On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations

It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transformations on a finite chain Xn is a semilattice of idempotents, and so the semigroup of all order-preserving transformations of Xn is not covered by its inverse subsemigroups. This result is used to show that the semigroup of all orientation-preserving transformations and the semigroup of all orientation-preserving or orientation-reversing transformations of the chain Xn are covered by their inverse subsemigroups precisely when n≤3

Slowly synchronizing automata and digraphs

We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.Comment: 13 pages, 5 figure

Synchronizing automata with a letter of deficiency 2

AbstractWe present two infinite series of synchronizing automata with a letter of deficiency 2 whose shortest reset words are longer than those for synchronizing automata obtained by a straightforward modification of Černý’s construction

Omega-3 polyunsaturated fatty acids: Their potential role in blood pressure prevention and management

Omega-3 polyunsaturated fatty acids (PUFAs) from fish and fish oils appear to protect against coronary heart disease: their dietary intake is in fact inversely associated to cardiovascular disease morbidity/mortality in population studies. Recent evidence suggests that at least part of their heart protective effect is mediated by a relatively small but significant decrease in blood pressure level. In fact, omega-3 PUFAs exhibit wide-ranging biological actions that include regulating both vasomotor tone and renal sodium excretion, partly competing with omega-6 PUFAs for common metabolic enzymes and thereby decreasing the production of vasocostrincting rather than vasodilating and anti-inflammatory eicosanoids. PUFAs also reduce angiotensin-converting enzyme (ACE) activity, angiotensin II formation, TGF-beta expression, enhance eNO generation and activate the parasympathetic nervous system. The final result is improved vasodilation and arterial compliance of both small and large arteries. Preliminary clinical trials involving dyslipidemic patients, diabetics and elderly subjects, as well as normotensive and hypertensive subjects confirm this working hypothesis. Future research will clarify if PUFA supplementation could improve the antihypertensive action of specific blood pressure lowering drug classes and of statins

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Moral courage in the workplace: moving to and from the desire and decision to act

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72135/1/j.1467-8608.2007.00484.x.pd