Citation: Dalmaijer ES, Nijenhuis BG and Van der Stigchel S (2016) Commentary: Life is unfair, and so are racing sports: some athletes can randomly benefit from alerting effects due to inconsistent starting procedures. Front. Psychol. 7:119. doi: 10.3389/fpsyg.2016.00119 Commentary: Life is unfair, and so are racing sports: some athletes can randomly benefit from alerting effects due to inconsi...

Abstract We give several explicit examples of compact manifolds with a 1-parameter family almost complex structures having arbitrarily small Nijenhuis tensor in the C 0 -norm. The 4-dimensional possess no structure, whereas 6-dimensional example does not left invariant and whether it possesses structure appears to be unknown.

We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the associative version of Nijenhuis tensors. Explicit examples, e.g. for the harmonic oscillator, are given.

After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson–Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.

BACKGROUND AND AIMS Diverse gauges have been used to measure and determine bracket height for correct bracket positioning. The aim of the present study was to determine and compare bracket positioning accuracy by using height bracket positioning gauge (HBPG) and Boone gauge (BG). MATERIALS AND METHODS Nineteen sets of stone models were prepared from one patient. One set was employed to de-ter...