We generalize Gel’fond’s criterion of algebraic independence to the context of a sequence of polynomials whose first derivatives take small values on large subsets of a fixed subgroup of C, instead of just one point (one extension deals with a subgroup of C).

Let C be a smooth projective irreducible curve defined over a finite field k. Let G be a finite subgroup of Aut(C) of order prime to char(k) and M the |G|-th cyclotomic field. We show that certain idempotent relations in M [G] imply relations among arithmetic invariants of the fundamental groups of the quotient curves (C/H)×k k, where H is a subgroup of G.

Given a normal subgroup bundle A of the isotropy groupoid ?, we obtain twisted action quotient ?/A on group C?-algebras determined by whose crossed product recovers C?-algebra C?(?). Restricting to case where is abelian, describe C?(?) as associated T-groupoid over tranformation obtained from canonical Pontryagin dual space A. We give some illustrative examples this result.

conclusions presence of cae in patients with cas increases its cardiovascular event rate. isolated cae is not a benign finding and mi can occur. risk factors of cae are similar to cas, but c/s is more associated with cae than cas. dm is seen in cae patients less than cas. results hypertension (htn), dyslipidemia (dlp), and male sex were matched in both groups without significant difference. cig...