots + λ_m α_m^n$ has bounded $v$-adic absolute value (where $v$ is any non-Archimedian place) for $n \geq n_0$, then the $α_i$'s are algebraic integers. Finally we present several open problem and topics for further research.
math.NT↗
A Mirror Based Event Cloaking Device
We propose a way of implementing an event cloaking device without the use of metamaterials. Rather than slowing down and speeding up light, we manipulate an obscurity gap by diverting the light through paths of appropriate length with an arrangement of switchable transreflective mirrors.
physics.optics↗