In this paper, we generalize the notion of border bases of zerodimensional polynomial ideals to the module setting. To this end, we introduce order modules as a generalization of order ideals and module border bases of submodules with finite codimension in a free module as a generalization of border bases of zero-dimensional ideals in the first part of this paper. In particular, we extend the d...

Cationic and anionic species of heavier low-valent group 14 elements are intriguing targets in main group chemistry due to their synthetic potential and industrial applications. In the present study, we describe the synthesis of cationic (MCl(+)) and anionic (MCl(3)(-)) species of heavier low-valent group 14 elements of germanium(II) and tin(II) by using the substituted Schiff base 2,6-diacetyl...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

geographical bases have significant function in human settlements in terms of distribution and sustainability. thisstudy attempted to provide an insight into the role of geographical bases in rural settlement distribution in arid areas.accordingly, this study was done in the rural area of khour-biabanak, naein city in esfahan province. themethodology was that of a correlative research, to reali...

This paper presents a simple method that reduces the problem of detecting conflict-free assumption-based knowledge bases to the problem of testing satisfiability.

Using selected theoretical methods the affinity of a large range of Lewis bases towards model cations has been quantified. The range of model cations includes the methyl cation as the smallest carbon-centered electrophile, the benzhydryl and trityl cations as models for electrophilic substrates encountered in Lewis base-catalyzed synthetic procedures, and the acetyl cation as a substrate model ...