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1. Solutions of ϕ (n) = ϕ (n + k) and σ (n) = σ (n + k)

   https://doi.org/10.1093/imrn/rnaa218  

   Ford, Kevin (August 2020, International Mathematics Research Notices)

   null (Ed.)

   Abstract We show that for some even $$k\leqslant 3570$$ and all  $$k$$ with $442720643463713815200|k$, the equation $$\phi (n)=\phi (n+k)$$ has infinitely many solutions $$n$$, where $$\phi $$ is Euler’s totient function. We also show that for a positive proportion of all $$k$$, the equation $$\sigma (n)=\sigma (n+k)$$ has infinitely many solutions $$n$$. The proofs rely on recent progress on the prime $$k$$-tuples conjecture by Zhang, Maynard, Tao, and PolyMath. 

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2. Measurement of the energy dependence of the e+e− → $$ B\overline{B} $$, $$ B{\overline{B}}^{\ast } $$ and $$ {B}^{\ast }{\overline{B}}^{\ast } $$ exclusive cross sections

   https://doi.org/10.1007/JHEP06(2021)137  

   Mizuk, R.; Bondar, A.; Adachi, I.; Aihara, H.; Al Said, S.; Asner, D. M.; Atmacan, H.; Aulchenko, V.; Aushev, T.; Ayad, R.; et al (June 2021, Journal of High Energy Physics)

   A bstract We report the first measurement of the exclusive cross sections e + e − → $$ B\overline{B} $$ B B ¯ , e + e − → $$ B{\overline{B}}^{\ast } $$ B B ¯ ∗ , and e + e − → $$ {B}^{\ast }{\overline{B}}^{\ast } $$ B ∗ B ¯ ∗ in the energy range from 10 . 63 GeV to 11 . 02 GeV. The B mesons are fully reconstructed in a large number of hadronic final states and the three channels are identified using a beam-constrained-mass variable. The shapes of the exclusive cross sections show oscillatory behavior with several maxima and minima. The results are obtained using data collected by the Belle experiment at the KEKB asymmetric-energy e + e − collider. 

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3. Measurement of the energy dependence of the e+e− → $$ B\overline{B} $$, $$ B{\overline{B}}^{\ast } $$, and $$ {B}^{\ast }{\overline{B}}^{\ast } $$ cross sections at Belle II

   https://doi.org/10.1007/JHEP10(2024)114  

   Adachi, I; Aggarwal, L; Ahmed, H; Aihara, H; Akopov, N; Aloisio, A; Althubiti, N; Anh_Ky, N; Asner, D M; Atmacan, H; et al (October 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We report measurements of thee⁺e⁻→$$ B\overline{B} $$ $B\overline{B}$,$$ B{\overline{B}}^{\ast } $$ $B{\overline{B}}^{\ast }$, and$$ {B}^{\ast }{\overline{B}}^{\ast } $$ $B^{\ast }{\overline{B}}^{\ast }$cross sections at four energies, 10653, 10701, 10746 and 10805 MeV, using data collected by the Belle II experiment. We reconstruct oneBmeson in a large number of hadronic final states and use its momentum to identify the production process. In the first 2 – 5 MeV above$$ {B}^{\ast }{\overline{B}}^{\ast } $$ $B^{\ast }{\overline{B}}^{\ast }$threshold, thee⁺e⁻→$$ {B}^{\ast }{\overline{B}}^{\ast } $$ $B^{\ast }{\overline{B}}^{\ast }$cross section increases rapidly. This may indicate the presence of a pole close to the threshold. 

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4. Fast Sampling of b-Matchings and b-Edge Covers

   Chen, Zongchen; Gu, Yuzhou (January 2024, Society for Industrial and Applied Mathematics)
5. Variation in δ ¹⁵ N and δ ¹³ C values of forages for Arctic caribou: effects of location, phenology and simulated digestion: Variation in δ ¹⁵ N and δ ¹³ C values of forages for Arctic caribou

   https://doi.org/10.1002/rcm.7849  

   Vansomeren, Lindsay L.; Barboza, Perry S.; Gustine, David D.; Syndonia Bret-Harte, M. (May 2017, Rapid Communications in Mass Spectrometry)