Let n, r ∈ N. The affine Schur algebra S̃(n, r) (of type A) over a field K is defined to be the endomorphism algebra of certain tensor space over the extended affine Weyl group of type Ar−1. By the affine Schur–Weyl duality it is isomorphic to the image of the representation map of the U(ĝl n ) action on the tensor space when K is the field of complex numbers. We show that S̃(n, r) can be defined...

An affine manifold is a differentiable manifold together with an atlas of coordinate charts whose coordinate changes extend to affine automorphisms of Euclidean space. These charts are called atline coordinates. A map between affine manifolds is called affine it its expression in affine coordinates is the restriction of an aftine map between vector spaces. Thus we form the category of affine ma...

This paper proposes a Bayesian affine transformation of hidden Markov model (HMM) parameters for reducing the acoustic mismatch problem in telephone speech recognition. Our purpose is to transform the existing HMM parameters into its new version of specific telephone environment using affine function so as to improve the recognition rate. The maximum a posteriori (MAP) estimation which merges t...

It is known that piecewise affine surface homeomorphisms always have measures of maximal entropy. This is easily seen to fail in the discontinuous case. Here we describe a piecewise affine, globally continuous surface map with no measure of maximal entropy.

An affine manifold is a manifold with a distinguished system of affine coordinates, namely, an open covering by charts which map homeomorphically onto open sets in an affine space E such that on overlapping charts the homeomorphisms differ by an affine automorphism of E. Some, but certainly not all, affine manifolds arise as quotients Ω/Γ of a domain in E by a discrete group Γ of affine transfo...

Let M be a compact connected Fujiki manifold, G semisimple affine algebraic group over C with one simple factor and P fixed proper parabolic subgroup of G. For holomorphic principal G–bundle EG M, let EP the P–bundle EG⟶EG/P given by quotient map. We prove that following three statements are equivalent: (1) ad(EG) is numerically flat, (2) line bundle ⋀topad(EP)⁎ nef, (3) for every reduced irred...

Abstract Let $${\mathcal {C}} \subset {\mathbb {N}}^p$$ C ⊂ N p be a finitely generated integer cone and $$S\subset {\mathcal {C}}$$ S an affine semigroup such that the real cones by S are equal. ...

This problem is related to a conjecture of Kobayashi and Zaidenberg which states that for a sufficiently general curve D ⊂ P of degree d ≥ 5, as general in the sense that D lies in |OP2(d)| ∼= P d(d+3)/2 with countably many closed proper subvarieties removed, the affine variety P\D is hyperbolic. One necessary condition for P\D being hyperbolic is that there is no rational curve C ⊂ P meeting D...

We consider the inverse problem of determining the twisting function in a infinite cylindrical twisted waveguide from the corresponding DN map. This problem, which is naturally linked to some inverse anisotropic conductivity problem in a straight waveguide, remains generally open, unless the twisting function is assumed to be affine. Namely we prove Lipschitz stability in the determination of a...