scholarly journals A Numerical Method for Computing Double Integrals with Variable Upper Limits

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 108
Author(s):  
Olha Chernukha ◽  
Yurii Bilushchak ◽  
Natalya Shakhovska ◽  
Rastislav Kulhánek
Keyword(s):  
Numerical Method ◽  
Grid Size ◽  
Double Integral ◽  
Variable Boundary ◽  
Upper Limit ◽  
Integration Region ◽  
Upper Limits ◽  
Relative Errors ◽  
Similar Triangles ◽  
Double Integrals

We propose and justify a numerical method for computing the double integral with variable upper limits that leads to the variableness of the region of integration. Imposition of simple variables as functions for upper limits provides the form of triangles of integration region and variable in the external limit of integral leads to a continuous set of similar triangles. A variable grid is overlaid on the integration region. We consider three cases of changes of the grid for the division of the integration region into elementary volumes. The first is only the size of the imposed grid changes with the change of variable of the external upper limit. The second case is the number of division elements changes with the change of the external upper limit variable. In the third case, the grid size and the number of division elements change after fixing their multiplication. In these cases, the formulas for computing double integrals are obtained based on the application of cubatures in the internal region of integration and performing triangulation division along the variable boundary. The error of the method is determined by expanding the double integral into the Taylor series using Barrow’s theorem. Test of efficiency and reliability of the obtained formulas of the numerical method for three cases of ways of the division of integration region is carried out on examples of the double integration of sufficiently simple functions. Analysis of the obtained results shows that the smallest absolute and relative errors are obtained in the case of an increase of the number of division elements changes when the increase of variable of the external upper limit and the grid size is fixed.

Vitamin-A-Exzess durch Pferdefleischprodukte mit hohen Leberanteilen

2013 ◽  
Vol 41 (01) ◽  
pp. 31-36
Author(s):  
E. Kienzle ◽  
N. Becker
Keyword(s):  
Vitamin A ◽  
Eine Analyse ◽  
Upper Limit ◽  
Upper Limits

ZusammenfassungIm Rahmen einer Eliminationsdiät wird regelmäßig Pferdefleisch eingesetzt. Aus Gründen der Praktikabilität verwenden Tierbesitzer häufig kommerziell erhältliches Pferdefleisch aus der Dose. Aufgrund eines Berichts von Zervikalspondylosen bei einer auf Futtermittel allergischen Katze erfolgte eine Analyse verschiedener auf Pferdefleisch basierender Produkte hinsichtlich des Vitamin-AGehalts.In 14 Pferdefleischerzeugnissen wurde der Vitamin-A-Gehalt (Retinol) analysiert. Der Gehalt an umsetzbarer Energie wurde mithilfe von Schätzformeln auf Basis der Deklaration berechnet.In Produkten mit deklarierten Anteilen von Leber, Innereien oder tierischen Nebenprodukten konnten zum Teil erhebliche Vitamin-A-Gehalte festgestellt werden. Bei alleiniger Verfütterung eines dieser Produkte (Deckung des durchschnittlichen Energiebedarfs) würde die Vitamin-A-Versorgung nur knapp unter dem Safe Upper Limit der Katze sowie oberhalb des Safe Upper Limits beim Hund liegen.Bei All-Meat-Produkten sollte nicht nur die Deklaration, sondern auch der Inhalt näher betrachtet werden, um einen Hinweis auf eventuell hohe Leberanteile zu erhalten.Aufgrund der Ergebnisse ist eine exzessive Vitamin-A-Aufnahme bei langfristiger Verfütterung von Pferdefleischprodukten mit hohen Leberanteilen nicht auszuschließen.

scholarly journals Search for π0 decays to invisible particles

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
E. Cortina Gil ◽  
◽  
A. Kleimenova ◽  
E. Minucci ◽  
S. Padolski ◽  
...  
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Confidence Level ◽  
Branching Ratio ◽  
Standard Model Higgs Boson ◽  
Scalar Mixing ◽  
Upper Limit ◽  
Upper Limits ◽  
The Standard Model ◽  
Model Independent

