In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Gröbner basis of Z[x]-lattices, regular and coherent difference ascending chains, and partial characters over Z[x]-lattices, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, and perfect a...

Emergence has a long and controversial history. In this paper we briefly review the primary strands of the debate, paying attention to its use in the fields of philosophy of science and mind, social science and systems theory including the theory of complex systems. We argue that it is important to recognize why emergence in social systems is fundamentally different from other natural systems. ...

We study the cohomology of reflexive rank 2 sheaves on smooth projective threefolds. Applications are given to the moduli space of reflexive sheaves.

Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.

Abstract. Let δ(P) be the δ-vector of a reflexive polytope P ⊂ R of dimension d and δ(P) the δ-vector of the dual polytope P ⊂ R. In general, δ(P) = δ(P) does not hold. In this paper, we give a higher-dimensional construction of a reflexive polytope whose δ-vector equals the δ-vector of the dual polytope. In particular, we consider the case that the reflexive polytope and the dual polytope are ...

An Autonomous Mobile Robot is an artificially intelligent vehicle capable of traveling in unknown and unstructured environments independently. Among the proposed approaches in the literature to handle the navigation problem of a mobile robot is the simple fuzzy reactive approach. This approach, however, occasionally suffers from two major problems, i.e., escaping from trap situations and the co...