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.

Many image processing applications require computing approximate solutions of very large, ill-conditioned linear systems. Physical assumptions of the imaging system usually dictate that the matrices in these linear systems have exploitable structure. The specific structure depends on (usually simplifying) assumptions of the physical model and other considerations such as boundary conditions. Wh...

We associate to a finite digraph D a lattice polytope PD whose vertices are the rows of the Laplacian matrix of D. This generalizes a construction introduced by Braun and the third author. As a consequence of the Matrix-Tree Theorem, we show that the normalized volume of PD equals the complexity of D, and PD contains the origin in its relative interior if and only if D is strongly connected. In...

The quotient space theory based on fuzzy tolerance relation is put forward to solve the problem of clustering in this paper. The similarity matrix does not always satisfy ultrametric inequality, theoretically and practically. We give the method to construct the hierarchical quotient space chain if the similarity matrix is only reflexive and symmetric. We consider not only the subset of data (cl...

Abstract. One of the most interesting dynamical systems used in numerical analysis is the QR algorithm. An added maneuver to improve the convergence behavior is the QR iteration with shift which is of fundamental importance in eigenvalue computation. This paper is a theoretical study of the set of all isospectral matrices “reachable” by the dynamics of QR algorithm with shift. A matrix B is sai...

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.

Whether a matrix A over a complex field is singular square, or rectangular, it has always a generalized inverse (g-inverse) over the (complex) field. The true inverse exists only when ,4 is nonsingular (i.e., a square matrix whose determinant is not zero). However, a g-inverse of an m x n matrix of rank r involves considerable errors if the rth order submatrices are near-singular. Further, the ...