Abstract The NA62 experiment at the CERN SPS reports a study of a sample of 4 × 109 tagged π0 mesons from K+ → π+π0(γ), searching for the decay of the π0 to invisible particles. No signal is observed in excess of the expected background fluctuations. An upper limit of 4.4 × 10−9 is set on the branching ratio at 90% confidence level, improving on previous results by a factor of 60. This result can also be interpreted as a model- independent upper limit on the branching ratio for the decay K+ → π+X, where X is a particle escaping detection with mass in the range 0.110–0.155 GeV/c2 and rest lifetime greater than 100 ps. Model-dependent upper limits are obtained assuming X to be an axion-like particle with dominant fermion couplings or a dark scalar mixing with the Standard Model Higgs boson.

scholarly journals Upper limits on the extent of seafloor anoxia during the PETM from uranium isotopes

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Matthew O. Clarkson ◽  
Timothy M. Lenton ◽  
Morten B. Andersen ◽  
Marie-Laure Bagard ◽  
Alexander J. Dickson ◽  
...  
Keyword(s):  
Carbon Cycle ◽  
Global Scale ◽  
Uranium Isotopes ◽  
Biogeochemical Model ◽  
Emission Scenarios ◽  
Isotope Data ◽  
Upper Limit ◽  
Thermal Maximum ◽  
Upper Limits ◽  
Anoxic Events

AbstractThe Paleocene Eocene Thermal Maximum (PETM) represents a major carbon cycle and climate perturbation that was associated with ocean de-oxygenation, in a qualitatively similar manner to the more extensive Mesozoic Oceanic Anoxic Events. Although indicators of ocean de-oxygenation are common for the PETM, and linked to biotic turnover, the global extent and temporal progression of de-oxygenation is poorly constrained. Here we present carbonate associated uranium isotope data for the PETM. A lack of resolvable perturbation to the U-cycle during the event suggests a limited expansion of seafloor anoxia on a global scale. We use this result, in conjunction with a biogeochemical model, to set an upper limit on the extent of global seafloor de-oxygenation. The model suggests that the new U isotope data, whilst also being consistent with plausible carbon emission scenarios and observations of carbon cycle recovery, permit a maximum ~10-fold expansion of anoxia, covering <2% of seafloor area.

Separation Standards—II

1966 ◽  
Vol 19 (2) ◽  
pp. 169-186 ◽  
Author(s):  
P. G. Reich
Keyword(s):  
One Dimension ◽  
Collision Risk ◽  
Practical Applications ◽  
Upper Limit ◽  
Intensive Observation ◽  
Relative Errors ◽  
Separation Standards

In the first part of this series of papers an outline was given of the approach made at the Royal Aircraft Establishment to the problems of estimating collision risk and of specifying the quality of navigation needed to make separation standards safe. It was stressed that estimates should be based on intensive observation of flying errors, rather than on speculative theories, and that it is more feasible to develop ‘upper limit’ estimating techniques than those which purport to give the exact risk. In summary, a list of seven ‘requirements’ was given, as a reminder of the essential principles which can so easily be overlooked in the piecemeal task of relating separation standards to collision risk.The purpose of this paper is to show some of the theoretical techniques which have been developed at R.A.E. to satisfy five of these requirements. (The remaining two do not call for special techniques and will be dealt with when practical applications are described in Part III.) The paper contains three Appendixes, dealing with the frequency of losing separation in one dimension, the computation of P's from the assumed tail shapes, and the treatment of relative errors. These are not included here but will appear in the off-printed version which may be obtained from the Royal Aircraft Establishment.Both this paper and the paper that follows by Mr. Attwooll are crown copyright and are reproduced with the permission of H.M. Stationery Office.

scholarly journals Reactive quenching of electronically excited NO<sub>2</sub><sup>∗</sup> and NO<sub>3</sub><sup>∗</sup> by H<sub>2</sub>O as potential sources of atmospheric HO<sub><i>x</i></sub> radicals

2018 ◽  
Vol 18 (19) ◽  
pp. 14005-14015 ◽  
Author(s):  
Terry J. Dillon ◽  
John N. Crowley
Keyword(s):  
Gas Phase ◽  
Laser Excitation ◽  
Pulsed Laser ◽  
Work Rate ◽  
Rate Coefficients ◽  
Phase Reaction ◽  
Gas Phase Reaction ◽  
Upper Limit ◽  
Upper Limits ◽  
Electronically Excited

