As stated above, (A) is aimed at establishing a Non-Abelian Class Field Theory. The starting point here is the following classical result: Over a compact Riemann surface, a line bundle is of degree zero if and only if it is flat, i.e., induced from a representation of fundamental group of the Riemann surface. Clearly, being a bridge connecting divisor classes and fundamental groups, this result...

Cousin's lemma is a compactness principle that naturally arises when studying the gauge integral, generalisation of Lebesgue integral. We study axiomatic strength for various classes functions, using Friedman and Simpson's reverse mathematics in second-order arithmetic. prove that, over $\mathsf{RCA}_0$: (i) continuous functions equivalent to $\mathsf{WKL}_0$; (ii) Baire class 1 $\mathsf{AC...

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...

The amplitude distribution in a SAR image can present a heavy tail. Indeed, very high–valued outliers can be observed. In this paper, we propose the usage of the Harmonic, Geometric and Arithmetic temporal means for amplitude statistical studies along time. In general, the arithmetic mean is used to compute the mean amplitude of time series. In this study, we will show that comparing the behavi...