Let M∗(l) = M∗(Γ1(l),C) be the ring of holomorphic modular forms on Γ1(l). In this talk we use the combinatorics of complete toric varieties to construct a subring T∗(l) ⊂ M∗(l), the subring of toric modular forms (§2). This is a natural subring, in the sense that it behaves nicely with respect to natural operations on M∗(l) (namely, Hecke operators, Fricke involution, and the theory of oldform...

The goal of this paper is to develop a theory of content for vague language. My proposal is based on the following three theses: (1) language-mastery is not rulebased—it involves a certain kind of decision-making; (2) a theory of content is to be thought of instrumentally—it is a tool for making sense of our linguistic practice; and (3) linguistic contents are only locally defined—they are only...

In this paper, we study some of the properties of interval valued intuitionistic fuzzy subring of a ring and prove some results on these. 2000 AMS SUBJECT CLASSIFICATION: 03F55, 08A72, 20N25.

An expansion of a definably complete field either defines a discrete subring, or the image of every definable discrete set under every definable map is nowhere dense. As an application we show a definable version of Lebesgue’s differentiation theorem.

The notion of an amenable equivalence relation was introduced by Zimmer in the course of his analysis of orbit equivalence relations in ergodic theory (see [12]). Recently it played an important role in Monod’s striking family of examples of nonamenable groups which do not contain nonabelian free subgroups. If A is a subring of R, define H(A) to be the group of all piecewise PSL2(A) homeomorphi...

We prove that for a subring R⊆Q and free group F of rank at least 2 the length Bousfield's HR-localization tower is ω+ω. The key ingredient proof theory polynomial functors over Q.

Vagueness is a common human knowledge and linguistic phenomenon, typically manifested by predicates that lack clear applicability conditions and boundaries such as High, Expert or Bad. In the context of ontologies and semantic data, the usage of such predicates within ontology element definitions (classes, relations etc.) can hamper the latter’s quality, primarily in terms of shareability and m...