Matrices that commute with their derivative. On a letter from Schur to Wielandt

We examine when a matrix whose elements are differentiable functions in one variable commutes with its derivative. This problem was discussed in a letter from Issai Schur to Helmut Wielandt written in 1934, which we found in Wielandt's Nachlass. We present this letter and its translation into English. The topic was rediscovered later and partial results were proved. However, there are many subtle observations in Schur's letter which were not obtained in later years. Using an algebraic setting, we put these into perspective and extend them in several directions. We present in detail the relationship between several conditions mentioned in Schur's letter and we focus in particular on the characterization of matrices called Type 1 by Schur. We also present several examples that demonstrate Schur's observations.Comment: 21 pages, 1 facsimile, some inaccuracies corrected, historical comments and acknowledgments added; final version to appear in Linear Algebra and its Application

Physical Activity and Exercise for Hot Flashes: Trigger or Treatment?

Importance and Objective: Hot flashes (HFs) are a prevalent feature of menopause. Hot flashes can be bothersome and affect quality of life. However, HFs have also been associated with the risk for cardiovascular disease. Therefore, providing current evidence on the effect of therapies to reduce HFs can help patients and providers with decision making. This review provides details on the scientific evidence to date related to the effect of physical activity (PA) and exercise to alter the HF experience in women Methods: The PubMed database was searched between June 2020 and June 2022 for currently available evidence regarding the relation between PA and exercise and HFs. Our analysis included randomized control trials on exercise training, epidemiological studies, and studies evaluating acute exercise on the self-reported and objectively measured HF experience in addition to systematic reviews on the topic published as of June 2022. Discussion and Conclusions: The majority of evidence from randomized control trials indicates that aerobic and resistance exercise training lead to a decrease in subjectively experienced HFs. The limited available studies on acute exercise indicate that a bout of moderate-intensity exercise may decrease objectively measured and self-reported HFs but acute increases in PA intensity above accustomed levels may influence subjective HF experience. Some evidence suggests that for those with depression, habitual PA may be an effective way to reduce HF symptoms. Weighing the avail- able evidence, for people who experience HFs, engaging in regular moderate-intensity PA, including aerobic and resistance exercise, may be an effective therapy to reduce HFs and women should be counseled on the benefits of regular, moderate exercise. However, significant gaps in knowledge remain about the optimal exercise prescription, effectiveness for a diverse population, meaning of differences between objective and subjective experience, and mechanisms that lead to changes in HFs

Search for CPCP violation in D0^0→\to KS0^0_\mathrm{S}KS0^0_\mathrm{S} decays in proton-proton collisions at s\sqrt{s} = 13 TeV

International audienceA search is reported for charge-parity D$^0$$\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$$CP$ violation in D$^0$$\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ decays, using data collected in proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by the CMS experiment in 2018. The analysis uses a dedicated data set that corresponds to an integrated luminosity of 41.6 fb$^{-1}$, which consists of about 10 billion events containing a pair of ẖadrons, nearly all of which decay to charm hadrons. The flavor of the neutral D meson is determined by the pion charge in the reconstructed decays D$^{*+}$$\to$ D$^0\pi^+$ and D$^{*-}$$\to$ D$^0\pi^-$. The D$^0$$\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$$CP$ asymmetry in D$^0$$\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ is measured to be $A_{CP}$( K$^0_\mathrm{S}$K$^0_\mathrm{S}$) = (6.2 $\pm$ 3.0 $\pm$ 0.2 $\pm$ 0.8)%, where the three uncertainties represent the statistical uncertainty, the systematic uncertainty, and the uncertainty in the measurement of the D$^0$ $\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ $CP$ asymmetry in the D$^0$ $\to$ K$^0_\mathrm{S}\pi^+\pi^-$ decay. This is the first D$^0$ $\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ $CP$ asymmetry measurement by CMS in the charm sector as well as the first to utilize a fully hadronic final state

Search for the Z boson decay to ττμμ\tau\tau\mu\mu in proton-proton collisions at s\sqrt{s} = 13 TeV

International audienceThe first search for the Z boson decay to $\tau\tau\mu\mu$ at the CERN LHC is presented, based on data collected by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb$^{-1}$. The data are compatible with the predicted background. For the first time, an upper limit at the 95% confidence level of 6.9 times the standard model expectation is placed on the ratio of the Z $\to$ $\tau\tau\mu\mu$ to Z $\to$ 4$\mu$ branching fractions. Limits are also placed on the six flavor-conserving four-lepton effective-field-theory operators involving two muons and two tau leptons, for the first time testing all such operators

Search for the Z boson decay to ττμμ\tau\tau\mu\mu in proton-proton collisions at s\sqrt{s} = 13 TeV

International audienceThe first search for the Z boson decay to $\tau\tau\mu\mu$ at the CERN LHC is presented, based on data collected by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb$^{-1}$. The data are compatible with the predicted background. For the first time, an upper limit at the 95% confidence level of 6.9 times the standard model expectation is placed on the ratio of the Z $\to$ $\tau\tau\mu\mu$ to Z $\to$ 4$\mu$ branching fractions. Limits are also placed on the six flavor-conserving four-lepton effective-field-theory operators involving two muons and two tau leptons, for the first time testing all such operators

Search for new resonances decaying to pairs of merged diphotons in proton-proton collisions at s\sqrt{s} = 13 TeV

International audienceA search is presented for an extended Higgs sector with two new particles, X and $\phi$, in the process X $\to$$\phi\phi$$\to$$(\gamma\gamma)(\gamma\gamma)$. Novel neural networks classify events with diphotons that are merged and determine the diphoton masses. The search uses LHC proton-proton collision data at $\sqrt{s}$ = 13 TeV collected with the CMS detector, corresponding to an integrated luminosity of 138 fb$^{-1}$. No evidence of such resonances is seen. Upper limits are set on the production cross section versus the resonance masses, representing the most sensitive search in this channel