Topic
Valency
About: Valency is a research topic. Over the lifetime, 1632 publications have been published within this topic receiving 26141 citations.
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01 Jan 1976
08 Dec 2022
TL;DR: In this article , an analytic norm-increasing $3$-isometric weighted shift on a rootless directed tree was constructed, which does not have the wandering subspace property.
Abstract: We construct an analytic norm-increasing $3$-isometric weighted shift on a rootless directed tree, which does not have the wandering subspace property. This answers a question of Shimorin [S2001, p. 185] in the negative. The counterexample in question is built over the rootless quasi-Brownian directed tree of valency $2.$
27 Oct 2022
TL;DR: In this paper , a non-linear differential equation describing surface charging was constructed by combining chemical Langmuir kinetics and electrostatic Poisson-Boltzmann theory, which revealed a clear distinction between late-time and short-time relaxation rates, the ratio of which contained information on the charge valency and ad- or desorption mechanism of the charging process.
Abstract: While important for many industrial applications, chemical reactions responsible for charging of solids in water are often poorly understood. We theoretically investigate the charging kinetics of solid-liquid interfaces, and find that the time-dependent equilibration of surface charge contains key information not only on the reaction mechanism, but also on the valency of the reacting ions. We construct a non-linear differential equation describing surface charging by combining chemical Langmuir kinetics and electrostatic Poisson-Boltzmann theory. Our results reveal a clear distinction between late-time (near-equilibrium) and short-time (far-from-equilibrium) relaxation rates, the ratio of which contains information on the charge valency and ad- or desorption mechanism of the charging process. Similarly, we find that single-ion reactions can be distinguished from two-ion reactions as the latter show an inflection point during equilibration. Interestingly, such inflection points are characteristic of autocatalytic reactions, and we conclude that the Coulombic ion-surface interaction is an autocatalytic feedback mechanism.
02 Apr 2023
TL;DR: In this article , a sufficient condition for a Cayley graph to be a graphical regular representation (GRR) was given, that is, for the graph to have full automorphism group isomorphic to the group.
Abstract: For groups $G$ that can be generated by an involution and an element of odd prime order, this paper gives a sufficient condition for a certain Cayley graph of $G$ to be a graphical regular representation (GRR), that is, for the Cayley graph to have full automorphism group isomorphic to $G$. This condition enables one to show the existence of GRRs of prescribed valency for a large class of groups, and in this paper, $k$-valent GRRs of finite nonabelian simple groups with $k\geq5$ are considered.