Relative differential forms and complex polynomials

Brenstien polynomials and its application to fractional differential equation

The paper is devoted to the study of Brenstien Polynomials and development of some new operational matrices of fractional order integrations and derivatives. The operational matrices are used to convert fractional order differential equations to systems of algebraic equations. A simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

Fractional differential equations with Legendre polynomials

Ozeki Polynomials and Jacobi Forms

A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over F2. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broué-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F2f . We show how to construct Jacobi forms with various ind...

Complex manifolds, Kahler metrics, differential and harmonic forms

Definition 1.1 (Complex Manifold). A complex manifold is a manifold with coordinates holomorphic on C rather than C∞ on R. What is the difference betwene holomorphic and C∞? From the PDE point of view, they must satisfy the Cauchy-Riemann equations: f(z) = u+ iv is holomorphic if and only if ∂u ∂x = ∂v ∂y and ∂u ∂y = − ∂v ∂x . The fact that this causes the function f to be analytic(holomorphic)...

Computing difference-differential dimension polynomials by relative Gröbner bases in difference-differential modules

In this paper we present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural double filtration. The approach is based on a method of special Gröbner bases with respect to “generalized term orders” on Nm × Zn and on difference-differential modules. We define a special type of reduction for two generalized ...