Local Weyl modules over two-dimensional currents with values in glr are deformed into spaces with bases related to parking functions. Using this construction we 1) reproof that dimension of the space of diagonal coinvariants is not less than the number of parking functions; 2) describe the limit of Weyl modules in terms of semi-infinite forms and find the limit of characters; 3) propose a lower...

Introduction Some recent functional-structural plant models (FSPMs) combine an explicit representation of plant architecture with a mechanistic approach to carbohydrate (C) allocation [1]. In this context, a plant is represented by a set of connected semi-autonomous modules and the C flow into the growing modules is determined by the intrinsic properties of the modules, environmental conditions...

3-methyl-1-sulfonic acid imidazolium tetrachloroferrate {[Msim]FeCl4} as an efficient sulfur catalyst was prepared and applied, as an efficient catalyst, for the cross-aldol condensation reaction between cycloalkanones and arylaldehydes to give α,αʹ- bis(arylidene)cycloalkanones in high yields and short reaction times at 75 °C under solvent-free conditions. 3-methyl-1-sulfonic acid imidazolium...

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We prove that these categories are strongly complete, strongly cocomplete, and (Epi,Mono)-structured. We prove...

This article treats the problem of deriving the reflector of a semi-abelian category A onto a Birkhoff subcategory B of A. Basing ourselves on Carrasco, Cegarra and Grandjeán’s homology theory for crossed modules, we establish a connection between our theory of Baer invariants with a generalization—to semi-abelian categories— of Barr and Beck’s cotriple homology theory. This results in a semi-a...

Stability plays a central role in arithmetic. In this article, we explain some basic ideas and present certain constructions for such studies. There are two aspects: namely, general Class Field Theories for Riemann surfaces using semistable parabolic bundles & for p-adic number fields using what we call semi-stable filtered (φ,N;ω)-modules; and non-abelian zeta functions for function fields ove...

Let R be a commutative Noetherian ring of prime characteristic p. Assume R (or, more generally, a finitely generated R-module N with SuppR(N) = Spec(R)) has finite F-representation type (abbreviated FFRT) by finitely generated R-modules. Then, for every c ∈ R◦, there is a uniform test exponent Q = p for c and for all R-modules. As a consequence, we show the existence of uniform test exponents o...

We investigate a generalization of extending modules relative to a class of modules and a proper class of short exact sequences of modules.