# MATH Research Publications

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The collection of peer-reviewed research articles (co)authored by faculty of the Department of Mathematics and Statistics.

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Item Biholomorphic transformations(CRC Press, 2024) Fridman, Buma L.; Ma, DaoweiThe problem of biholomorphic classification of complex manifolds has been one of the central problems in Complex Analysis. Biholomorphic transformations are a very active and productive area of research. This article presents several directions in this work. After the general introduction of the subject, we examine related topics, which by themselves are highly interesting: invariant metrics, the extension of biholomorphic transformations to the boundary, automorphism groups of complex manifolds, fixed points, and determining sets of holomorphic self-maps of a domain. In the last section, we present some results on "approximate" biholomorphisms. © 2022 Taylor & Francis Group, LLC.Item Almost isotropy-maximal manifolds of non-negative curvature(American Mathematical Society, 2024) Dong, Zheting; Escher, Christine; Searle, CatherineWe extend the equivariant classification results of Escher and Searle for closed, simply connected, Riemannian n-manifolds with non-negative sectional curvature admitting isometric isotropy-maximal torus actions to the class of such manifolds admitting isometric strictly almost isotropy-maximal torus actions. In particular, we prove that any such manifold is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to three. © 2024 American Mathematical Society.Item Expanding neutrino oscillation parameter measurements in NOvA using a Bayesian approach(American Physical Society, 2024) Acero, Mario A.; Acharya, B.; Adamson, P.; Anfimov, Nikolay V.; Antoshkin, A.; Arrieta-Diaz, E.; Asquith, L.; Aurisano, A.; Back, A.; Balashov, N.; Baldi, P.; Bambah, B.A.; Bat, A.; Bays, K.; Bernstein, R.; Bezerra, T.J.C.; Bhatnagar, V.; Bhattarai, D.; Bhuyan, B.; Bian, J.; Booth, A.C.; Bowles, Reed; Brahma, B.; Bromberg, C.; Buchanan, N.; Butkevich, A.; Calvez, S.; Carroll, T.J.; Catano-Mur, E.; Cesar, J.P.; Chatla, A.; Chaudhary, S.; Chirco, R.; Choudhary, B.C.; Christensen, A.; Coan, T.E.; Cooleybeck, A.; Cremonesi, L.; Davies, G.S.; Derwent, P.F.; Ding, P.; Djurcic, Z.; Dolce, M.; Doyle, D.; Dueñas Tonguino, D.; Dukes, E.C.; Dye, A.; Ehrlich, R.; Elkins, M.; Ewart, E.; Filip, P.; Franc, J.; Frank, M.J.; Gallagher, H.R.; Gao, F.; Giri, A.; Gomes, R.A.; Goodman, M.C.; Groh, M.; Group, R.; Habig, Alec; Hakl, F.; Hartnell, J.; Hatcher, R.; He, M.; Heller, K.; Hewes, V.; Himmel, A.; Jargowsky, B.; Jarosz, J.; Jediny, F.; Johnson, C.; Judah, M.; Kakorin, I.; Kaplan, D. M.; Kalitkina, A.; Kleykamp, J.; Klimov, O.; Koerner, L.W.; Kolupaeva, L.; Kralik, R.; Kumar, A.; Kuruppu, C.D.; Kus, V.; Lackey, T.; Lang, K.; Lasorak, P.; Lesmeister, J.; Lister, A.; Liu, J.; Lock, J.A.; Lokajicek, M.; Macmahon, M.; Magill, S.; Mann, W.A.; Manoharan, M.T.; Manrique Plata, M.; Marshak, M.L.; Martinez-Casales, M.; Matveev, V.; Mehta, B.; Messier, M.D.; Meyer, Holger; Miao, T.; Mikola, V.; Miller, W.H.; Mishra, S.; Mishra, S.R.; Mohanta, R.; Moren, A.; Morozova, A.; Mu, W.; Mualem, Leon; Muether, Mathew; Mulder, K.; Myers, D.; Naples, D.; Nath, A.; Nelleri, S.; Nelson, J.K.; Nichol, R.; Niner, E.; Norman, Andrew; Norrick, A.; Nosek, T.; Oh, H.; Olshevskiy, A.; Olson, T.; Pal, A.; Paley, Jonathan; Panda, L.; Patterson, R.B.; Pawloski, G.; Petrova, O.; Petti, R.; Plunkett, R.K.; Prais, L.R.; Rafique, A.; Raj, V.; Rajaoalisoa, M.; Ramson, B.; Rebel, B.; Roy, P.; Samoylov, O.; Sanchez, M.C.; Sánchez Falero, S.; Shanahan, Peter; Sharma, P.; Sheshukov, A.; Shukla, S.; Singha, D.K.; Shorrock, W.; Singh, I.; Singh, P.; Singh, V.; Smith, E.; Smolik, J.; Snopok, P.; Solomey, Nickolas; Sousa, A.; Soustruznik, K.; Strait, M.; Suter, Louise; Sutton, A.; Sutton, K.; Swain, S.; Sweeney, C.; Sztuc, A.; Tapia