The breadth of a Lie algebra $L$ is defined to be the maximal dimension image $ad_x=[x,-]:L\to L$, for $x\in L$. Here, we initiate an investigation into three families algebras by posets and provide combinatorial formulas members each family.

A 1984 problem of S. Z. Ditor asks whether there exists a lattice of cardinality א2, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martin’s Axiom restricted to collections of א1 dense subsets in posets of ...

The amount of information that can be perceived and processed will be partly determined by attentional breadth (i.e., the scope of attention), which might be narrowed in social anxiety due to a negative attentional bias. The current study examined the effects of stimulus valence on socially anxious individuals’ attentional breadth. Seventy-three undergraduate students completed a computerized d...

The objective of this investigation was to compare the accuracy of mandibular measurements using a stabilizer (MS) with gold standard computed tomography (GS) images. Sixty mandibles were studied. Werth TomoScope HV Compact® was used to obtain CT images (GS), and the MS was also used. Analysis of the CT scans was performed using the VG Studio Max software® (Volume Graphics GmbH, Heidelberg, Ger...

BFS is one of the classical graph theory algorithms, typically expressed under the imperative style. However, it has applications in other domains such as artiicial intelligence. All known algorithms of BFS use iteration. This article focuses on the information maintained by BFS during exploration of an arbitrary graph component. To better understand the structure of this information, BFS is re...

We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that were known before, but that were not put together so far: the algorithm LexBFS due to Rose, Tarjan and Lueker, one of its properties discovered by Berry and Bordat, and a local decomposition property of graphs discovered by Maffray, Trotignon and Vu...

UNLABELLED The concept of frame size has not undergone a thorough evaluation in non-Caucasian populations. Using data from the Central Asia High Altitude Population (CAHAP) study, we tested whether: (1) the relationship between frame size and body composition is different in high-, medium- and low-altitude populations; (2) elbow breadth is a better index of frame size than biacromial and biilia...

A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic Breadth-First Search (LBFS) and Maximum Cardinality Search (MCS), Corneil and Krueger propose in 2008 the so-called Maximal Neighborhood Search (MNS) and show...