In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a box-shaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not onl...

Energy-momentum tensor for the toroidal Lie algebras. Abstract. We construct vertex operator representations for the full (N + 1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine sl N VOA and a twisted Heisenberg-Virasoro VOA. The modules for the toroidal VOA are also modules...

We study a family of symmetric functions $\hat F_z$ indexed by involutions $z$ in the affine group. These power series are analogues Lam's Stanley and generalizations involution introduced Hamaker, Pawlowski, first author. Our main result is to prove transition formula for which can be used define an analogue Lascoux-Sch\"utzenberger tree. proof this relies on Lam Shimozono's some new technical...

In the present paper, we introduce a new variant of Bernstein-Kantorovich operators which reproduce affine functions. The approximation rate for continuous functions and Voronovskaja?s asymptotic estimate are obtained.