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"Eccentricity"
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The 10 p.m. question
Twelve-year-old Frankie Parsons has a quirky family, a wonderful best friend, and a head full of worrying questions that he shares with his mother each night, but when free-spirited Sydney arrives at school with questions of her own, Frankie is forced to face the ultimate ten p.m. question.
Book
Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants
A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices. A topological index is a numerical value related to the chemical structure that claims to show a relationship between chemical structure and various physicochemical attributes, chemical reactivity, or, you could say, biological activity. In this article, we examined the topological properties of a planar octahedron network of m dimensions and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to determine the distance between the vertices of a planar octahedron network.
Journal Article
Distance and Degree Based Topological Indices of Cog-Wheel Graph, n-Barbell Graph and Boron Kagome Lattice
Let G = ( V, E ), be a graph with vertex and edge set, say V ( G ) and E ( G ). In chemical graphs the vertices and edges of the graphs represents atoms and chemical bond of the molecule. Since the distance based topological indices having high degree of predictability of pharmacological properties. In this paper we compute Eccentricity connectivity polynomial, Total eccentricity polynomial of Barbell graph and Cog wheel graph and degree based topological indices of Boron kagome lattice chemical structure.
Journal Article
A new modelling method considering gear geometry eccentricity
In gear work, the gear transmission system will inevitably exhibit post-assembly geometric eccentricity due to assembly and manufacturing. This phenomenon can cause the centre of rotation to differ from the gear system’s centre of mass, with a significant impact on the gear system’s overall dynamic response. In this paper, a dynamic model of the gear shaft is proposed to account for the geometric eccentricity fault of the gear. Lastly, the dynamic responses are discussed for varying eccentricities and initial eccentric phase angles.
Journal Article
Design and Analysis of the Differential Pump Driven by the Novel Eccentric Non-Circular Gears
In order to obtain a better driving mechanism of the differential pump, a high-performance differential velocity vane pump was presented. The pump was driven by the novel eccentric non-circular gears. The working principle and structure of the differential pump were studied. The transmission mechanism of the high-order multisegment deformed eccentric non-circular gears were established, then the transmission characteristics were discussed. Finally an example was given. The example showed that the high-order multisegment deformed, eccentric non-circular gears could meet the large displacement requirements of the differential velocity vane pump.
Journal Article
Parafoveal vision reveals qualitative differences between fusiform face area and parahippocampal place area
The center‐periphery visual field axis guides early visual system organization with enhanced resources devoted to central vision leading to reduced peripheral performance relative to that of central vision (i.e., behavioral eccentricity effect) for many visual functions. The center‐periphery organization extends to high‐order visual cortex where, for example, the well‐studied face‐sensitive fusiform face area (FFA) shows sensitivity to central vision and the place‐sensitive parahippocampal place area (PPA) shows sensitivity to peripheral vision. As we have recently found that face perception is more sensitive to eccentricity than place perception, here we examined whether these behavioral findings reflect differences in FFA's and PPA's sensitivities to eccentricity. We assumed FFA would show higher sensitivity to eccentricity than PPA would, but that both regions' modulation by eccentricity would be invariant to the viewed category. We parametrically investigated (fMRI, n = 32) how FFA's and PPA's activations are modulated by eccentricity (≤8°) and category (upright/inverted faces/houses) while keeping stimulus size constant. As expected, FFA showed an overall higher sensitivity to eccentricity than PPA. However, both regions' activation modulations by eccentricity were dependent on the viewed category. In FFA, a reduction of activation with growing eccentricity (“BOLD eccentricity effect”) was found (with different amplitudes) for all categories. In PPA however, qualitatively different BOLD eccentricity effect modulations were found (e.g., at 8° mild BOLD eccentricity effect for houses but a reverse BOLD eccentricity effect for faces and no modulation for inverted faces). Our results emphasize that peripheral vision investigations are critical to further our understanding of visual processing. Here, we find with parafoveal stimulation that high‐order visual fusiform face area (FFA) and parahippocampal place area (PPA) are differently affected by eccentricity where PPA's modulation shows qualitative different BOLD eccentricity effects for different visual categories. Our results emphasize that peripheral vision investigations are critical to further our understanding of visual processing.
