In this paper, we consider translation and multiplication operators acting on the rings of symmetric and nonsymmetric polynomials and study their matrix coefficients with respect to the bases of Jack polynomials and interpolation polynomials. The main new insight is that the symmetric and nonsymmetric cases share a key combinatorial feature, that of a locally finite graded poset with a minimum ...

We construct explicitly regular sequences in the semigroup ring R = C[K] of lattice points of the graded cone K. We conjecture that the quotients of R by these sequences describe locally string-theoretic cohomology of a toroidal singularity associated to K. As a byproduct, we give an elementary proof of the result of Hochster that semigroup rings of rational polyhedral cones are Cohen-Macaulay.

Functionally graded material (FGM) arches may be subjected to a locally radial load and have different distributions leading nonlinear in-plane buckling behavior. Little studies is presented about effects of the type on FGM under in literature insofar. This paper focuses investigating behavior fixed uniformly distributed incorporating distributions. New theoretical solutions for limit point bif...

Graded electrodes for Li-ion batteries aim to exploit controlled variations in local electrode microstructure improve overall battery performance, including reduced degradation rates and increased capacity at high discharge rates. However, the mechanisms by which grading might deliver performance benefit, under what conditions, are not yet fully understood. A electrochemical model (a modified D...

Let D be the ring of differential operators on a smooth irreducible affine variety X over C; or, more generally, the enveloping algebra of any locally free Lie algebroid on X. The category of finitely-generated graded modules of the Rees algebra e D has a natural quotient category qgr( e D) which imitates the category of modules on Proj of a graded commutative ring. We show that the derived cat...

where t· x denotes the action of t on x. The set Xw is known to be a locally-closed c* -stable algebraic subvariety of X isomorphic to an affine space. The pieces Xw form a cell decomposition X = UWEW XW ' W E W, the socalled Bialynicki-Birula decomposition. We assume this decomposition to be an algebraic stratification of X (the closure of a cell may not be a union of cells, in general). Let ....

0 Introduction This is a reasonably faithful account of the ve lectures I delivered at the summer course \Geometria Algebraica no Commutativa y Espacios Cuanti-cos" for graduate students, in Spain, July 25{29, 1994. The material covered was, for the most part, an abridged version of Artin and Zhang's paper 2]. Fix a eld k. Given a Z-graded k-algebra, A say, which for simplicity is assumed to be...

We construct a classification of coherent sheaves with an integrable log connection, or, more precisely, sheaves with an integrable connection on a smooth log analytic space X over C. We do this in three contexts: sheaves and connections which are equivariant with respect to a torus action, germs of holomorphic connections, and finally global log analytic spaces. In each case, we construct an e...

A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of “gauge fields” (sections in the category of graded manifolds) and each cohomology class of a certain subcomplex of forms on the fiber we associate a cohomology class on the base. Any ...