Particle drag race leads to most precise estimate yet of the proton’s mass

2021 ◽  
Keyword(s):  
Precise Estimate

scholarly journals On Hermite-Fejér type interpolation on the Chebyshev nodes

1993 ◽  
Vol 47 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Graeme J. Byrne ◽  
T.M. Mills ◽  
Simon J. Smith
Keyword(s):  
Approximation Error ◽  
Interpolation Polynomial ◽  
Precise Estimate ◽  
Type Interpolation ◽  
Interpolation Methods ◽  
Chebyshev Nodes ◽  
Interpolatory Process

Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the Chebyshev nodes to obtain a convergent rational interpolatory process.

Asymptotic Estimates of the First Eigenvalue of the p-Laplacian

2003 ◽  
Vol 3 (2) ◽  
Author(s):  
Bruno Colbois ◽  
Ana-Maria Matei
Keyword(s):  
Direct Application ◽  
Parameter Family ◽  
Precise Estimate ◽  
First Eigenvalue ◽  
Asymptotic Estimates ◽  
Hyperbolic Surfaces ◽  
The First Eigenvalue

AbstractWe consider a 1-parameter family of hyperbolic surfaces M(t) of genus ν which degenerate as t → 0 and we obtain a precise estimate of λAs a direct application, we obtain that the quotientTo prove our results we use in an essential way the geometry of hyperbolic surfaces which is very well known. We show that an eigenfunction for λ

Precise estimate of fundamental in-vivo MT parameters in human brain in clinically feasible times

2002 ◽  
Vol 20 (10) ◽  
pp. 721-731 ◽  
Author(s):  
A. Ramani ◽  
C. Dalton ◽  
D.H. Miller ◽  
P.S. Tofts ◽  
G.J. Barker
Keyword(s):  
Human Brain ◽  
Precise Estimate

scholarly journals New Estimates of the Singular Series Corresponding to Positive Quaternary Quadratic Forms

2006 ◽  
Vol 13 (4) ◽  
pp. 687-691
Author(s):  
Guram Gogishvili
Keyword(s):  
Quadratic Form ◽  
General Result ◽  
Quadratic Forms ◽  
Positive Definite ◽  
Precise Estimate ◽  
Definite Integral ◽  
Singular Series ◽  
Prime Factors ◽  
Quaternary Quadratic Form ◽  
Best Estimates

Abstract Let 𝑚 ∈ ℕ, 𝑓 be a positive definite, integral, primitive, quaternary quadratic form of the determinant 𝑑 and let ρ(𝑓,𝑚) be the corresponding singular series. When studying the best estimates for ρ(𝑓,𝑚) with respect to 𝑑 and 𝑚 we proved in [Gogishvili, Trudy Tbiliss. Univ. 346: 72–77, 2004] that where 𝑏(𝑘) is the product of distinct prime factors of 16𝑘 if 𝑘 ≠ 1 and 𝑏(𝑘) = 3 if 𝑘 = 1. The present paper proves a more precise estimate where 𝑑 = 𝑑0𝑑1, if 𝑝 > 2; 𝑕(2) ⩾ –4. The last estimate for ρ(𝑓,𝑚) as a general result for quaternary quadratic forms of the above-mentioned type is unimprovable in a certain sense.

scholarly journals On a Counting Theorem for Weakly Admissible Lattices

2020 ◽  
Author(s):  
Reynold Fregoli
Keyword(s):  
Diophantine Approximation ◽  
General Setting ◽  
Upper Bounds ◽  
Lattice Points ◽  
Precise Estimate ◽  
Linear Subspaces ◽  
Minimal Structure ◽  
Partition Method

Abstract We give a precise estimate for the number of lattice points in certain bounded subsets of $\mathbb{R}^{n}$ that involve “hyperbolic spikes” and occur naturally in multiplicative Diophantine approximation. We use Wilkie’s o-minimal structure $\mathbb{R}_{\exp }$ and expansions thereof to formulate our counting result in a general setting. We give two different applications of our counting result. The 1st one establishes nearly sharp upper bounds for sums of reciprocals of fractional parts and thereby sheds light on a question raised by Lê and Vaaler, extending previous work of Widmer and of the author. The 2nd application establishes new examples of linear subspaces of Khintchine type thereby refining a theorem by Huang and Liu. For the proof of our counting result, we develop a sophisticated partition method that is crucial for further upcoming work on sums of reciprocals of fractional parts over distorted boxes.

Determination of Diphenylhydantoin in Human Serum by Spin Immunoassay

1975 ◽  
Vol 21 (2) ◽  
pp. 221-226 ◽  
Author(s):  
Mark R Montgomery ◽  
Jordan L Holtzman ◽  
Richard K Leute ◽  
John S Dewees ◽  
Gunner Bolz
Keyword(s):  
Human Serum ◽  
Cross Reactivity ◽  
Precise Estimate ◽  
Reliable Technique ◽  
Precise Method

Abstract A spin immunoassay for diphenylhydantoin is reported, which appears to give an accurate and precise estimate of serum diphenylhydantoin concentrations, as judged by the disappearance of [14C] diphenylhydantoin from the serum of a rabbIt. The assay also appears to be a reliable technique for routine diphenylhydantoin determinations, as judged from our experience with 28 patients. Serum diphenylhydantoin concentrations in the range of 1.0-50.0 mg/liter are easily determined on a 50-µl sample. Except for primidone, no significant cross reactivity was observed with eight drugs that are commonly used in conjunction with diphenylhydantoin therapy. This fast, simple, and precise method therefore appears to be readily applicable to routine determination of diphenylhydantoin.

scholarly journals A Precise Estimate of the Radius of HD 149026b

2008 ◽  
Vol 4 (S253) ◽  
pp. 466-469
Author(s):  
Philip Nutzman ◽  
David Charbonneau ◽  
Joshua N. Winn ◽  
Heather A. Knutson ◽  
Jonathan J. Fortney ◽  
...  
Keyword(s):  
Accurate Determination ◽  
Stellar Mass ◽  
Radius Ratio ◽  
Light Curves ◽  
Heavy Elements ◽  
Precise Estimate ◽  
Extrasolar Planet ◽  
Orbital Inclination ◽  
Limb Darkening

AbstractWe present Spitzer 8 μm transit observations of the extrasolar planet system HD 149026b. At this wavelength, transit light curves are weakly affected by stellar limb-darkening, allowing for a simpler and more accurate determination of planetary parameters. We measure a planet-star radius ratio of Rp/R∗=0.05158±0.00077, and in combination with ground-based data and independent constraints on the stellar mass and radius, we derive an orbital inclination of i = 85°.4+0°.9−0°.8 and a planet radius of 0.755 ± 0.040 RJ. These measurements further support models in which the planet is greatly enriched in heavy elements.

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