The notion of locally finite part of the dual coalgebra of certain quantized coordinate rings is introduced. In the case of irreducible flag manifolds this locally finite part is shown to coincide with a natural quotient coalgebra U of Uq(g). On the way the coradical filtration of U is determined. A graded version of the duality between U and the quantized coordinate ring is established. This l...

‎let $g$ be a group with identity $e.$ let $r$ be a $g$-graded‎ ‎commutative ring and $m$ a graded $r$-module‎. ‎in this paper‎, ‎we‎ ‎introduce several results concerning graded classical prime‎ ‎submodules‎. ‎for example‎, ‎we give a characterization of graded‎ ‎classical prime submodules‎. ‎also‎, ‎the relations between graded‎ ‎classical prime and graded prime submodules of $m$ are studied‎.‎

let  be a graded ring and  be a graded -module. we define a topology on graded prime spectrum  of the graded -module  which is analogous to that for , and investigate several properties of the topology.

A theory of graded manifolds can be viewed as a generalization differential geometry smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also $\mathbb{Z}$-graded variables either commute or anticommute, according their degree. To obtain consistent global description manifolds, resorts sheaves commutative associative algebras secon...

Additive manufacturing has emerged as a promising approach for fabricating graded refractive index structures that control the electromagnetic response of radio frequency (RF) devices. However, current 3D printing methods cannot produce continuous gradients from multiple materials. Here, low-loss dielectrics via active mixing nanocomposite inks composed block copolymers and oxide nanoparticles ...

It is a classical observation of Serre that the Hecke algebra acts locally nilpotently on the graded ring of modular forms modulo 2 for the full modular group. Here we consider the problem of classifying spaces of modular forms for which this phenomenon continues to hold. We give a number of consequences of this investigation as they relate to quadratic forms, partition functions, and central v...

We investigate the possibility of constructing a locally supersymmetric extension of NGT (Nonsymmetric Gravitation Theory), based on the graded extension of the Poincaré group. In the framework of the simple model that we propose, we end up with a no-go result, namely the impossibility of cancelling some linear contribution in the gravitino field. This drawback seems to seriously undermine the ...

Abstract. An interior penalty method for certain two-dimensional curl-curl problems is investigated in this paper. This method computes the divergence-free part of the solution using locally divergence-free discontinuous P1 vector fields on graded meshes. It has optimal order convergence (up to an arbitrarily small ) for the source problem and the eigenproblem. Results of numerical experiments ...