scholarly journals Verifying the Firoozbakht, Nicholson, and Farhadian Conjectures up to the 81st Maximal Prime Gap

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 691
Author(s):  
Visser
Keyword(s):  
General Proof ◽  
Prime Gaps ◽  
Minor Improvement

The Firoozbakht, Nicholson, and Farhadian conjectures can be phrased in terms of increasingly powerful conjectured bounds on the prime gaps g n : = p n + 1 - p n . While a general proof of any of these conjectures is far out of reach, I shall show that all three of these conjectures are unconditionally and explicitly verified for all primes below the as yet unknown location of the 81st maximal prime gap, certainly for all primes p < 2 64 . For the Firoozbakht conjecture itself this is a rather minor improvement on currently known results, but for the somewhat stronger Nicholson and Farhadian conjectures this may be considerably more interesting. Sequences: A005250 A002386 A005669 A000101 A107578 A246777 A246776.

scholarly journals Largest-Crown-Width Prediction Models for 53 Species in the Western United States

2004 ◽  
Vol 19 (4) ◽  
pp. 245-251 ◽  
Author(s):  
William A. Bechtold
Keyword(s):  
United States ◽  
Prediction Models ◽  
Basal Area ◽  
Stem Diameter ◽  
Western United States ◽  
Quadratic Term ◽  
Crown Width ◽  
Coefficients Of Variation ◽  
Bioclimatic Index ◽  
Minor Improvement

Abstract The mean crown diameters of stand-grown trees 5.0-in. dbh and larger were modeled as a function of stem diameter, live-crown ratio, stand-level basal area, latitude, longitude, elevation, and Hopkins bioclimatic index for 53 tree species in the western United States. Stem diameter was statistically significant in all models, and a quadratic term for stem diameter was required for some species. Crown ratio and/or Hopkins index also improved the models for most species. A term for stand-level basal area was not generally needed but did yield some minor improvement for a few species. Coefficients of variation from the regression solutions ranged from 17 to 33%, and model R2 ranged from 0.15 to 0.85. Simpler models, based solely on stem diameter, are also presented. West. J. Appl. For. 19(4):245–251.

scholarly journals General proof of Osterwalder-Schrader positivity for the Wilson action

1987 ◽  
Vol 113 (3) ◽  
pp. 369-373 ◽  
Author(s):  
P. Menotti ◽  
A. Pelissetto
Keyword(s):  
General Proof

General proof of Carruthers theorem

1967 ◽  
Vol 24 (8) ◽  
pp. 411-412 ◽  
Author(s):  
Y.S. Jin
Keyword(s):  
General Proof

ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED

2021 ◽  
pp. 1-23
Author(s):  
FÁBIO NATALI ◽  
SABRINA AMARAL
Keyword(s):  
Traveling Wave ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Spectral Stability ◽  
Dispersive Equations ◽  
Periodic Waves ◽  
General Proof ◽  
Wave Solutions ◽  
Periodic Traveling Wave

Abstract The purpose of this paper is to present an extension of the results in [8]. We establish a more general proof for the moving kernel formula to prove the spectral stability of periodic traveling wave solutions for the regularized Benjamin–Bona–Mahony type equations. As applications of our analysis, we show the spectral instability for the quintic Benjamin–Bona–Mahony equation and the spectral (orbital) stability for the regularized Benjamin–Ono equation.

Psychiatric illness, medication and driving: an audit of documentation

2015 ◽  
Vol 33 (3) ◽  
pp. 171-174 ◽  
Author(s):  
A. Gallagher ◽  
S. Shah ◽  
W. Abassi ◽  
E. Walsh
Keyword(s):  
Road Safety ◽  
Psychiatric Patients ◽  
Fitness To Drive ◽  
Team Members ◽  
The Road ◽  
Significant Difference ◽  
New Guidelines ◽  
A Minor ◽  
Inpatient Psychiatric Unit ◽  
Minor Improvement

ObjectivesGuidelines on advising patients on fitness to drive have been published recently by the Road Safety Authority in collaboration with the Royal College of Physicians of Ireland. The aim of this audit is to assess if the new guidelines are being adhered to.MethodExamination of the documentation and adherence to the guidelines in the inpatient psychiatric unit, Mayo General Hospital.ResultsOf the 100 patients included in audit cycle one, none had any specific documentation about driving. One patient was admitted with alcohol misuse and was driving. On re-auditing, following presentation at academic meeting and education of team members on the guidelines, there was a minor improvement of 7%.ConclusionThere was no significant difference in documentation on re-audit. However, an increase of 7% is nonetheless encouraging. Information concerning driving should be a standard part of advice given to all psychiatric patients.

AN APPLICATION OF THE TOPOLOGICAL DEGREE TO GRAVITATIONAL LENSES

1998 ◽  
Vol 13 (02) ◽  
pp. 83-86 ◽  
Author(s):  
MARCO LOMBARDI
Keyword(s):  
Point Source ◽  
Mass Distribution ◽  
Topological Degree ◽  
General Theorem ◽  
Gravitational Lens ◽  
Gravitational Lenses ◽  
General Proof ◽  
Special Case

In this letter we provide a new proof of a general theorem on gravitational lenses, first proven by Burke (1981) for the special case of thin lenses. The theorem states that a transparent gravitational lens with non-singular mass distribution produces an odd number of images of a point source. Our general proof shows that the topological degree finds natural and interesting applications in the theory of gravitational lenses.

scholarly journals The general proof of certain fundamental equations in the theory of metallic conduction

1934 ◽  
Vol 144 (851) ◽  
pp. 101-117 ◽  
Keyword(s):  
Wave Equation ◽  
Periodic Potential ◽  
Thermal Motion ◽  
Electronic Conduction ◽  
Modern Theory ◽  
General Proof ◽  
Metallic Conduction ◽  
Fundamental Equations

In the modern theory of electronic conduction the electrons are considered, when the thermal motion of the lattice is neglected, as moving in a periodic potential with the property V ( x + la , y + ma , z + na ) = V ( x, y, z ). The wave equation for an electron in this field is { h 2/8π2 m ∇ 2 + E K - V} ψ K = 0. Block has shown that this equation has solutions of the form ψ K = e i K.R U K (R), where U K has the periodicity of the lattice.

scholarly journals Dostępność dziczyzny na polskim rynku w kontekście potrzeb konsumentów

2018 ◽  
pp. 83-91 ◽  
Author(s):  
Katarzyna Kwiecińska ◽  
Jerzy Gębski ◽  
Małgorzata Kosicka-Gębska
Keyword(s):  
Qualitative Study ◽  
Nutritional Value ◽  
Consumer Interest ◽  
Limited Availability ◽  
Game Meat ◽  
Wild Game ◽  
Significant Barrier ◽  
Main Factors ◽  
Minor Improvement

Game meat, despite its high nutritional value, appears in the diet of Poles sporadically. The main factors limiting consumer interest in game are limited availability of game meat at stores and high prices of meat and game products. In the paper results of the qualitative study carried out using the CATI method were presented. The study was conducted in 2016 with 450 consumers declaring eating game meat. Study shows that the physical and economic availability of game meat affects consumer interest in its consumption. Minor improvement in the availability of venison in the Polish market are being observed. High prices still seem to be a significant barrier to consumers’ interest in wild game.

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