A classical theorem of R. Baer describes the nilpotent radical of a finite group G as the set of all Engel elements, i.e. elements y ∈ G such that for any x ∈ G the nth commutator [x, y, . . . , y] equals 1 for n big enough. We obtain a characterization of the solvable radical of a finite dimensional Lie algebra defined over a field of characteristic zero in similar terms. We suggest a conjectu...

China has experienced remarkably stable growth and inflation in recent years according to official statistics. We use systematic discrepancies between cross-sectional and time-series Engel curves to construct alternative estimates of Chinese growth and inflation. Our estimates suggest that official statistics present a smoothed version of reality. Official inflation rose in the 2000s, but our e...

We reviewed the videotapes of 49 consecutive patients with a history of medically refractory temporal lobe epilepsy for the presence and laterality of unilateral hand posturing (UHP), unilateral hand automatism (UHA), non-forced head turning (HT), and post-ictal dysphasia (PID). All of these patients underwent temporal resections with follow-up for more than 2 years after the surgery. We examin...

OBJECT Occipital lobe epilepsy (OLE) accounts for a small percentage of extratemporal epilepsies and only few and mostly small patient series have been reported. Preoperative findings, surgical strategies, histopathological bases, and postoperative outcomes for OLE remain to be elucidated. METHODS A group of 54 patients with occipital lobe involvement were identified from a prospective epilep...

Engel curves are often estimated within a linear, or at least approximately linear system of equations. However, Engel curves are required to lie on or within the unit interval, while summing to unity. These restrictions are not easily accommodated within a linear system. Therefore, we apply the fractional multinomial logit model in our estimation of expenditure shares, because it more readily ...

Classificatory notes are presented for various stem lineages relative to the Trichoptera+ Lepidoptera clade. The following new groups established clades above family-group ranks: Protomeroptera Engel, Metamphiesmenoptera Cladochoroptera Euamphiesmenoptera Eocoronoptera Panendymenoptera Necrotrichoptera Endymenoptera Stelloptera Engel. Additionally, families Marimerobiidae family, and Microptysm...