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Kyoto Journal of Mathematics, 1986 We want to add here another two proofs that the resolvent set of a linear operator is open. The first proof depends on the Hahn-Banach theorem and the second on the Neumann series construction of a linear isomorphism between Ran(A-\(\lambda)\) and Ran(A-\(\mu)\).
Ikebe, Teruo, Yoshioka, Takashi
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Progress toward resolving the attentional capture debate
Visual Cognition, 2020 For over 25 years, researchers have debated whether physically salient stimuli capture attention in an automatic manner, independent of the observer’s goals, or whether the capture of attention depends on the match between a stimulus and the observer’s ...
S. Luck +4 more
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Resolving sets for breaking symmetries of graphs [PDF]
, 2014 This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent study on other functions related to these sets. Thus, we obtain lower and upper bounds on all these functions by means
Delia Garijo +2 more
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A CHARACTERIZATION OF LOCAL RESOLVENT SETS [PDF]
Communications of the Korean Mathematical Society, 2006 Let T be a bounded linear operator on a Banach space X. And let be the local resolvent set of T at . Then we prove that a complex number belongs to if and only if there is a sequence in X such that for n = 0, 1, 2,..., = x and is bounded.
Hyuk Han, Jong-Kwang Yoo
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Secure Resolving Sets in a Graph [PDF]
Symmetry, 2018 Let G = (V, E) be a simple, finite, and connected graph. A subset S = {u1, u2, …, uk} of V(G) is called a resolving set (locating set) if for any x ∈ V(G), the code of x with respect to S that is denoted by CS (x), which is defined as CS (x) = (d(u1, x), d(u2, x), .., d(uk, x)), is different for different x.
Subramanian, Hemalathaa +1 more
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DETERMINING THE DOMINANT METRIC DIMENSION FOR VARIOUS GRAPHS [PDF]
Journal of Mechanics of Continua and Mathematical SciencesIn this paper, we examine the dominating metric dimension of various graph types. A resolving set is a subset of vertices that uniquely identifies each vertex in the graph based on its distances to others, and the metric dimension is the minimum size of
Iqbal M. Batiha +2 more
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Limit sets of stable Cellular Automata [PDF]
, 2013 We study limit sets of stable cellular automata standing from a symbolic dynamics point of view where they are a special case of sofic shifts admitting a steady epimorphism.
Alexis Ballier, Santiago Chile
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Application of Metric Dimensions to Minimize the Installation of Fire Sensors on The Rectorate Building of Pasifik Morotai University [PDF]
MATEC Web of Conferences, 2022 The metric dimension of the connected graph G for each 𝑣 𝜖 𝑉(𝐺) to the set W is . The set r (ν|W) = (d(ν, w1), d(ν,w2),…d(ν,wk) W is called the resolving set if every vertex u,v in G, if u ≠ ν , then r (u|W) ≠ r (ν|W) .
Parera Cicilya Orissa F. +3 more
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Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters [PDF]
International Symposium on Mathematical Foundations of Computer Science, 2022 For a graph $G$, a subset $S \subseteq V(G)$ is called a \emph{resolving set} if for any two vertices $u,v \in V(G)$, there exists a vertex $w \in S$ such that $d(w,u) \neq d(w,v)$.
Esther Galby +4 more
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Levenshtein graphs: Resolvability, automorphisms & determining sets
Discrete Mathematics, 2023 22 pages, 3 ...
Perrin E. Ruth, Manuel E. Lladser
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