In this part I continue the discussion of role computers in current research on additive number theory, particular solution easier Waring problem. This problem consists finding for each natural k smallest such s =v(k) that all numbers n can be written as sums integer k-th powers = ± x1k ... xsk with signs. turned out to much harder than original It is intimately related many other problems arit...

By electrical characterization of thin films deposited by atomic layer deposition, Hf x Zr 1−x O 2 (HZO) is shown to be ferroelectric as-deposited, i.e., without any annealing step, using a thermal budget 300 °C. fabricating laminated HZO rather than the traditional solid-solution HZO, remanent polarization P r = 11 μC/cm and endurance exceeding 10 6 are obtained. Films grown on thermally react...

let g be a simple connected graph. the first and second zagreb indices have been introducedas  vv(g)(v)2 m1(g) degg and m2(g)  uve(g)degg(u)degg(v) , respectively,where degg v(degg u) is the degree of vertex v (u) . in this paper, we define a newdistance-based named hyperzagreb as e uv e(g) .(v))2 hm(g)     (degg(u)  degg inthis paper, the hyperzagreb index of the cartesian product...