Oregui, B.; Tas, P.; Thakore, T.; Thomas, J.; Tiras, E.; Torun, Y.; Trokan-Tenorio, J.; Urheim, J.; Vahle, P.; Vallari, Z.; Vockerodt, K.J.; Vrba, T.; Wallbank, M.; Warburton, T.K.; Wetstein, M.; Whittington, D.; Wickremasinghe, D.A.; Wieber, T.; Wolcott, J.; Wrobel, M.; Wu, S.; Wu, W.; Xiao, Y.; Yaeggy, B.; Yankelevich, A.; Yonehara, K.; Yu, Y.; Zadorozhnyy, S.; Zalesak, J.; Zwaska, R.NOvA is a long-baseline neutrino oscillation experiment that measures oscillations in charged-current νμ→νμ (disappearance) and νμ→νe (appearance) channels, and their antineutrino counterparts, using neutrinos of energies around 2 GeV over a distance of 810 km. In this work we reanalyze the dataset first examined in our previous paper [Phys. Rev. D 106, 032004 (2022)PRVDAQ2470-001010.1103/PhysRevD.106.032004] using an alternative statistical approach based on Bayesian Markov chain Monte Carlo. We measure oscillation parameters consistent with the previous results. We also extend our inferences to include the first NOvA measurements of the reactor mixing angle θ13, where we find 0.071≤sin22θ13≤0.107, and the Jarlskog invariant, where we observe no significant preference for the CP-conserving value J=0 over values favoring CP violation. We use these results to examine the effects of constraints from short-baseline measurements of θ13 using antineutrinos from nuclear reactors when making NOvA measurements of θ23. Our long-baseline measurement of θ13 is shown to be consistent with the reactor measurements, supporting the general applicability and robustness of the Pontecorvo-Maki-Nakagawa-Sakata framework for neutrino oscillations. © 2024 authors.Item New lower background and higher rate technique for anti-neutrino detection using Tungsten 183 Isotope(Institute of Physics, 2024) Novak, Jarred; Solomey, Nickolas; Hartsock, Brooks; Doty, Brian; Folkerts, JonathanLow energy anti-neutrinos detected from reactors or other sources have typically used the conversion of an anti-neutrino on Hydrogen, producing a positron and a free neutron. This neutron is subsequently captured on a secondary element with a large neutron capture cross-section such as gadolinium or cadmium. With most neutron captures on gadolinium, it is possible to get two or three delayed gamma signals of known energy to occur. Modern experiments can make measurements with timing on the order of 25 ns. Fast electronics like these allow for the possibility of accessing the very fast signals from the nuclear de-excitation of a heavy nucleus following the prompt positron signal, rather than relying on traditional IBD techniques. We have found an isotope of tungsten, $^{183}$W that produces tantalum in the ground state at 2.094 MeV or the first excited state at 2.167 MeV. The excited state of $^{183}$Ta* emits a signature secondary gamma pulse of 73 keV with a 106 ns half-life. This offers a new delayed coincidence technique that can be used to identify anti-neutrinos with lower background noise. This allows for less shielding than required for modern inverse beta decay detectors. © 2024 IOP Publishing Ltd and Sissa Medialab.Item Equality conditions for the fractional superadditive volume inequalities(Springer, 2024) Meyer, MarkWhile studying set function properties of Lebesgue measure, F. Barthe and M. Madiman proved that Lebesgue measure is fractionally superadditive on compact sets in R$^n$. In doing this they proved a fractional generalization of the Brunn–Minkowski–Lyusternik (BML) inequality in dimension n=1. In this paper we will prove the equality conditions for the fractional superadditive volume inequalites for any dimension. The non-trivial equality conditions are as follows. In the one-dimensional case we will show that for a fractional partition (G,β) and nonempty sets A1,⋯,A$_m$⊆R, equality holds iff for each S∈G, the set ∑$_{i∈S}$A$_i$ is an interval. In the case of dimension n≥2 we will show that equality can hold if and only if the set ∑i=1$^m$A$_i$ has measure 0. © The Author(s) 2024.