English-speaking children with specific language impairment (SLI) are known to have particular difficulty with the acquisition of grammatical morphemes that carry tense and agreement features, such as the past tense -ed and third-person singular present -s. In this study, an Extended Optional Infinitive (EOI) account of SLI is evaluated. In this account, -ed, -s, BE, and DO are regarded as fini...

In this paper, we examine a new approach to topos theory – rather than considering subobjects, look at quotients. This leads to the notion of a copower object, which is the object of quotients of a given object. We study some properties of copower objects, many of which are similar to the properties of a power objects. Given enough categorical structure (i.e. in a pretopos) it is possible to ge...

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...

The notion of the Cousin complex of a module was given by Sharp in 1969. It wasn’t known whether its cohomologies are finitely generated until recently. In 2001, Dibaei and Tousi showed that the Cousin cohomologies of a finitely generated A-module M are finitely generated if the base ring A is local, has a dualizing complex, M satisfies Serre’s (S2)-condition and is equidimensional. In the pres...

Abstract We prove the finiteness of formal analogs spherical function (Spherical Finiteness), ${\textbf c}$-function (Gindikin–Karpelevich and obtain a analog Harish-Chandra’s limit (Approximation Theorem) relating in setting $p$-adic Kac–Moody groups. The theorems imply that Gindikin–Karpelevich integral is well defined local settings. These results extend Braverman–Garland–Kazhdan–Patnaik’s a...

Consider a ring K, a topological space X and a sheaf A on X of K[[~]]-algebras. Assuming that A is ~-complete and without ~torsion, we first show how to deduce a coherency theorem for complexes of A -modules from a corresponding property for complexes of A /~A -modules. We apply this result to prove that, under a natural properness condition, the convolution of two coherent kernels over deforma...

Torelli space Tg (g ≥ 2) is the quotient of Teichmüller space by the Torelli group Tg. It is the moduli space of compact, smooth genus g curves C together with a symplectic basis of H1(C;Z) and is a model of the classifying space of Tg. Mess, in his thesis [12], proved that T2 has the homotopy type of a bouquet of a countable number of circles. Johnson and Millson (cf. [12]) pointed out that a ...

By imposing on the most general renormalizable quantum field theory the requirement of the absence of ultraviolet-divergent renormalizations of the physical parameters (masses and coupling constants) of the theory, finite quantum field theories in four space-time dimensions may be constructed. Famous “prototypes” of these form certain well-known classes of supersymmetric finite quantum field th...

We establish the ultraviolet finiteness of various classes of noncommutative gauge theories.