On r-Compactness in Topological and Bitopological Spaces

Oudetallah, Jamal; Alharbi, Rehab; Batiha, Iqbal M.

doi:10.3390/axioms12020210

Cited by 9 publications

(16 citation statements)

References 8 publications

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“…We have subtracted the hole electrostatic energy at equilibrium −2Q and added a reference value E 0 , so as E n = E 0 at the equilibrium distance. The value of E 0 has no physical consequences, and it will be generally taken as zero, however, some other values may be more convenient than others for numerical integration and to obtain periodic solutions [35]. The terms J n−1,n have to be negligible for the equilibrium distance and become large only at the distance where the two electronic clouds of the K + ions interact.…”

Section: Hole or Electron Potentialmentioning

confidence: 99%

“…A value of E 0 ̸ = 0 implies only a shift in the c n frequencies of E 0 /τ , which can be convenient for integration purposes but has no physical consequences as always the products c n c * m that appear in the dynamical equations are invariant with respect to a global frequency shift [35]. Note that the variables u n and c n become decoupled at the linear limit.…”

Section: Linearizationmentioning

confidence: 99%

“…In many aspects, the model is similar to the phenomenological model used in Ref. [34,35], but it is more complicated as the diagonal terms of the quantum charge Hamiltonian are not constant but correspond to the interaction with the other electric charges in the crystal. The vibronic interaction between the nuclei and the extra electron or hole is strongly nonlinear with the consequence that the tunneling or an electron between nearest-neighbor ions is only probable when the nuclei are close enough and the transition probability increases strongly as they approach.…”

Section: Introductionmentioning

confidence: 99%

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A semiclassical model for charge transfer along ion chains in silicates

Archilla,

Bajārs,

Doi

et al. 2024

J. Phys.: Conf. Ser.

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It has been observed in fossil tracks and experiments in the layered silicate mica muscovite the transport of charge through the cation layers sandwiched between the layers of tetrahedra-octahedra-tetrahedra. A classical model for the propagation of anharmonic vibrations along the cation chains has been proposed based on first principles and empirical functions. In that model, several propagating entities have been found as kinks or crowdions and breathers, both with or without wings, the latter for specific velocities and energies. Crowdions are equivalent to moving interstitials and transport electric charge if the moving particle is an ion, but they also imply the movement of mass, which was not observed in the experiments. Breathers, being just vibrational entities, do not transport charge. In this work, we present a semiclassical model obtained by adding a quantum particle, electron or hole to the previous model. We present the construction of the model based on the physics of the system. In particular, the strongly nonlinear vibronic interaction between the nuclei and the extra electron or hole is essential to explain the localized charge transport, which is not compatible with the adiabatic approximation. The formation of vibrational localized charge carriers breaks the lattice symmetry group in a similar fashion to the Jahn-Teller Effect, providing a new stable dynamical state. We study the properties and the coherence of the model through numerical simulations from initial conditions obtained by tail analysis and other means. We observe that although the charge spreads from an initial localization in a lattice at equilibrium, it can be confined basically to a single particle when coupled to a chaotic quasiperiodic breather. This is coherent with the observation that experiments imply that a population of charge is formed due to the decay of potassium unstable isotopes.

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Section: Hole or Electron Potentialmentioning

confidence: 99%

Section: Linearizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A semiclassical model for charge transfer along ion chains in silicates

Archilla,

Bajārs,

Doi

et al. 2024

J. Phys.: Conf. Ser.

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“…Similarly, these parameters beneficial for electronic devices are found in [ 42 ]. For more recent work on this topic, we refer to see [ 43 – 48 ].…”

Section: Introductionmentioning

confidence: 99%

Edge based metric dimension of various coffee compounds

Ahmad,

Koam,

Azeem

et al. 2024

PLoS ONE

Self Cite

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An important dietary source of physiologically active compounds, coffee also contains phenolic acids, diterpenes, and caffeine. According to a certain study, some coffee secondary metabolites may advantageously modify a number of anti-cancer defense systems. This research looked at a few coffee chemical structures in terms of edge locating numbers or edge metric size to better understand the mechanics of coffee molecules. Additionally, this research includes graph theoretical properties of coffee chemical structures. The chemicals found in coffee, such as caffeine, diterpene or cafestol, kahweol, chlorogenic, caffeic, gallotannins, and ellagitannins, are especially examined in these publications.

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“…Recent studies have focused on bitopological spaces (X, V 1 , V 2 ), a nonempty set X endowed with two topologies V 1 and V 2 [1][2][3][4][5]. In 2006, Noiri and Rajesh studied the generalized closed sets concerning an ideal in bitopological spaces [6].…”

Section: Introductionmentioning

confidence: 99%

On Strong $(i,j)$-Semi$^{*}$-$\Gamma $-Open Sets in Ideal Bitopological Space

Bukhatwa,

Demiralp

2024

Journal of New Theory

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In this study, we introduce the concepts of $(i,j)$-semi$^{*}$-$\Gamma $-open sets within the context of ideal bitopological spaces. This concept is demonstrated to be weaker than the established the notion of $(i,j)$-semi-$\Gamma $-open sets. Subsequently, we define strong $(i,j)$-semi$^{*}$-$\Gamma $-open sets in ideal bitopological spaces, elucidating some of their essential characteristics. Furthermore, leveraging this newly introduced concept, we establish the notions of strong $(i,j)$-semi$^{*}$-$\Gamma $-interior and strong $(i,j)$-semi$^{*}$-$\Gamma $-closure.

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On r-Compactness in Topological and Bitopological Spaces

Cited by 9 publications

References 8 publications

A semiclassical model for charge transfer along ion chains in silicates

A semiclassical model for charge transfer along ion chains in silicates

Edge based metric dimension of various coffee compounds

On Strong $(i,j)$-Semi$^{*}$-$\Gamma $-Open Sets in Ideal Bitopological Space

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