We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in Aoki and Takemura [2008a]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof in Aoki and Takemura [2008a] which was based on stabilizers o...

In earlier papers it was shown that the generic tropical variety of an ideal can contain information on algebraic invariants as for example the depth in a direct way. The existence of generic tropical varieties has so far been proved in the constant coefficient case for the usual notion of genericity. In this paper we generalize this existence result to include the case of non-constant coeffici...

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [2]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof in [2] which was based on stabilizers of a subset of indeterminates, the perturbati...

A number of typologies have been developed in the strategic management literature to categorize strategies that an organization can pursue at the business level. Extensive research has established Porter's generic strategies of (1) cost leadership, (2) differentiation, (3) differentiation focus, (4) cost focus, and (5) stuck-in-the-middle as the dominant paradigm in the literature. The purpose ...

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in Aoki and Takemura [2008b]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof in Aoki and Takemura [2008b] which was based on stabilizers o...

This paper has two aims. The first is to study ideals of minors of matrices whose entries are among the variables of a polynomial ring. Specifically, we describe matrices whose ideals of minors of a given size are prime. The “generic” case, where all the entries are distinct variables has been studied extensively (cf. [1] and [2] for a thorough account.) While some special cases, such as catale...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...