Related papers: On convergence structures in graphs
By a closure space we will mean a pair $(A,\mathcal{C})$, in which $A$ is a set and $\mathcal{C}$ a set of subsets of $A$ closed under arbitrary intersections. The purpose of this paper is to initiate a development of descent theory of…
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…
A commuting tuple of operators $(S_1,\dots, S_{n-1},P)$, defined on a Hilbert space $\mathcal H$, for which the closed symmetrized polydisc \[ \Gamma_n =\left\{ \left(\sum_{1\leq i\leq n} z_i,\sum_{1\leq i<j\leq n}z_iz_j,\dots,…
Let $E$ be a sublattice of a vector lattice $F$. $\left( x_\alpha \right)\subseteq E$ is said to be $ F $-order convergent to a vector $ x $ (in symbols $ x_\alpha \xrightarrow{Fo} x $), whenever there exists another net $…
Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$…
A network is a countable, connected graph X viewed as a one-complex, where each edge [x,y]=[y,x] (x,y in X^0, the vertex set) is a copy of the unit interval within the graph's one-skeleton X^1 and is assigned a positive conductance c(xy). A…
We study a closure operator derived from the matrix endofunctor on the category of rings with unity. We investigate the invariance of various ring-theoretic properties under this operator. A key finding is the decisive nature of this…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…
Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if…
The $p$-Laplacian for graphs, as well as the vertex Laplace operator and the hyperedge Laplace operator for the general setting of oriented hypergraphs, are generalized. In particular, both a vertex $p$-Laplacian and a hyperedge…
The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…
Closeness is an important measure of network centrality. In this article we will calculate the closeness of graphs, created by using operations on graphs. We will prove a formula for the closeness of shadow graphs. We will calculate the…
We associate vertex operator algebras to $(p,q)$-webs of interfaces in the topologically twisted $\mathcal{N}=4$ super Yang-Mills theory. Y-algebras associated to trivalent junctions are identified with truncations of…
The closure of a graph $G$ is the graph $G^*$ obtained from $G$ by repeatedly adding edges between pairs of non-adjacent vertices whose degree sum is at least $n$, where $n$ is the number of vertices of $G$. The well-known Closure Lemma…
Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static…
Characterizing the solution sets in a problem by closedness under operations is recognized as one of the key aspects of algorithm development, especially in constraint satisfaction. An example from the Boolean satisfiability problem is that…
On a conformal net $\mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $\mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call…
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…
The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on…
Let $\M$ be a von Neumann algebra with a faithful normal trace $\T$, and let $H^\infty$ be a finite, maximal, subdiagonal algebra of $\M$. Fundamental theorems on conjugate functions for weak$^*$\!-Dirichlet algebras are shown to be valid…