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1. Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements

   https://doi.org/10.1007/s11856-024-2613-1  

   Hung, Nguyen Ngoc; Sambale, Benjamin; Tiep, Pham Huu (September 2024, Israel Journal of Mathematics)

   Abstract Letk(B₀) andl(B₀) respectively denote the number of ordinary andp-Brauer irreducible characters in the principal blockB₀of a finite groupG. We prove that, ifk(B₀)−l(B₀) = 1, thenl(B₀) ≥p− 1 or elsep= 11 andl(B₀) = 9. This follows from a more general result that for every finite groupGin which all non-trivialp-elements are conjugate,l(B₀) ≥p− 1 or elsep= 11 and$$G/{{\bf{O}}_{{p^\prime }}}(G) \cong C_{11}^2\, \rtimes\,{\rm{SL}}(2,5)$$ $G/O_{p^{\prime }}\left(G\right)\cong C_{11}^2⋊\text{SL}(2,5)$. These results are useful in the study of principal blocks with few characters. We propose that, in every finite groupGof order divisible byp, the number of irreducible Brauer characters in the principalp-block ofGis always at least$$2\sqrt {p - 1} + 1 - {k_p}(G)$$ $2\sqrt{p-1}+1-k_p\left(G\right)$, wherek_p(G) is the number of conjugacy classes ofp-elements ofG. This indeed is a consequence of the celebrated Alperin weight conjecture and known results on bounding the number ofp-regular classes in finite groups. 

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2. The Missing Link of Sulfur Chemistry in TMC-1: The Detection of c -C ₃ H ₂ S from the GOTHAM Survey

   https://doi.org/10.3847/1538-4357/adb84c  

   Remijan, Anthony J; Changala, P Bryan; Xue, Ci; Yuan, Elsa_Q H; Duffy, Miya; Scolati, Haley N; Shingledecker, Christopher N; Speak, Thomas H; Cooke, Ilsa R; Loomis, Ryan; et al (March 2025, The Astrophysical Journal)

   Abstract We present the spectroscopic characterization of cyclopropenethione in the laboratory and detect it in space using the Green Bank Telescope Observations of TMC-1: Hunting Aromatic Molecules survey. The detection of this molecule—the missing link in understanding the C₃H₂S isomeric family in TMC-1—completes the detection of all three low-energy isomers of C₃H₂S, as both CH₂CCS and HCCCHS have been previously detected in this source. The total column density of this molecule (N_Tof $5.72_{-1.61}^{+2.65}\times 10^{10}$cm⁻²at an excitation temperature of $4.7_{-1.1}^{+1.3}$K) is smaller than both CH₂CCS and HCCCHS and follows nicely the relative dipole principle (RDP), a kinetic rule of thumb for predicting isomer abundances that suggests that, all other chemistry among a family of isomers being the same, the member with the smallest dipole (μ) should be the most abundant. The RDP now holds for the astronomical abundance ratios of both the S-bearing and O-bearing counterparts observed in TMC-1; however, CH₂CCO continues to elude detection in any astronomical source. 

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3. Constraining Cosmological Parameters Using the Cluster Mass–Richness Relation

   https://doi.org/10.3847/1538-4357/ace773  

   Abdullah, Mohamed H.; Wilson, Gillian; Klypin, Anatoly; Ishiyama, Tomoaki (September 2023, The Astrophysical Journal)

   Abstract The cluster mass–richness relation (MRR) is an observationally efficient and potentially powerful cosmological tool for constraining the matter density Ω_mand the amplitude of fluctuationsσ₈using the cluster abundance technique. We derive the MRR relation usingGalWCat19, a publicly available galaxy cluster catalog we created from the Sloan Digital Sky Survey-DR13 spectroscopic data set. In the MRR, cluster mass scales with richness as $\log M_{200}=\alpha +\beta \log N_{200}$. We find that the MRR we derive is consistent with both the IllustrisTNG and mini-Uchuu cosmological numerical simulations, with a slope ofβ≈ 1. We use the MRR we derived to estimate cluster masses from theGalWCat19catalog, which we then use to set constraints on Ω_mandσ₈. Utilizing the all-member MRR, we obtain constraints of Ω_m= ${0.31}_{-0.03}^{+0.04}$andσ₈= ${0.82}_{-0.04}^{+0.05}$, and utilizing the red member MRR only, we obtain Ω_m= ${0.31}_{-0.03}^{+0.04}$andσ₈= ${0.81}_{-0.04}^{+0.05}$. Our constraints on Ω_mandσ₈are consistent and very competitive with the Planck 2018 results. 

