{"component": "definition", "props": {"groups": [{"snippet": "in respect to the class E passing beam, the class W passing beam, designed for right-hand traffic only and a driving beam. The score above \"E\" and \"W\" indicates that these passing beam classes are provided on that side of the system by more than this installation unit.", "size": 5, "samples": [{"hash": "dYrc3sGyk52", "uri": "/contracts/dYrc3sGyk52#figure-10", "label": "Agreement Concerning the Adoption of Uniform Technical Prescriptions for Wheeled Vehicles", "score": 21.0, "published": true}, {"hash": "5GTiZLpC4W6", "uri": "/contracts/5GTiZLpC4W6#figure-10", "label": "Agreement Concerning the Adoption of Uniform Technical Prescriptions for Wheeled Vehicles", "score": 21.0, "published": true}], "snippet_links": [{"key": "class-e", "type": "clause", "offset": [18, 25]}, {"key": "class-w", "type": "definition", "offset": [44, 51]}, {"key": "designed-for", "type": "definition", "offset": [66, 78]}, {"key": "driving-beam", "type": "clause", "offset": [109, 121]}, {"key": "the-system", "type": "definition", "offset": [222, 232]}, {"key": "installation-unit", "type": "definition", "offset": [251, 268]}], "hash": "4b0daab35032c8577b0e9c963585b98b", "id": 1}, {"snippet": "Class D in respect of the passing beam and driving beam. 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Right: eigenfunction corresponding to \u03bb1 of the same pumpkin chain. D2 Since G has only one pumpkin, \u03bb (G) = \u03c02 with an eigenfunction \u03c8(z) = sin \u03c0S(z) for z \u2208 G, and \u03c8 vanishes at all vertices of G (here the only vertices of G are the two endpoints of the pumpkin). Define another function \u03c8\u02dc on G by \u03c8\u02dc(z) := cos \u03c0S(z) . Clearly, \u03c8\u02dc is also an eigenfunction of \u03bb1(G), but \u03c8\u02dc(v0) = 1 and \u03c8\u02dc(vD) = \u22121. (Figure 11) In conclusion, for any eigenfunction \u03c8 associated with \u03bb1(G) which vanishes at all vertices of G, we can find another eigenfunction \u03c8\u02dc associated with \u03bb1(G) which does not vanish on at least one vertex of \u2587. \u2587\u2587\u2587\u2587\u2587, we can always perform the averaging strategy to generate the eigenfunction \u03c81 which only depends on the level of points in G. This implies that we only need to consider one-dimensional functions in the Rayleigh Figure 11: Eigenfunction corresponding to \u03bb1 on a single pumpkin. There exists a sine eigenfunction which vanishes at endpoints, but also another cosine eigenfunction which does not vanish at endpoints. quotient with the weight function \u03c1(x) := #S\u20141(x) for x \u2208 [0, D]. The weight function counts the number of edges at the given level. Therefore, the formula from Theorem 2.1 reduces to the following: (\u222b r|u (x)| \u03c1(x) dx D 2 \u222b |u(x)| \u03c1(x) dx 1 \u03bb (G) = inf 0 D 2 : u \u2208 H1 ([0, D]) , \u222b ) u(x)\u03c1(x) dx = 0 . By Lemma 4.2 and Lemma 4.3, to estimate the spectral gap of quantum graphs in terms of diameter and total length, it suffices to consider the one-dimensional \u2587\u2587\u2587\u2587\u2587-Liouville problem on pumpkin chains. \u2587\u2587\u2587\u2587\u2587\u2587\u2587 et al. [8] give the following upper estimate.\nTheorem 5.1 ( Theorem 7.1 of [8]). Any quantum graph G satisfying the assumptions in the introduction and having diameter D > 0 and total length L \u2265 D satisfies \u03c02 4L \u2212 3D \u03bb1(G) \u2264 D2 D . In the original proof provided in [8], the test function serving as the upper estimate is defined by Acos(\u03c0S(z)) if S(z) \u2264 D \u03d5(z) := Bcos(\u03c0S(z)) if S(z) > D \u222b where A, B are chosen to satisfy the orthogonality condition G \u03d5 = 0. \u2587\u2587\u2587\u2587\u2587\u2587\u2587 et al. [8] claimed that this estimate is far from optimal and is only sharp in the trivial case, meaning when the pumpkin chain consists of a single interval and hence L = D. In this section, we will investigate the sharpness of this estimate through an example. To be specific, we will numerically compute the first positive eigenvalue of a specific type of graph by fixing the diameter