Related papers: Core-EP Decomposition and its Applications
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
K-core decomposition is a commonly used metric to analyze graph structure or study the relative importance of nodes in complex graphs. Recent years have seen rapid growth in the scale of the graph, especially in industrial settings. For…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
In [arXiv:1006.4939] the enumeration order reducibility is defined on natural numbers. For a c.e. set A, [A] denoted the class of all subsets of natural numbers which are co-order with A. In definition 5 we redefine co-ordering for rational…
Let $R$ be a polynomial ring over a field. We describe the extremal rays and the facets of the cone of local cohomology tables of finitely generated graded $R$-modules of dimension at most two. Moreover, we show that any point inside the…
This paper aims to establish the theoretical foundation for shift inclusion in mathematical morphology. In this paper, we prove that the morphological opening and closing concerning structuring elements of shift inclusion property would…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for…
We consider the problem of constructing a convex ear decomposition for a poset. The usual technique, first used by Nyman and Swartz, starts with a CL-labeling and uses this to shell the `ears' of the decomposition. We axiomatize the…
Decomposition of tomographic reconstructions has many different practical application. We propose two new reconstruction methods that combines the task of tomographic reconstruction with object decomposition. We demonstrate these…
The precise theoretical characterization of a fractionalized phase in spatial dimensions higher than one is through the concept of ``topological order''. We describe a physical effect that is a robust and direct consequence of this hidden…
The derivation of linear response theory within polarizable embedding is carried out from a rigorous quantum-mechanical treatment of a composite system. Two different subsystem decompositions (symmetric and nonsymmetric) of the linear…
Let $\mathscr{C}$ be an additive category with an involution $\ast$. Suppose that $\varphi : X \rightarrow X$ is a morphism with kernel $\kappa : K \rightarrow X$ in $\mathscr{C}$, then $\varphi$ is core invertible if and only if $\varphi$…
We give $\operatorname{CMSO}$-transductions that, given a graph $G$, output its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who…
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
The structure of large networks can be revealed by partitioning them to smaller parts, which are easier to handle. One of such decompositions is based on $k$--cores, proposed in 1983 by Seidman. In the paper an efficient, $O(m)$, $m$ is the…
We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall…