Cantor Series Constructions Contrasting Two Notions of Normality

A. R\'enyi \cite{Renyi} made a definition that gives a generalization of simple normality in the context of $Q$-Cantor series. In \cite{Mance}, a definition of $Q$-normality was given that generalizes the notion of normality in the context of $Q$-Cantor series. In this work, we examine both $Q$-normality and $Q$-distribution normality, treated in \cite{Laffer} and \cite{Salat}. Specifically, while the non-equivalence of these two notions is implicit in \cite{Laffer}, in this paper, we give an explicit construction witnessing the nontrivial direction. That is, we construct a base $Q$ as well as a real $x$ that is $Q$-normal yet not $Q$-distribution normal. We next approach the topic of simultaneous normality by constructing an explicit example of a base $Q$ as well as a real $x$ that is both $Q$-normal and $Q$-distribution normal

Two short proofs of the bounded case of S.B. Rao's degree sequence conjecture

S. B. Rao conjectured that graphic sequences are well-quasi-ordered under an inclusion based on induced subgraphs. This conjecture has now been settled completely by M. Chudnovsky and P. Seymour. One part of the proof proves the result for the bounded case, a result proved independently by C. J. Altomare. We give two short proofs of the bounded case of S. B. Rao's conjecture. Both the proofs use the fact that if the number of entries in an integer sequence (with even sum) is much larger than its highest term, then it is necessarily graphic.Comment: 4 page

Ultra narrow AuPd and Al wires

In this letter we discuss a novel and versatile template technique aimed to the fabrication of sub-10 nm wide wires. Using this technique, we have successfully measured AuPd wires, 12 nm wide and as long as 20 $\mu$m. Even materials that form a strong superficial oxide, and thus not suited to be used in combination with other techniques, can be successfully employed. In particular we have measured Al wires, with lateral width smaller or comparable to 10 nm, and length exceeding 10 $\mu$m.Comment: 4 pages, 4 figures. Pubblished in APL 86, 172501 (2005). Added erratum and revised Fig.

Position estimation delays in signal injection-based sensorless PMSM drives

The causes of position estimation delays and their effects on the sensorless control of permanent magnet synchronous motor drives are investigated. The position of a permanent magnet synchronous machine is estimated via the injection of high frequency voltage signals. The delays under investigation are due to the digital implementation of the control algorithm and to the digital filters adopted for decoupling the inspection signals from the fundamental components of the stator current measures. If not correctly modeled and compensated, such delays can reduce the performance of the control scheme. Experimental results are provided, proving the accuracy of the modeling approach and the effectiveness of the related compensation strateg

La notwithstanding clause come l'«arma» dei Governi provinciali di maggioranza. Il dibattito sui difficili equilibri tra Corti e Legislativi nel sistema di protezione dei diritti

Section 33 is a sleeping giant within the Charter: now mostly quiet and unthreatening but, if awakened by increased and unnoticed or unopposed use, still capable of significantly changing Canada’s constitutional and legislative landscape”. Così si esprime la costituzionalista Barbara Billingsley in riferimento alla section 33 della Carta canadese dei diritti e delle libertà, meglio nota come notwithstanding clause o override clause