In this note, we prove that the projective normality of (P(V )/G,L), the celebrated theorem of Erdös-Ginzburg-Ziv and normality of an affine semigroup are all equivalent, where V is a finite dimensional representation of a finite cyclic group G over C and L is the descent of the line bundle O(1)⊗|G|.

We propose a class of weighted least squares estimators for the tail index distribution function with regularly varying tail. Our approach is based on method developed by Holan and McElroy (2010) Parzen index. prove asymptotic normality consistency under suitable assumptions. These earlier are compared in various models through simulation study using mean squared error as criterion. The results...

We show that the poset of regions (with respect to a canonical base region) of a supersolvable hyperplane arrangement is a congruence normal lattice. Specifically, the poset of regions of a supersolvable arrangement of rank k is obtained via a sequence of doublings from the poset of regions of a supersolvable arrangement of rank k − 1. An explicit description of the doublings leads to a proof t...

We study the combination of the following already known ideas for showing connuence of unconditional or conditional term rewriting systems into practically more useful connuence criteria for conditional systems: Our syntactic separation into constructor and non-constructor symbols, Huet's introduction and Toyama's generalization of parallel closedness for non-noetherian unconditional systems, t...