introdouction: the aim of this study was to compare the ratios of the mesiodistal width of the upper and lower central incisors between natural teeth and those produced artificially by ideal makoo, ivoclar, and vitapan, in iran. materials and methods: the mesiodistal width of the upper and lower central incisors was measured in 120 students, using calipers placed at the height of contour of the...

Introdouction: The aim of this study was to compare the ratios of the mesiodistal width of the upper and lower central incisors between natural teeth and those produced artificially by Ideal Makoo, Ivoclar, and Vitapan, in Iran. Materials and methods: The mesiodistal width of the upper and lower central incisors was measured in 120 students, using calipers placed at the height of contour...

We obtain, using the Birman-Schwinger method, a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics. These conditions yield a monotonic series of lower limits on the “critical” value of the strength of the potential (for which a first bound state appears) which converges to th...

We take a step towards the development of a nilpotency theory for loops based on the commutatorassociator filtration instead of the lower central series. This nilpotency theory shares many essential features with the associative case. In particular, we show that the isolator of the nth commutator-associator subloop coincides with the nth dimension subloop over a field of characteristic zero. Th...