Spatial planning in border areas in Iran because of long borders and settling more than half ofthe provinces in the country's international borders with neighbouring countries play particular role in the planningsystem. This article aims to clarify the position of border areas spatial planning in the country planning system,identifying its elements, elucidating how these elements relate to othe...

In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite programming. While the border basis algorithms of [17] are efficient and numerically stable for computing ...

This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal I . The criterion used in the computation involves specific commutation polynomials and leads to an algorithm and an implementation extending the one provided in [29]. This general border basis algorithm weakens the monomial ordering requirement for Gröbner bases computations. It is up to date the ...

Transporting epithelial cells build apical microvilli to increase membrane surface area and enhance absorptive capacity. The intestinal brush border provides an elaborate example with tightly packed microvilli that function in nutrient absorption and host defense. Although the brush border is essential for physiological homeostasis, its assembly is poorly understood. We found that brush border ...

In this paper we generalize the Macaulay-Buchberger basis theorem to the case, where the residue class polynomial ring over a Noetherian ring is not necessarily a free module. Recently, this theorem has been extended from polynomial rings over fields to rings, when residue class polynomial ring is free in (Francis & Dukkipati, 2014). As an application of this generalization we develop a theory ...

Land border crossings in North America that serve high volumes of automobile and truck traffic experience congestion and delay, resulting in adverse effects on level of service, transportation costs, commerce, tourism, and the environment. Although efforts have been underway to expedite the customs inspection process (without compromising security), improving the reliability of delay estimates ...

The Buchberger-Möller algorithm is a well-known efficient tool for computing the vanishing ideal of a finite set of points. If the coordinates of the points are (imprecise) measured data, the resulting Gröbner basis is numerically unstable. In this paper we introduce a numerically stable Approximate Vanishing Ideal (AVI) Algorithm which computes a set of polynomials that almost vanish at the gi...

A recent physiological finding of neural coding for border ownership (BO) that defines the direction of a figure with respect to the border has provided a possible basis for figure-ground segregation. To explore the underlying neural mechanisms of BO, we investigated stimulus configurations that activate BO circuitry through psychophysical investigation of the BO-dependent tilt aftereffect (BO-...