while altering the total length.", "size": 1, "samples": [{"hash": "JLsgcg9Njn", "uri": "/contracts/JLsgcg9Njn#figure-10", "label": "Distribution Agreement", "score": 29.7314968109, "published": true}], "snippet_links": [{"key": "figure-11", "type": "definition", "offset": [510, 519]}, {"key": "in-conclusion", "type": "clause", "offset": [521, 534]}, {"key": "associated-with", "type": "definition", "offset": [560, 575]}, {"key": "to-generate", "type": "definition", "offset": [781, 792]}, {"key": "number-of", "type": "clause", "offset": [1247, 1256]}, {"key": "terms-of", "type": "definition", "offset": [1530, 1538]}, {"key": "total-length", "type": "definition", "offset": [1552, 1564]}, {"key": "satisfying-the", "type": "clause", "offset": [1762, 1776]}, {"key": "the-original", "type": "definition", "offset": [1897, 1909]}, {"key": "an-example", "type": "clause", "offset": [2382, 2392]}, {"key": "be-specific", "type": "clause", "offset": [2397, 2408]}, {"key": "first-positive", "type": "clause", "offset": [2442, 2456]}, {"key": "type-of", "type": "definition", "offset": [2482, 2489]}, {"key": "the-total", "type": "clause", "offset": [2534, 2543]}], "hash": "65f33aa7e879a80aa46bd1201476c78b", "id": 6}, {"snippet": "Schematic view of the 1-bit electronically reconfigurable transmitarray (a) including the steering logic and (b) 3D view of the realized 400-element flat-lens array.", "size": 1, "samples": [{"hash": "33qexRLTUX5", "uri": "/contracts/33qexRLTUX5#figure-10", "label": "Grant Agreement", "score": 22.9137573242, "published": true}], "snippet_links": [], "hash": "c9601f0cbb9e09d5de6d313f8c31a5f8", "id": 7}, {"snippet": "Original stigma scale from Coreil et al. (2010) paper that was formulated for their Haitian community 46 Tuberculosis Burden\u200c\u200c\u200c According to the World Health Organization, nearly 10 million people suffer from tuberculosis (TB) \u2013 a curable and preventable disease \u2013 worldwide, with 98% of those cases reported in low- and middle-income countries (LMICs) (2021). This airborne respiratory infection is spread from person to person. Active TB disease may represent either new infection or reactivation of previously - acquired latent infection. Prisons represent a dangerous location due to several factors. The congregate nature of prison facilities not just facilitates transmission of airborne organisms, but it also creates the most ideal environment for a maximum likelihood of transmission. Populations in prison are composed of persons who tend to be low-income (\u2587\u2587\u2587\u2587 et al., 2016). Those who cannot afford adequate legal representation are more likely to not have adequate health care before confinement. This makes them more likely to live with untreated acquired TB. Incarcerated persons are more likely to have TB reactivated either due to co-morbid medical conditions such as HIV, or newly acquired factors such as malnutrition. This holds especially true in lower income countries. Prison Health in Low- and Middle-Income Countries\u200c Nearly 70% of the world\u2019s total prison population is incarcerated in LMICs (\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587, 2016). With overcrowding, whereby confined spaces are filled beyond designed capacity, these prisons often having limited space for social distancing. Adding to high population density, poorly designed facilities may have poor to no ventilation. It is no surprise that TB prevalence is up to 20 times higher in LMICs versus high income countries (HIC) (WHO, 2015). This same association is prevalent within LMIC prisons with these prisons experiencing an 8-fold increase in higher TB incidence compared to HIC prisons (Vinkeles Melchers et al., 2013). Access to laboratories in LMIC prisons is often inadequate or nonexistent, which delays those who are in prison from obtaining TB test results in a timely manner (Vinkeles \u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587 et al., 2013). A lag in diagnosing active disease also places everyone in the facility at risk of contracting an infectious pathogen. With a high prevalence of inadequate frequency of testing, often under-supervised and understaffed prison health services, , and inadequate healthcare infrastructure and resources LMIC prisons witness a higher prevalence of infectious diseases among those who are incarcerated. While treatment is cheap and available due to the national health services, there lies a challenge in getting medications into patients. Additionally, LMIC prisons, especially in a country like Haiti, are often in remote areas of the country, which exacerbates the problems because of shortages of adequately trained health care workers in these parts of the country. 