Abstract. Pulsed laser excitation of NO2 (532–647 nm) or NO3 (623–662 nm) in the presence of H2O was used to initiate the gas-phase reaction NO2∗+H2O → products (Reaction R5) and NO3∗+H2O → products (Reaction R12). No evidence for OH production in Reactions (R5) or (R12) was observed and upper limits for OH production of k5b/k5<1×10-5 and k12b/k12<0.03 were assigned. The upper limit for k5b∕k5 renders this reaction insignificant as a source of OH in the atmosphere and extends the studies (Crowley and Carl, 1997; Carr et al., 2009; Amedro et al., 2011) which demonstrate that the previously reported large OH yield by Li et al. (2008) was erroneous. The upper limit obtained for k12b∕k12 indicates that non-reactive energy transfer is the dominant mechanism for Reaction (R12), though generation of small but significant amounts of atmospheric HOx and HONO cannot be ruled out. In the course of this work, rate coefficients for overall removal of NO3∗ by N2 (Reaction R10) and by H2O (Reaction R12) were determined: k10=(2.1±0.1)×10-11 cm3 molecule−1 s−1 and k12=(1.6±0.3)×10-10 cm3 molecule−1 s−1. Our value of k12 is more than a factor of 4 smaller than the single previously reported value.

Oxygen and the upper limits to animal design and performance.

1998 ◽  
Vol 201 (8) ◽  
pp. 1065-1072 ◽  
Author(s):  
R K Suarez
Keyword(s):  
Energy Metabolism ◽  
Surface Area ◽  
Body Mass ◽  
Current Evidence ◽  
Tracheal System ◽  
Flying Insects ◽  
Upper Limit ◽  
O2 Transport ◽  
Upper Limits ◽  
Functional Capacities

Mass-specific rates of aerobic metabolism VO2/Mb) scale in inverse proportion to body mass (Mb). Thus, small hummingbirds display the highest VO2/Mb known among vertebrates. Among all animals, higher VO2/Mb values are known only in flying insects. The high body-mass-specific rates of metabolism seen in hummingbirds are made possible by high lung O2 diffusing capacities, cardiac outputs, ratios of capillary surface area to muscle fiber surface area, mitochondrial volume densities, cristae surface densities and concentrations of enzymes involved in energy metabolism. Current evidence from control analyses of O2 transport through the respiratory and cardiovascular systems and of metabolic fluxes through pathways of energy metabolism indicates shared control of maximum flux rates among multiple steps (i.e. the absence of single rate-limiting steps). This supports the suggestion that functional capacities at each step in linear pathways or processes are matched to each other, and provides an explanation for why the up-regulation of functional capacities has occurred at virtually all steps in the evolution of the smallest vertebrate homeotherms. Flying insects make use of a tracheal system for O2 transport and, like hummingbirds, possess a highly up-regulated biochemical machinery for substrate oxidation. Studies of hummingbirds and honeybees reveal closer matches between biochemical flux capacities and maximum physiological flux rates than in animals capable of lower maximum VO2/Mb. It is proposed that the upper limits to functional capacities set the upper limit to VO2/Mb. This upper limit to aerobic metabolic rate may contribute, along with other factors, towards establishing the lower limit to vertebrate homeotherm size.

On the Amount of Dust in the Asteroid Belt

1971 ◽  
Vol 12 ◽  
pp. 389-393
Author(s):  
Fred L. Whipple
Keyword(s):  
Solar Radiation ◽  
Particle Density ◽  
Asteroid Belt ◽  
Space Vehicles ◽  
The Sun ◽  
Small Particles ◽  
Zodiacal Cloud ◽  
Upper Limit ◽  
Upper Limits

Calculations of upper limits to the quantity of small particles in the asteroid belt are based on (1) the brightness of the counterglow coupled with observations and theory for the zodiacal cloud near Earth's orbit and (2) the destruction and erosion of asteroidal particles as they spiral toward the Sun because of solar radiation via the Poynting-Robertson effect. These calculations place the likely upper limit on asteroidal space particle density at the order of 5 to 10 times and the hazard to space vehicles at 2 to 4 times those near Earth's orbit. No such evidence indicates, however, that the hazard from small particles is actually much greater in the asteroid belt.

