A theorem on Green's modular representation ring

Reducing brown ring patch severity on Poa annua greens

We have conducted joint research studies on the management of brown ring patch since 2010. From a feld research perspective, this disease has been challenging to work with because it is diffcult to fnd naturally infected putting greens with uniform disease incidence and severity. The main body of research presented in this paper comes from work conducted in 2010 and 2011 on a putting green in N...

The Jónsson Theorem about the Representation of Modular Lattices

Let A be a non empty set and let P , R be binary relations on A. Let us observe that P ⊆ R if and only if: (Def. 1) For all elements a, b of A such that 〈a, b〉 ∈ P holds 〈a, b〉 ∈ R. Let L be a relational structure. We say that L is finitely typed if and only if the condition (Def. 2) is satisfied. (Def. 2) There exists a non empty set A such that (i) for every set e such that e ∈ the carrier of...

Hyperseparoids: A Representation Theorem

In this note, hyperseparoids are introduced; hyperseparoids are to separoids as Tverberg’s theorem is to Radon’s theorem. Also, a geometric representation theorem for acyclic kseparoids is presented which generalises that for separoids exhibited in [2].

Beilinson ’ S Theorem on Modular Curves

0. Introduction. The purpose of this chapter is to give a detailed account of the known evidence ([Be1], §5) for Beilinson’s conjecture concerning the values at s = 2 of L-functions of modular forms of weight two. We do not discuss here the results concerning the L-values at other integers s ≥ 2 (for which see [Be2]), nor do we treat the case of the product of two modular curves (also to be fou...

A Theorem on Matrices over a Commutative Ring