196 research outputs found
Nonlinear stability analysis of the Emden-Fowler equation
In this paper we qualitatively study radial solutions of the semilinear
elliptic equation with and on the
positive real line, called the Emden-Fowler or Lane-Emden equation. This
equation is of great importance in Newtonian astrophysics and the constant
is called the polytropic index. By introducing a set of new variables, the
Emden-Fowler equation can be written as an autonomous system of two ordinary
differential equations which can be analyzed using linear and nonlinear
stability analysis. We perform the study of stability by using linear stability
analysis, the Jacobi stability analysis (Kosambi-Cartan-Chern theory) and the
Lyapunov function method. Depending on the values of these different
methods yield different results. We identify a parameter range for where
all three methods imply stability.Comment: 12 pages; new reference added; 3 new references added; fully revised
versio
Algebraic structure of gravity in Ashtekar variables
The BRST transformations for gravity in Ashtekar variables are obtained by
using the Maurer-Cartan horizontality conditions. The BRST cohomology in
Ashtekar variables is calculated with the help of an operator
introduced by S.P. Sorella, which allows to decompose the exterior derivative
as a BRST commutator. This BRST cohomology leads to the differential invariants
for four-dimensional manifolds.Comment: 19 pages, report REF. TUW 94-1
The Effect of Polyphenols, Minerals, Fibers, and Fruits on Irritable Bowel Syndrome: A Systematic Review
Background: Irritable bowel syndrome (IBS) is a chronic gastrointestinal disorder characterized by abdominal pain, bloating, and changes in bowel habits. Various dietary factors have been implicated in the pathogenesis and management of IBS symptoms. This systematic review aims to evaluate the effects of polyphenols, minerals, fibers, and fruits on the symptoms and overall well-being of individuals with IBS. Materials and Methods: A comprehensive literature search was conducted in several electronic databases, including PubMed, Scopus, and Web of Science. Studies published up until July 2023 were included. Results: The selected studies varied in terms of study design, participant characteristics, intervention duration, and outcome measures. Overall, the findings suggest that dietary interventions involving polyphenols, minerals, fibers, and fruits can have a positive impact on IBS symptoms. Dietary fiber supplementation, particularly soluble fiber, has been associated with reduced bloating and enhanced stool consistency. Conclusions: This systematic review provides evidence supporting the beneficial effects of polyphenols, minerals, fibers, and fruits in IBS patients. These dietary components hold promise as complementary approaches for managing IBS symptoms. However, due to the heterogeneity of the included studies and the limited number of high-quality randomized controlled trials, further well-designed trials are warranted to establish the optimal dosages, duration, and long-term effects of these interventions. Understanding the role of specific dietary components in IBS management may pave the way for personalized dietary recommendations and improve the quality of life for individuals suffering from this complex disorder
A new system for quantitative evaluation of infant gaze capabilities in a wide visual field
Clocking Auger Electrons
Intense X-ray free-electron lasers (XFELs) can rapidly excite matter, leaving
it in inherently unstable states that decay on femtosecond timescales. As the
relaxation occurs primarily via Auger emission, excited state observations are
constrained by Auger decay. In situ measurement of this process is therefore
crucial, yet it has thus far remained elusive at XFELs due to inherent timing
and phase jitter, which can be orders of magnitude larger than the timescale of
Auger decay. Here, we develop a new approach termed self-referenced attosecond
streaking, based upon simultaneous measurements of streaked photo- and Auger
electrons. Our technique enables sub-femtosecond resolution in spite of jitter.
We exploit this method to make the first XFEL time-domain measurement of the
Auger decay lifetime in atomic neon, and, by using a fully quantum-mechanical
description, retrieve a lifetime of fs for the KLL
decay channel. Importantly, our technique can be generalised to permit the
extension of attosecond time-resolved experiments to all current and future FEL
facilities.Comment: Main text: 20 pages, 3 figures. Supplementary information: 17 pages,
6 figure
Clocking Auger electrons
Intense X-ray free-electron lasers (XFELs) can rapidly excite matter, leaving it in inherently unstable states that decay on femtosecond timescales. The relaxation occurs primarily via Auger emission, so excited-state observations are constrained by Auger decay. In situ measurement of this process is therefore crucial, yet it has thus far remained elusive in XFELs owing to inherent timing and phase jitter, which can be orders of magnitude larger than the timescale of Auger decay. Here we develop an approach termed âself-referenced attosecond streakingâ that provides subfemtosecond resolution in spite of jitter, enabling time-domain measurement of the delay between photoemission and Auger emission in atomic neon excited by intense, femtosecond pulses from an XFEL. Using a fully quantum-mechanical description that treats the ionization, core-hole formation and Auger emission as a single process, the observed delay yields an Auger decay lifetime of 2.2_â0.3^+0.2 fs for the KLL decay channel
InfluĂȘncia da Velocidade de Rotação do Rebite na Microestrutura e no Desempenho MecĂąnico de Juntas de CompĂłsito Termofixo Rebitadas por Fricção
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