scholarly journals LOFAR 144-MHz follow-up observations of GW170817

2020 ◽  
Vol 494 (4) ◽  
pp. 5110-5117
Author(s):  
J W Broderick ◽  
T W Shimwell ◽  
K Gourdji ◽  
A Rowlinson ◽  
S Nissanke ◽  
...  
Keyword(s):  
Neutron Star ◽  
Low Frequency ◽  
Radio Spectrum ◽  
Central Frequency ◽  
Binary Neutron Star ◽  
Upper Limit ◽  
Upper Limits ◽  
Maximum Elevation ◽  
Merger Event

ABSTRACT We present low-radio-frequency follow-up observations of AT 2017gfo, the electromagnetic counterpart of GW170817, which was the first binary neutron star merger to be detected by Advanced LIGO–Virgo. These data, with a central frequency of 144 MHz, were obtained with LOFAR, the Low-Frequency Array. The maximum elevation of the target is just 13${_{.}^{\circ}}$7 when observed with LOFAR, making our observations particularly challenging to calibrate and significantly limiting the achievable sensitivity. On time-scales of 130–138 and 371–374 d after the merger event, we obtain 3σ upper limits for the afterglow component of 6.6 and 19.5 mJy beam−1, respectively. Using our best upper limit and previously published, contemporaneous higher frequency radio data, we place a limit on any potential steepening of the radio spectrum between 610 and 144 MHz: the two-point spectral index $\alpha ^{610}_{144} \gtrsim$ −2.5. We also show that LOFAR can detect the afterglows of future binary neutron star merger events occurring at more favourable elevations.

scholarly journals Upper limits on the water vapour content of the β Pictoris debris disk

2019 ◽  
Vol 628 ◽  
pp. A127 ◽  
Author(s):  
M. Cavallius ◽  
G. Cataldi ◽  
A. Brandeker ◽  
G. Olofsson ◽  
B. Larsson ◽  
...  
Keyword(s):  
Solar System ◽  
Far Infrared ◽  
Kinetic Temperature ◽  
Line Flux ◽  
Water Vapour Content ◽  
Water Ice ◽  
Upper Limit ◽  
Upper Limits ◽  
Debris Disk ◽  
Lower Limits

Context. The debris disk surrounding β Pictoris has been observed with ALMA to contain a belt of CO gas with a distinct peak at ~85 au. This CO clump is thought to be the result of a region of enhanced density of solids that collide and release CO through vaporisation. The parent bodies are thought to be comparable to solar system comets, in which CO is trapped inside a water ice matrix. Aims. Since H2O should be released along with CO, we aim to put an upper limit on the H2O gas mass in the disk of β Pictoris. Methods. We used archival data from the Heterodyne Instrument for the Far-Infrared (HIFI) aboard the Herschel Space Observatory to study the ortho-H2O 110–101 emission line. The line is undetected. Using a python implementation of the radiative transfer code RADEX, we converted upper limits on the line flux to H2O gas masses. The resulting lower limits on the CO/H2O mass ratio are compared to the composition of solar system comets. Results. Depending on the assumed gas spatial distribution, we find a 95% upper limit on the ortho-H2O line flux of 7.5 × 10−20 W m−2 or 1.2 × 10−19 W m−2. These translate into an upper limit on the H2O mass of 7.4 × 1016–1.1 × 1018 kg depending on both the electron density and gas kinetic temperature. The range of derived gas-phase CO/H2O ratios is marginally consistent with low-ratio solar system comets.

The Testimony and Application of Inequality Cauchy-Schwarz

2014 ◽  
Vol 687-691 ◽  
pp. 1223-1226
Author(s):  
Qi Shen
Keyword(s):  
Integral Inequality ◽  
Function Method ◽  
Integral Function ◽  
Parameter Method ◽  
Definite Integral ◽  
Double Integral ◽  
Upper Limit

This paper discusses the form of inequality Cauchy-Schwarz in the field of calculus, giving the different methods of proof, which includes Parameter method, variable upper limit integral function method, the double integral and definite integral definition method. What’s more, through a series of examples, it also reflects that the inequality Cauchy-Schwarz can make the process of proving the inequality more simple while certifying the Integral inequality.

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