This article presents interesting generalizations of three well-known results related to pedal triangles and distances, and the Simson-Wallace line. Nested Miquel triangles The triangle whose vertices are the feet of the perpendiculars from a point P inside a triangle ABC to each of its sides AB

Le travail présenté dans le cadre de ce mémoire concerne l’étude de deux zones: la marge algérienne et la zone du glissement de Nice en 1979. La marge au large d’Alger n’avait fait l’objet d’aucune campagne scientifique majeure jusqu’à la réalisation de la campagne Maradja en 2003. Du coup, le travail de thèse sur la zone d’Alger a d’abord concerné la caractérisation morpho-sédimentaire de la zone et la cartographie des instabilités et des dépôts gravitaires. Dans un deuxième temps, il s’est concentré sur la caractérisation des propriétés physiques et mécaniques des sédiments, l’identification des mécanismes responsables de l’initiation des instabilités observées dans la zone d’étude et l’évaluation de la stabilité actuelle de la zone d’étude. Plusieurs résultats importants ont été obtenus: les processus sédimentaires sont très clairement influencés par la morphologie de la marge, elle-même contrôlée par l’activité tectonique. La sédimentation sur la marge algérienne est donc très hétérogène, contrastée et contrôlée par deux processus: (a) les processus gravitaires incluant les courants turbiditiques et les glissements sous-marins et (b) la sédimentation hémipélagique; de nombreux glissements ont été observés et décrits sur la zone d’étude. La majorité des

Abstract. Miquel’s Five-Circle Theorem is difficult to prove algebraically. In this paper, the details of the first algebraic proof of this theorem is provided. The proof is based on conformal geometric algebra and its accompanying invariant algebra called null bracket algebra, and is the outcome

The Centre d’Estudis Olímpics (CEO-UAB) publishes works aimed to facilitate their scientific discussion. The inclusion of this text in this series does no limit future publication by its author who reserves the integrity of his rights. This publication may not be reproduced, neither partially nor totally, without the author’s permission. The text was presented at the Symposium “Olympic Arts and Culture Festivals: Recent Experiences and Future Design”, held in Chicago on the 23-24 June 2008.

Abstract. We present a simple proof for the generalizations of a result due to Wallace and a result due to Miquel to higher dimensions. 1.

An interesting, elementary theorem first stated by Wallace in 1799 and proved by Miquel in 1838 can be stated as follows (see Figure 1 It provides a nice result for high school students to explore with dynamic geometry and is easy to prove with basic cyclic quadrilateral geometry. It appears

Abstract—This paper proposes a methodology to study the data reuse quality of task-parallel runtimes. We introduce an extension to the reuse distance method called the Kernel Reuse Distance (KRD). The metric is a low-overhead alternative designed to ana-lyze data reuse at the socket level while minimizing perturbation to the parallel schedule. Using the KRD metric we show that reuse depends considerably on the system configuration (sockets, cores) and on the runtime scheduler. Furthermore, we correlate KRD with hardware metrics such as cache misses and work time inflation. Overall we found that KRD can be used effectively to assess data reuse in parallel applications. The study also revealed that several current runtimes suffer from severe bottlenecks at scale which often dominate performance. I. INTRODUCTION AND BACKGROUND Tasking has become an established technique to program

The realizability of countable Cox configurations on Miquelian planes is proved. A simple way to determine the automorphisms of the Cox configura-tions is presented.

Proof-term = computational + logical information logical parts can interfere with computational ones when elaborating proofs (2, π), (2, π ′ ) : {n: nat | even n} π ̸ = π ′ ⇒ (2, π) ̸ = (2, π ′) Can we build a type system avoiding that? Motivation

BACKGROUND/OBJECTIVES: Rubus Coreanus Miquel (RCM), used as a traditional Korean medicine, reduces chronic inflammatory diseases such as cancer and rheumatoid arthritis. However, its mechanism has not been elucidated. In this study, we examine the anti-inflammatory effects of RCM and their possible