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1. Keeping the name clean: [2 + 2] photocycloaddition

   https://doi.org/10.1007/s43630-022-00239-7  

   Sivaguru, Jayaraman; Bach, Thorsten; Ramamurthy, Vaidhyanathan (April 2022, Photochemical & Photobiological Sciences)
2. Linear maps preserving the Lorentz spectrum: the $$2 \times 2$$ case

   https://doi.org/10.13001/ela.2022.6925  

   Bueno, María I.; Furtado, Susana; Klausmeier, Aelita; Veltri, Joey (December 2021, The Electronic Journal of Linear Algebra)

   In this paper, a complete description of the linear maps $$\phi:W_{n}\rightarrow W_{n}$$ that preserve the Lorentz spectrum is given when $n=2$, and $$W_{n}$$ is the space $$M_{n}$$ of $$n\times n$$ real matrices or the subspace $$S_{n}$$ of $$M_{n}$$ formed by the symmetric matrices. In both cases, it has been shown that $$\phi(A)=PAP^{-1}$$ for all $$A\in W_{2}$$, where $$P$$ is a matrix with a certain structure. It was also shown that such preservers do not change the nature of the Lorentz eigenvalues (that is, the fact that they are associated with Lorentz eigenvectors in the interior or on the boundary of the Lorentz cone). These results extend to $n=2$ those for $$n\geq 3$$ obtained by Bueno, Furtado, and Sivakumar (2021). The case $n=2$ has some specificities, when compared to the case $$n\geq3,$$ due to the fact that the Lorentz cone in $$\mathbb{R}^{2}$$ is polyedral, contrary to what happens when it is contained in $$\mathbb{R}^{n}$$ with $$n\geq3.$$ Thus, the study of the Lorentz spectrum preservers on $$W_n = M_n$$ also follows from the known description of the Pareto spectrum preservers on $$M_n$$. 

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3. Ultraviolet photochemistry of the 2-buten-2-yl radical

   https://doi.org/10.1039/D4CP03076A  

   Lucas, Michael; Qin, Yuan; Yang, Lei; Sun, Ge; Zhang, Jingsong (October 2024, Physical Chemistry Chemical Physics)

   The ultraviolet (UV) photodissociation dynamics of the 2-buten-2-yl (C4H7) radical were studied using the high-n Rydberg atom time-of-flight (HRTOF) technique in the photolysis region of 226–246 nm. 2-Buten-2-yl radicals were generated by 193 nm photodissociation of the precursor 2-chloro-2-butene. The H-atom photofragment yield (PFY) spectrum of 2-buten-2-yl is broad, peaking at 234 nm. Quantum chemistry calculations show that the UV absorption is due to the 3py and 3px Rydberg states (parallel to the plane of C[double bond, length as m-dash]C double bond). The translational energy distributions of the H-atom loss product channel, P(ET)'s, of 2-buten-2-yl show a bimodal distribution indicating two dissociation pathways. The major pathway peaks at ET ∼ 7 kcal mol−1 with a nearly constant fraction of average ET in the total excess energy, 〈fT〉, at ∼0.11–0.12. This main pathway has an isotropic product angular distribution with β ∼ 0, consistent with the unimolecular dissociation of a hot 2-buten-2-yl radical following internal conversion from the electronically excited state, resulting in the formation of 2-butyne + H (∼84%) and 1,2-butadiene + H (∼16%). Additionally, there is a minor non-statistical pathway with an isotropic angular distribution. The minor pathway peaks at ET ∼ 35 kcal mol−1 in the P(ET) distributions and exhibits a large 〈fT〉 of ∼0.40–0.46. This fast pathway suggests a direct dissociation of the methyl H-atom on a repulsive excited state surface or on the repulsive part of the ground state surface, forming 1,2-butadiene + H. The fast/slow pathway branching ratio is in the range of 0.03–0.08. 

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4. On the Lebesgue–Nagell equation $$x^2-2 = y^p$$

   https://doi.org/10.1007/s11139-026-01334-4  

   Katz, Ethan; Pratt, Kyle (March 2026, The Ramanujan Journal)
5. Some results concerning the SRT 2 2 vs. COH problem

   https://doi.org/10.3233/COM-190251  

   Cholak, Peter A.; Dzhafarov, Damir D.; Hirschfeldt, Denis R.; Patey, Ludovic (April 2020, Computability)