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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. QTL × environment interactions underlie ionome divergence in switchgrass

   https://doi.org/10.1093/g3journal/jkab144  

   Zhang, Li ; MacQueen, Alice ; Bonnette, Jason ; Fritschi, Felix B ; Lowry, David B ; Juenger, Thomas E ( April 2021 , G3 Genes|Genomes|Genetics)

   Wisser, R J (Ed.)

   Abstract Ionomics measures elemental concentrations in biological organisms and provides a snapshot of physiology under different conditions. In this study, we evaluate genetic variation of the ionome in outbred, perennial switchgrass in three environments across the species’ native range, and explore patterns of genotype-by-environment interactions. We grew 725 clonally replicated genotypes of a large full sib family from a four-way linkage mapping population, created from deeply diverged upland and lowland switchgrass ecotypes, at three common gardens. Concentrations of 18 mineral elements were determined in whole post-anthesis tillers using ion coupled plasma mass spectrometry (ICP-MS). These measurements were used to identify quantitative trait loci (QTL) with and without QTL-by-environment interactions (QTLxE) using a multi-environment QTL mapping approach. We found that element concentrations varied significantly both within and between switchgrass ecotypes, and GxE was present at both the trait and QTL level. Concentrations of 14 of the 18 elements were under some genetic control, and 77 QTL were detected for these elements. Seventy-four percent of QTL colocalized multiple elements, half of QTL exhibited significant QTLxE, and roughly equal numbers of QTL had significant differences in magnitude and sign of their effects across environments. The switchgrass ionome is under moderate genetic control and by loci with highly variable effects across environments. 

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3. Synthesis, Structure, and Spectroscopy of the Biscarboranyl Stannylenes ( bc )Sn·THF and K 2 [( bc )Sn] 2 ( bc = 1,1′( ortho -Biscarborane)) and Dibiscarboranyl Ethene ( bc )CH═CH( bc )

   https://doi.org/10.1021/acs.organomet.3c00190  

   Phung, Alice C. ; Fettinger, James C. ; Power, Philip P. ( June 2023 , Organometallics)
4. 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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5. Quantitative Assessment of B−B−B, B−H b −B, and B−H t Bonds: From BH 3 to B 12 H 12 2−

   https://doi.org/10.1002/cphc.201900364  

   Sethio, Daniel ; Daku, Latévi Max Lawson ; Hagemann, Hans ; Kraka, Elfi ( July 2019 , ChemPhysChem)