The space l^p with 1≤p∞ is the set of real numbers that satisfy _(n=1)^∞▒〖|x_n |^p∞〗.The function in vector X which has value fulfills norm-2 properties denoted by ,⋅‖ and pair (X,‖⋅,⋅‖) called space.A said to be complete or a Banach-2 if every Cauchy sequence converges an element space.This research was conducted prove norm-2.The first step completeness norm contained satisfies norm-2.Next, de...

We estimate spectral gaps for the Hodge norm on quadratic differentials. To each tangent direction at any point (X, q) in principal stratum of differentials, we associate a norm, and control logarithmic derivative vectors perpendicular to directions terms q-areas components corresponding thick–thin decompositions lengths short curves q-metric. In worst case scenario, one gets gap size $$C_{g,n}...