LetG be a finite group andX a conjugacy class ofG.We denote rank(G : X) to be theminimumnumber of elements ofX generating G. In the present article, we determine the ranks for two sporadic simple groups, namely the O’Nan sporadic simple group O’N and the Lyons sporadic simple group, Ly. Computations were carried with the aid of the computer algebra systemGAP [The GAP Group, GAP—Groups, Algorith...

The aim of this paper is to introduce a new numerical algorithm for solving the continuous time non-linear filtering problem. In particular, we present a particle filter that combines the Kusuoka-Lyons-Victoir cubature method on Wiener space (KLV) [13], [18] to approximate the law of the signal with a minimal variance ”thining” method, called the tree based branching algorithm (TBBA) to keep th...

Case name: Breathard v. Lyons, et al ., No. 1:21‐cv‐01352 (C.D. Ill. 08/11/22).

We give the first computer free proof of the uniqueness of groups of type Ly. We also show that certain simpicial complexes associated to the Lyons group Ly have the same homotopy type as the Quillen complex for Ly at the prime 3; we show this complex is simply connected, and we calculate its homology. Finally we supply simplified proofs of some properties of groups of type Ly, such as the grou...

When the young French physician Jean-Emmanuel Gilibert (1741-1814) addressed his readers in 1772, he probably had little hope of a positive response. His appeal, quoted from his Plan de recherches sur l'art de conserver la sante des enfans, de preserver & gue'rir leurs maladies, reads, "Citizens! Are you ready to let your children's doctor collect the data that are required in order to lay the ...

Informally, an amalgam is a group ‘sitting inside’ two other groups and the coset graph is a way to look at how the cosets of subgroups interact. These are combined in the amalgam method — a way of classifying amalgams satisfying certain conditions. The amalgam method was used in the classifications of finite simple groups, and is discussed in Classification of Finite Simple Groups no. 2 by Gor...

Other Patient Reported Outcomes in Older HIV-positive (HIV+) Adults Malcolm John, MD, MPH; Nancy Hessol, MSPH; C. Bradley Hare, MD; Catherine Lyons, NP, MPH; Roland Zepf, MS, RN; Terrence Marcotte, NP; Amanda Hutton Parrott, DPT, MS, NP; Robert Whirry, BA; Cameron Foreman, BA; Monica Gandhi, MD, MPH; Meredith Greene, MD; University of California San Francisco, San Francisco, CA; Kaiser Permanen...