Journal Article
Center Smooth Sets and Center Smooth Numbers of Graphs
For any proper set S of V in a graph G ( V, E ), the S-eccentricity, e G, S ( υ ) (in short e S ( υ )) of a vertex υ in G is max x ∈ S ( d ( υ , x ) ) . The S-center of G is C S ( G ) = υ ∈ V | e S ( x ) ≤ e S ( x )∀ x ∈ V and S 1 -eccentricity, e G,S 1 ( v ) (in short e S 1 ( V )) of a vertex v in S is max x ∈ V = S ( d ( υ , x ) ) . S 1 -center of G is C S 1 ( G ) = υ ∈ V | e S 1 ( x ) ≤ e S 1 ( x )∀ x ∈ V . Then G is called a center-smooth graph if C S ( G ) = C S 1 ( G ) and the set S is defined to be a center-smooth set. We identify the center smooth sets of certain classes of graphs namely, K q,p , K p – q , K p , wheel graphs and lollipop graph and enumerate them for many of these graph classes. We also introduce the concept of center smooth number, which is defined as the number of distinct center smooth set of a graph G, and determine the center smooth number of some graph classes.
Journal Article
Impact of 2D and 3D Rotor Eccentricity on End Winding Mechanics Behavior in Synchronous Generators
Investigations on static air-gap eccentricity (SAGE) faults about magnetic field variations, current/ voltage changes, and stator/ rotor vibrations have been widely carried out, while the mechanical properties of the end windings have been rarely studied, especially in 3D eccentricity cases. This article provides a detailed study on the stator end winding mechanics behavior in synchronous generators at typical rotor eccentricity running conditions. Such mechanics behavior includes not only the electromagnetic force (EF) properties, but also the end winding vibrations as well as the stress/strain/deformation responses due to the uneven EF excitation. The typical rotor eccentricity running conditions include: 1) radial static air-gap eccentricity (RSAGE), 2) axial static air-gap eccentricity (ASAGE), and 3) hybrid static air-gap eccentricity (HSAGE). The theoretical analysis, finite element analysis calculation and experimental verification are performed respectively, by taking a 5kVA synchronous generator as the research object in this paper. It is shown that in normal and SAGE cases, the end winding EF/vibration contains the DC component and even harmonics, especially the 2nd harmonic. RSAGE increases the end winding EF/vibration, whereas ASAGE increases the end winding EF/vibration at the extended end of the rotor while decreasing the EF/vibration on the retracted end. Under HSAGE, both RSAGE and ASAGE will affect the variation trend of end winding EF/vibration with the rule of single direction SAGE fault. The nose part and the joint to connect the end part and the linear sections are the most dangerous positions to afford the mechanics responses, and the occurrence of SAGE will make these parts more vulnerable.
Journal Article
Eccentricity Estimation for Five Binary Black Hole Mergers with Higher-order Gravitational-wave Modes
The detection of orbital eccentricity for a binary black hole system via gravitational waves is a key signature to distinguish between the possible binary origins. The identification of eccentricity has been difficult so far due to the limited availability of eccentric gravitational waveforms over the full range of black hole masses and eccentricities. Here we evaluate the eccentricity of five black hole mergers detected by the LIGO and Virgo observatories using the TEOBResumS-DALI, TEOBResumS-GIOTTO, and TEOBResumSP models. This analysis studies eccentricities up to 0.6 at the reference frequency of 5 Hz and incorporates higher-order gravitational-wave modes critical to model emission from highly eccentric orbits. The binaries have been selected due to previous hints of eccentricity or due to their unusual mass and spin. While other studies found marginal evidence for eccentricity for some of these events, our analyses do not favor the incorporation of eccentricity compared to the quasi-circular case. While lacking the eccentric evidence of other analyses, we find our analyses marginally shifts the posterior in multiple parameters for several events when allowing eccentricity to be nonzero.
Journal Article
A Rosetta Stone for Eccentric Gravitational Waveform Models
Orbital eccentricity is a key signature of dynamical binary black hole formation. The gravitational waves from a coalescing binary contain information about its orbital eccentricity, which may be measured if the binary retains sufficient eccentricity near merger. Dedicated waveforms are required to measure eccentricity. Several models have been put forward, and show good agreement with numerical relativity at the level of a few percent or better. However, there are multiple ways to define eccentricity for inspiralling systems, and different models internally use different definitions of eccentricity, making it difficult to compare eccentricity measurements directly. In this work, we systematically compare two eccentric waveform models, SEOBNRE and TEOBResumS, by developing a framework to translate between different definitions of eccentricity. This mapping is constructed by minimizing the relative mismatch between the two models over eccentricity and reference frequency, before evolving the eccentricity of one model to the same reference frequency as the other model. We show that for a given value of eccentricity passed to SEOBNRE, one must input a 20%–50% smaller value of eccentricity to TEOBResumS in order to obtain a waveform with the same empirical eccentricity. We verify this mapping by repeating our analysis for eccentric numerical relativity simulations, demonstrating that TEOBResumS reports a correspondingly smaller value of eccentricity than SEOBNRE.
Journal Article