Inverse Gröbner Basis Problem in Codimension Two

The Inverse Gröbner Basis Problem in Codimension Two

The inverse Gröbner basis problem is to find the ideals that have a given monomial ideal as its initial ideal. We consider the problem of finding when the given monomial ideal is the initial ideal of a prime ideal. Kalkbrenner and Sturmfels (1995), in Theorem 1, prove that the radical of the initial ideal of a prime ideal is equi-dimensional and connected in codimension one or equivalently, the...

Lifting Problem in Codimension 2 and Initial Ideals

Vanishing Cycles, the Generalized Hodge Conjecture and Gröbner Bases

Let X be a general complete intersection of a given multi-degree in a complex projective space. Suppose that the anti-canonical line bundle of X is ample. Using the cylinder homomorphism associated with the family of complete intersections contained in X, we prove that the vanishing cycles in the middle homology group of X are represented by topological cycles whose support is contained in a pr...

Determination of a Source Term in an Inverse Heat Conduction Problem by Radial Basis Functions

In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (I...

The use of inverse quadratic radial basis functions for the solution of an inverse heat problem

‎In this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎The method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...