Search results for " proof"

Mappings of finite distortion: a new proof for discreteness and openness

2008

We give a new and elementary proof of the known result: a non-constant mapping of finite distortion f : Ω ⊂ ℝn → ℝn is discrete and open, provided that its distortion function if n = 2 and that for some p > n − 1 if n ≥ 3.

Conceptualizing a Framework: A Critical Review of the Development of Change Management Theories

2020

Abstract Although approaches to manage change dated back to as early as human history, managing effective change is still the topic of today’s debates. One of the undeniable facts about this is that change per se keeps changing, and so does its management methodology. While this fact comes, on the one hand, to validate the reason why none of the early theories stands relevant across time, it, on the other hand, proofs that change methodology is certainly fluid, giving no room for an approach to really last. An effective change is achievable [not] by a prescription, but by a thorough consolidation of the various aspects relevant to change. This paper aims therefore at identifying those [mana…

1990

Towards a characterization of explanations in mathematics textbooks

2013

This work is part of a broader study which aims to examine the relation between explanation and proof in teachers’ practices and the way in which this relation emerges from the texts in the mathematics schoolbooks. Our hypothesis is that explanation and proof share some of their characterizing parameters and this makes possible an overlapping of meaning which favors a switch of roles during teaching/learning activities. First results from textbooks analysis are presented pointing out remarkable features of explanation arisen to date.

Combinatorial proofs of two theorems of Lutz and Stull

2021

Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if $K \subset \mathbb{R}^{n}$ is any set with equal Hausdorff and packing dimensions, then $$ \dim_{\mathrm{H}} π_{e}(K) = \min\{\dim_{\mathrm{H}} K,1\} $$ for almost every $e \in S^{n - 1}$. Here $π_{e}$ stands for orthogonal projection to $\mathrm{span}(e)$. The primary purpose of this paper is to present proofs for Lutz and Stull's projection theorems which do not refer to information theoretic concepts. Instead, they will rely on combinatori…

A permutation code preserving a double Eulerian bistatistic

2016

Visontai conjectured in 2013 that the joint distribution of ascent and distinct nonzero value numbers on the set of subexcedant sequences is the same as that of descent and inverse descent numbers on the set of permutations. This conjecture has been proved by Aas in 2014, and the generating function of the corresponding bistatistics is the double Eulerian polynomial. Among the techniques used by Aas are the M\"obius inversion formula and isomorphism of labeled rooted trees. In this paper we define a permutation code (that is, a bijection between permutations and subexcedant sequences) and show the more general result that two $5$-tuples of set-valued statistics on the set of permutations an…

Mahonian STAT on words

2016

In 2000, Babson and Steingrimsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006.In 2010, Burstein refined some of these results by giving a bijection between permutations with a fixed value for the major index and those with the same value for STAT , where STAT is one of the statistics defined and proved to be Mahonian in the 2000 Babson and Steingrimsson's paper. Several other statistics are preserved as well by Burstein's bijection.At…

Cryogenic nanoelectromechanical switch enabled by Bi2Se3 nanoribbons

2022

Abstract Nanoelectromechanical (NEM) switches are potential candidates for memory and logic devices for low standby-current and harsh environment applications. Cryogenic operation of these devices would allow to use them, e.g., in space probes and in conjunction with quantum computers. Herein, it is demonstrated that cryogenic application requirements such as good flexibility and conductivity are satisfied by using Bi2Se3 nanoribbons as active elements in NEM switches. Experimental proof of principle NEM switching at temperatures as low as 5 K is achieved in volatile and non-volatile reversible regimes, exhibiting distinct ON and OFF states, backed by theoretical modelling. The results open…

Flood proofing measures cost-efficiency analysis for hydraulic risk mitigation in an urbanized riverine area.

2020

<div> <div> <div> <p><strong>Flood proofing measures cost-efficiency analysis for hydraulic risk mitigation in an urbanized riverine area</strong></p> <p>Ugo Ventimiglia <sup>2</sup>, Angela Candela <sup>1,</sup> Giuseppe Tito Aronica <sup>2</sup></p> <p><sup>1 </sup>Department of Engineering, University of Palermo, Palermo, Italy</p> <p><sup>2 </sup>Department of Engineerin…

Finite Alphabet Control of Logistic Networks with Discrete Uncertainty

2014

We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative exampl…