We combine the fundamental results of Breuillard, Green, and Tao (Publ Math Inst Hautes Études Sci 116:115–221, 2012) on structure approximate groups, together with “tame” arithmetic regularity methods based work authors Terry (J Eur Soc (JEMS) 24(2):583–621, 2022), to give a theorem for finite subsets A arbitrary groups G where has “small tripling” bounded VC-dimension: Roughly speaking, up sm...

Given a finite n-element set X , a family of subsets F ⊂ 2 is said to separate X if any two elements of X are separated by at least one member of F . It is shown that if |F| > 2, then one can select ⌈logn⌉ + 1 members of F that separate X . If |F| ≥ α2 for some 0 < α < 1/2, then logn+O(log 1 α log log 1 α ) members of F are always sufficient to separate all pairs of elements of X that are separ...

Ciekawym, czy pjd polskie znaczki: .

OBJECTIVES Right ventricular (RV) contractile performance remains poorly characterised, particularly in humans. Conductance catheter techniques have the potential to overcome the geometric difficulties in RV volume measurement that have hindered systematic studies of RV pressure volume relations. The present study examines changes in parallel conductance (Vc) that may occur during the cardiac c...

The role of endogenous vitamin C (VC) in emotion and psychiatric measures has long been uncertain. We aimed to investigate how an individual's VC status impacts his or her mental health. Our hypothesis is that body VC levels modulate anxiety, anorexia, and depressive phenotypes under the influence of psychosocial rearing environments and sex. The VC status of senescence marker protein-30/glucon...