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 new series of heterometallic wheels, isolated as [Fe18M6(piv)12(Htea)18(tea)6(N3)6]·n(solvent) (MIII = Y (1a, 1b), Gd (2a, 2b), and Dy (3a, 3b); Hpiv pivalic acid, H3tea triethanolamine), forms by the reaction trinuclear μ3-oxo-linked or hexanuclear μ-OH-linked Fe(III) pivalate clusters with rare earth nitrates, H3tea, azide ligands in MeOH/MeCN EtOH/MeCN media under ultrasonic irradiation. S...

Abstract Robotic splicing of steel arches is a challenging task that necessary to realize the grasping and docking in limited space. Steel often have mass more than 200 kg length 4 m. Owing large volume high requirements for accurately positioning splicing, it difficult general manipulator meet stiffness requirements. To enhance structural arch manipulator, single-degree-of-freedom (DOF) closed...