A. Introduction.......................................................................................................... 2 I. The Puzzle....................................................................................................... 2 II. The Potential for Institutions ............................................................................ 3 III. Related Approaches in Literature......

In part I it was shown that for each k ≥ 1 the generalized Sato–Levine invariant detects a gap between k-quasi-isotopy of link and peripheral structure preserving isomorphism of the finest quotient Gk of its fundamental group, ‘functorially’ invariant under k-quasi-isotopy. Here we show that Cochran’s derived invariant β, provided k ≥ 3, and a series of μ̄-invariants, starting with μ̄(111112122) ...

In part I it was shown that for each k ≥ 1 the generalized Sato–Levine invariant detects a gap between k-quasi-isotopy of link and peripheral structure preserving isomorphism of the finest quotient Gk of its fundamental group, ‘functorially’ invariant under k-quasi-isotopy. Here we show that Cochran’s derived invariant β, provided k ≥ 3, and a series of μ̄-invariants, starting with μ̄(111112122) ...

Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.

We investigated the correlation of interictal epileptiform discharges (IED) in routine EEG 6 and 24 months after epilepsy surgery with regard to long-term seizure outcome. In 148 patients (74% temporal lobe epilepsy (TLE), 26% extratemporal epilepsy) EEG results (IED present or absent) were correlated with the postoperative outcome using the Engel classification 6 and 24 months after resection ...

An Engel curve describes how a consumer’s purchases of a good like food varies as the consumer’s total resources such as income or total expenditures vary. Engel curves may also depend on demographic variables and other consumer characteristics. A good’s Engel curve determines its income elasticity, and hence whether the good is an inferior, normal, or luxury good. Empirical Engel curves are cl...

The fauna of termites (Isoptera) preserved in Early Eocene amber from the Cambay Basin (Gujarat, India) are described and figured. Three new genera and four new species are recognized, all of them Neoisoptera - Parastylotermes krishnai Engel & Grimaldi, sp. n. (Stylotermitidae); Prostylotermes kamboja Engel & Grimaldi, gen. et sp. n. (Stylotermitidae?); Zophotermes Engel, gen. n., with Zophoter...

We find a bound for the exponent of the Schur multiplier of a finite p-group in terms of the exponent and Engel length of the given group. It is also proved that if G is a 3-Engel group of finite exponent, then the exponent of H2(G) divides exp G. When G is a 4-Engel group of exponent e, the exponent of H2(G) divides 10e.