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4. Ferrimagnetism and Half-metallicity in Cr-substituted Mn _4–x Cr _x Al ₁₁

   https://doi.org/10.1088/1361-648X/add8d8  

   Noor, Md_Fahel_Bin; Law, Ka_Ming; Yasmin, Nusrat; Hauser, Adam_J; Besara, Tiglet (May 2025, Journal of Physics: Condensed Matter)

   Abstract Single crystals of disordered Mn_4–xCr_xAl₁₁have been synthesized via the flux method. EDS on several crystals of various sizes and shapes revealed an average molar ratio of 17:9:74 for Mn:Cr:Al, while X-ray diffraction on three different crystals yield compositions Mn_2.26Cr_1.74Al₁₁(Mn_4–xCr_xAl₁₁,x= 1.74), Mn_0.83Cr_3.17Al₁₁, and Mn_1.07Cr_2.93Al₁₁. This compound crystallizes in space groupP–1, isostructural with both Mn₄Al₁₁and Cr₄Al₁₁. Magnetic measurements on several crystals show that this disordered compound is ferrimagnetic with a low effective moment ofμ_eff≈1.012±0.004 μ_B/f.u. and a non-reachable transition temperature. DFT calculations display opening of a bandgap in the spin-up channel near the Fermi level with increasing Cr content, an indication of half-metallicity. 

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5. Kepler and the Behemoth: Three Mini-Neptunes in a 40 Million Year Old Association

   https://doi.org/10.3847/1538-3881/ac93ff  

   Bouma, L G; Kerr, R; Curtis, J L; Isaacson, H; Hillenbrand, L A; Howard, A W; Kraus, A L; Bieryla, A; Latham, D W; Petigura, E A; et al (October 2022, The Astronomical Journal)

   Abstract Stellar positions and velocities from Gaia are yielding a new view of open cluster dispersal. Here we present an analysis of a group of stars spanning Cepheus (l= 100°) to Hercules (l= 40°), hereafter the Cep-Her complex. The group includes four Kepler objects of interest: Kepler-1643 b (R_p= 2.32 ± 0.13R_⊕,P= 5.3 days), KOI-7368 b (R_p= 2.22 ± 0.12R_⊕,P= 6.8 days), KOI-7913 Ab (R_p= 2.34 ± 0.18R_⊕,P= 24.2 days), and Kepler-1627 Ab (R_p= 3.85 ± 0.11R_⊕,P= 7.2 days). The latter Neptune-sized planet is in part of the Cep-Her complex called theδLyr cluster. Here we focus on the former three systems, which are in other regions of the association. Based on kinematic evidence from Gaia, stellar rotation periods from TESS, and spectroscopy, these three objects are also ≈40 million years (Myr) old. More specifically, we find that Kepler-1643 is ${46}_{-7}^{+9}$Myr old, based on its membership in a dense subcluster of the complex called RSG-5. KOI-7368 and KOI-7913 are ${36}_{-8}^{+10}$Myr old, and are in a diffuse region that we call CH-2. Based on the transit shapes and high-resolution imaging, all three objects are most likely planets, with false-positive probabilities of 6 × 10⁻⁹, 4 × 10⁻³, and 1 × 10⁻⁴for Kepler-1643, KOI-7368, and KOI-7913, respectively. These planets demonstrate that mini-Neptunes with sizes of ≈2 Earth radii exist at ages of 40 Myr. 

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