Let U( ) be the enveloping algebra of a semi-simple Lie algebra . Very little is known about the nature of AutU( ). However, if G is a finite subgroup of AutU( ) then very general results of Lorenz-Passman and of Montgomery can be used to relate SpecU( ) to SpecU( ). As noted by Alev-Polo one may read off the Dynkin diagram of from SpecU( ) and they used this to show that U( ) could not be agai...

Let R be a ring, CR and ′CR be the set of regular and left regular elements of R (CR ⊆ ′CR). Goldie’s Theorem is a semisimplicity criterion for the classical left quotient ring Ql,cl(R) := C −1 R R. Semisimplicity criteria are given for the classical left regular left quotient ring ′Ql,cl(R) := ′C −1 R R. As a corollary, two new semisimplicity criteria for Ql,cl(R) are obtained (in the spirit o...

Life usually ends with death, and ageing is defined here by the increase of the mortality rate with increasing age. Merryl Streep and Goldie Hawn showed in the movie “Death becomes her” the consequences of an elixir giving us eternal life. The present review instead deals with the consequences present foreseeable trends have on the demography of developed countries, and with the biological reas...

A two dimensional two-delays differential system modeling the dynamics of stem-like cells and white-blood cells in Chronic Myelogenous Leukemia under treatment is considered. Stability of equilibria is investigated and emergence of periodic solutions of limit cycle type, as a result of a Hopf bifurcation, is eventually shown. All three types of stem cell division (asymmetric division, symmetric...

We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions W=(W1,W2). Recently it has been observed that W1,W2 may exhibit regularly varying tails different indices, which is in contrast to well-known Kesten-type results. However, only partial results have derived. Under typical “Kesten–Goldie” “Grey...

I grasped the list of patients, fingering the crispness of the sheet that represented my first day of service on the medical wards. I knew that the sheet would soon be crumpled and covered with scrawl, as I scurried about, meeting 36 patients, 2 residents, 4 interns, and 6 medical students. But for now, the paper felt cool, controlled, and reliable in my grip. I was ashamed to admit it, but I w...