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Optimal range between 0.5-1.4ml. 70 Figure 16: Pressure-Volume characteristics of the gastric balloon catheter. Optimal range between 0.2-0.9ml 70 Figure 17: Equipment used to test for intrinsic delays between pressure and flow responses.72 Figure 18: Raw Labchart data file demonstrating the accuracy of our pressure and flow recordings (time delay between signals <0.006s) 73 Figure 19: Frequency response recording from a \u2018pop-test\u2019 using the gastric balloon (Yinghui Medical Technology Co., Ltd, Guangzhou, China) filled with 0.8ml of air 74 Figure 20: An example of the electroencephalography montage configuration according to the AASM manual for scoring sleep (removed for e-publication) 76 Figure 21: Example of respiratory events identified from overnight traces as defined by the SomnoNIV group. A) An example of an obstructive apnoea with preserved respiratory effort but reduction in flow. 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The score above \"E\" and \"W\" indicates that these passing beam classes are provided on that side of the system by more than this installation unit.", "size": 27, "title": "Figure 10", "id": "figure-10", "examples": ["Any time worked on the designated day off is considered overtime (<strong>Figure 10</strong>).", "The bars in <strong>Figure 10</strong> represent the 12-month flow-weighted mean TP concentrations from S332, S175 and S18C for water years 1989 through 2002.", "Consequently, as of the July 2002 report, only S332D, S174 and S18C data are presented for monthly tracking of data in <strong>Figure 10</strong>.", "Inflow TP concentrations to the ENP through Taylor Slough and the Coastal Basins are compared to the 11 ppb limit at the end of each water year using data from both the old (S175, S332, S18C) and new (S174, S332D, S18C) combinations of structures (<strong>Figure 10</strong>).", "Figure 9: Math Proficiency Scores at Grade 8, Percentages Scoring at Each Level <strong>Figure 10</strong>.", "It is clear from <strong>Figure 10</strong> that areas with the lowest population density have the lowest levels of household broadband connections and that further investment, particularly in areas outside of the main urban centres is required.", "The changes from <strong>Figure 10</strong> are minimal (lines 18 \u2013 19 are added).", "The majority of respondents primarily practiced in \u2587\u2587\u2587\u2587\u2587 County (47.3%) while Noble and Huntington Counties had the fewest area providers answer at just over 7% of the total sample each (<strong>Figure 10</strong>).", "The OXS technology belongs to a category known as spatial switching, which operates by simply deflecting the optical beam to different directions to realise switching (see <strong>Figure 10</strong>).", "During Project Start-Up Vendor collaborates with the County Project Manager to finalize procedures for Risk Management, confirming Vendor\u2019s approach aligns with established County risk <strong>Figure 10</strong>."], "related": [["sap-training-catalogue", "SAP Training Catalogue", "SAP Training Catalogue"], ["total-resource-cost-test", "Total resource cost test", "Total resource cost test"], ["reference-evapotranspiration", "Reference evapotranspiration", "Reference evapotranspiration"], ["gdp", "GDP", "GDP"], ["academy-financial-year", "Academy Financial Year", "Academy Financial Year"]], "related_snippets": [], "updated": "2025-07-24T04:27:56+00:00"}, "json": true, "cursor": ""}}