Noncommutative generalizations of theorems of Cohen and Kaplansky

This paper investigates situations where a property of a ring can be tested on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp. principal) iff every "prime right ideal" is finitely generated (resp. principal), where the phrase "prime right ideal" can be interpreted in one of many different ways. We also use our methods to show that other properties can be tested on special sets of right ideals, such as the right artinian property and various homological properties. Applying these methods, we prove the following noncommutative generalization of a result of Kaplansky: a (left and right) noetherian ring is a principal right ideal ring iff all of its maximal right ideals are principal. A counterexample shows that the left noetherian hypothesis cannot be dropped. Finally, we compare our results to earlier generalizations of Cohen's and Kaplansky's theorems in the literature.Comment: 41 pages. To appear in Algebras and Representation Theory. Minor changes were made to the numbering system, in order to remain consistent with the published versio

Parents' assessment of parent-child interaction interventions – a longitudinal study in 101 families

<p>Abstract</p> <p>Background</p> <p>The aim of the study was to describe families with small children who participated in parent-child interaction interventions at four centres in Sweden, and to examine long term and short term changes regarding the parents' experience of parental stress, parental attachment patterns, the parents' mental health and life satisfaction, the parents' social support and the children's problems.</p> <p>Methods</p> <p>In this longitudinal study a consecutive sample of 101 families (94 mothers and 54 fathers) with 118 children (median age 3 years) was assessed, using self-reports, at the outset of the treatment (T1), six months later (T2) and 18 months after the beginning of treatment (T3). Analysis of the observed differences was carried out using Wilcoxon's Signed-Rank test and Cohen's d.</p> <p>Results</p> <p>The results from commencement of treatment showed that the parents had considerable problems in all areas examined. At the outset of treatment (T1) the mothers showed a higher level of problem load than the fathers on almost all scales. In the families where the children's problems have also been measured (children from the age of four) it appeared that they had problems of a nature and degree otherwise found in psychiatric populations. We found a clear general trend towards a positive development from T1 to T2 and this development was also reinforced from T2 to T3. Aggression in the child was one of the most common causes for contact. There were few undesired or unplanned interruptions of the treatment, and the attrition from the study was low.</p> <p>Conclusion</p> <p>This study has shown that it is possible to reach mothers as well as fathers with parenting problems and to create an intervention program with very low dropout levels – which is of special importance for families with small children displaying aggressive behaviour. The parents taking part in this study showed clear improvement trends after six months and this development was reinforced a year later. This study suggests the necessity of clinical development and future research concerning the role of fathers in parent-child interaction interventions.</p

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm

We present a new measurement of the positive muon magnetic anomaly, a_{μ}≡(g_{μ}-2)/2, from the Fermilab Muon g-2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω[over ˜]_{p}^{'}, and of the anomalous precession frequency corrected for beam dynamics effects, ω_{a}. From the ratio ω_{a}/ω[over ˜]_{p}^{'}, together with precisely determined external parameters, we determine a_{μ}=116 592 057(25)×10^{-11} (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a_{μ}(FNAL)=116 592 055(24)×10^{-11} (0.20 ppm). The new experimental world average is a_{μ}(exp)=116 592 059(22)×10^{-11} (0.19 ppm), which represents a factor of 2 improvement in precision

Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 Experiment

The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency $\omega_a$ to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of $a_{\mu}({\rm FNAL}) = 116\,592\,040(54) \times 10^{-11}$ (0.46 ppm). This article describes the multiple techniques employed in the reconstruction, analysis and fitting of the data to measure the precession frequency. It also presents the averaging of the results from the eleven separate determinations of \omega_a, and the systematic uncertainties on the result.Comment: 29 pages, 19 figures. Published in Physical Review

Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$

Magnetic Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab

The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_\mu = (g^{}_\mu-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tilde{\omega}'^{}_p$, the denominator in the ratio $\omega^{}_a$/$\tilde{\omega}'^{}_p$ that together with known fundamental constants yields $a^{}_\mu$. The reported uncertainty on $\tilde{\omega}'^{}_p$ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb

Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$