Geometry of Matrix Polynomial Spaces

Matrix Models and Geometry of Moduli Spaces

We give the description of discretized moduli spaces (d.m.s.) M disc g,n introduced in [1] in terms of discrete de Rham cohomologies for moduli spaces Mg,n. The generating function for intersection indices (cohomological classes) of d.m.s. is found. Classes of highest degree coincide with the ones for the continuum moduli space Mg,n. To show it we use a matrix model technique. The Kontsevich ma...

Differential Polynomial Rings of Triangular Matrix Rings

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field

New Bases for Polynomial-Based Spaces

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...

Function spaces of Rees matrix semigroups

We characterize function spaces of Rees matrixsemigroups. Then we study these spaces by using the topologicaltensor product technique.