Large gauge transformations

Since under large gauge transformations Ai => WAiU+iWdiU, Ncs => Ncs + Nw where Nw is the winding number of the gauge transformation ... 

This distinction is largely formal, owing to the substantial identity of the unitary time-dependent transformation (8)-(9) with the gauge transformations of the Hamiltonian and its eigenfunctions [21-22]. However, alterna-... 

It is apparent that the numbers and masses of the flavor and quark-lepton transforming gauge bosons are larger than those of the SU(5) minimal model. This means that the value of a is lower, and assuming that the duration of the inflationary period is fixed, the scale for the expansion of the universe is reduced. This means that there is the enhanced prospect for deviations from flatness. So one may presume that the universe started as a small 3-sphere with a large curvature, where the inflationary period flattened out the universe, but maybe not completely. This leaves open the prospect that if before inflation that if the universe were open or closed, k = 1, that the universe today still contains this structure on a sufficiently large scale. The closer to flatness the universe is, the tighter are the constraints on the masses of particles in the early universe. 

Inductive sensors for displacement measurement are based on the fact that inductance of a cod, L = n Gfi, where n = number of turns of coil, G = form factor, and ju = effective permeability of the medium. Each of these three parameters can be changed by mechanical displacement. Linear variable differential transformer inductive sensors show good linearity over a large range of displacement, high resolution, and better sensitivity compared with strain gauge [11]. 

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