We consider a random walk Wn on the locally free group (or equivalently a signed random heap) with m generators subject to periodic boundary conditions. Let #T (Wn) denote the number of removable elements, which determines the heap's growth rate. We prove that limn→∞ E(#T (Wn)) m ≤ 0.32893 for m ≥ 4. This result disproves a conjecture (due to Vershik, Nechaev and Bikbov [4]) that the limit tend...

Any (global) deformation of a flag manifold F with b2 = 1 is biholomorphic to F .

A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. In the present paper we introduced a weak metric, called the Apollonian weak metric, on any subset of a Euclidean space which is either bounded or whose boundary is unbounded. We then relate this weak metric to some familiar metrics such as the Poincaré metric, the Klein-Hil...

In this review we report on the enantiomerization of tetrahedral racemic-[(NH4)4∩{Mg4(L1)6}] monitored by means variable temperature (VT) 1H NMR spectroscopy. The enantiotopization diastereotopic protons is due to simultaneous Bailar twists at four octahedrally coordinated magnesium centres, synchronized with atropisomerization six edge-bridging ligands (L1)2-.The VT spectrum meso-[In4(L2)4] co...

A field experiment entitled “standardization of nipping technique for enhancement seed yield and quality in sunn hemp” was conducted during Kharif 2019-20 2020-21 at Seed Production Block, NSP, Unit, UAS, Raichur. The laid out a randomized complete block design with fifteen treatments including foliar spray cycocel their combinations three replications. results emanated from the recorded maximu...