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   https://doi.org/10.1098/rspa.2020.0612  

   Cakoni, Fioralba; Colton, David; Haddar, Houssem (December 2020, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   null (Ed.)

   In this paper, we develop a conceptually unified approach for characterizing and determining scattering poles and interior eigenvalues for a given scattering problem. Our approach explores a duality stemming from interchanging the roles of incident and scattered fields in our analysis. Both sets are related to the kernel of the relative scattering operator mapping incident fields to scattered fields, corresponding to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Our discussion includes the scattering problem for a Dirichlet obstacle where duality is between scattering poles and Dirichlet eigenvalues, and the inhomogeneous scattering problem where the duality is between scattering poles and transmission eigenvalues. Our new characterization of the scattering poles suggests a numerical method for their computation in terms of scattering data for the corresponding interior scattering problem. 

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3. On the edit distance of powers of cycles

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   Berikkyzy, Zhanar; Martin, Ryan R.; Peck, Chelsea (October 2018, Discrete Mathematics)
4. On cohesive powers of linear orders

   https://doi.org/10.1017/jsl.2023.14  

   Dimitrov, Rumen; Harizanov, Valentina; Morozov, Andrey; Shafer, Paul; Soskova, Alexandra A; Vatev, Stefan V (September 2023, The Journal of Symbolic Logic)

   Abstract Cohesive powersof computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let$$\omega $$,$$\zeta $$, and$$\eta $$denote the respective order-types of the natural numbers, the integers, and the rationals when thought of as linear orders. We investigate the cohesive powers of computable linear orders, with special emphasis on computable copies of$$\omega $$. If$$\mathcal {L}$$is a computable copy of$$\omega $$that is computably isomorphic to the usual presentation of$$\omega $$, then every cohesive power of$$\mathcal {L}$$has order-type$$\omega + \zeta \eta $$. However, there are computable copies of$$\omega $$, necessarily not computably isomorphic to the usual presentation, having cohesive powers not elementarily equivalent to$$\omega + \zeta \eta $$. For example, we show that there is a computable copy of$$\omega $$with a cohesive power of order-type$$\omega + \eta $$. Our most general result is that if$$X \subseteq \mathbb {N} \setminus \{0\}$$is a Boolean combination of$$\Sigma _2$$sets, thought of as a set of finite order-types, then there is a computable copy of$$\omega $$with a cohesive power of order-type$$\omega + \boldsymbol {\sigma }(X \cup \{\omega + \zeta \eta + \omega ^*\})$$, where$$\boldsymbol {\sigma }(X \cup \{\omega + \zeta \eta + \omega ^*\})$$denotes the shuffle of the order-types inXand the order-type$$\omega + \zeta \eta + \omega ^*$$. Furthermore, ifXis finite and non-empty, then there is a computable copy of$$\omega $$with a cohesive power of order-type$$\omega + \boldsymbol {\sigma }(X)$$. 

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5. Dissociative photoionization of 1,3‐dioxolane: We need six channels to fit the elephant

   https://doi.org/10.1002/jms.4522  

   Weidner, Peter; Voronova, Krisztina; Bodi, Andras; Sztáray, Bálint (June 2020, Journal of Mass Spectrometry)

   Abstract The dissociative photoionization of 1,3‐dioxolane was studied by photoelectron photoion coincidence (PEPICO) spectroscopy in the photon energy range of 9.5–13.5 eV. Our statistical thermodynamics model shows that a total of six dissociation channels are involved in the formation of three fragment ions, namely, C₃H₅O₂⁺(m/z73), C₂H₅O⁺(m/z45), and C₂H₄O⁺(m/z44), with two channels contributing to the formation of each. By comparing the results of ab initio quantum chemical calculations to the experimentally derived appearance energies of the fragment ions, the most likely mechanisms for these unimolecular dissociation reactions are proposed, including a description of the relevant parts of the potential energy surface. 

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