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   https://doi.org/10.1093/imrn/rnae039  

   Kedlaya, Kiran S ( March 2024 , International Mathematics Research Notices)

   We prove that in either the convergent or overconvergent setting, an absolutely irreducible $F$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $p$, further equipped with actions of the partial Frobenius maps, is an external product of $F$-isocrystals over the multiplicands. The corresponding statement for lisse $\overline{{\mathbb{Q}}}_{\ell }$-sheaves, for $\ell \neq p$ a prime, is a consequence of Drinfeld’s lemma on the fundamental groups of absolute products of schemes in characteristic $p$. The latter plays a key role in V. Lafforgue’s approach to the Langlands correspondence for reductive groups with $\ell $-adic coefficients; the $p$-adic analogue will be considered in subsequent work with Daxin Xu.

    

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   Wang, Xikui ; Carey, Michael J. ( July 2019 , Proceedings of the VLDB Endowment)
3. Tabula Rasa for n ‐Cz silicon‐based photovoltaics

   https://doi.org/10.1002/pip.3068  

   LaSalvia, Vincenzo ; Youssef, Amanda ; Jensen, Mallory A. ; Looney, Erin E. ; Nemeth, William ; Page, Matthew ; Nam, Wooseok ; Buonassisi, Tonio ; Stradins, Paul ( August 2018 , Progress in Photovoltaics: Research and Applications)

   High‐temperature annealing, known asTabula Rasa(TR), proves to be an effective method for dissolving oxygen precipitate nuclei inn‐Cz silicon and makes this material resistant to temperature‐induced and process‐induced lifetime degradation.Tabula Rasais especially effective inn‐Cz wafers with oxygen concentration >15 ppma. Vacancies, self‐interstitials, and their aggregates result from TR as a metastable side effect. Temperature‐dependent lifetime spectroscopy reveals that these metastable defects have shallow energy levels ~0.12 eV. Their concentrations strongly depend on the ambient gases during TR because of an offset of the thermal equilibrium between vacancies and self‐interstitials. However, these metastable defects anneal out at typical cell processing temperatures ≥850°C and have little effect on the bulk lifetime of the processed cell structures. Without dissolving built‐in oxygen precipitate nuclei, high‐temperature solar cell processing severely degrades the minority carrier lifetimes to below 0.1 millisecond, while TR‐treatedn‐Cz wafers after the cell processing steps exhibit carrier lifetimes above 2.2 milliseconds.

    

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4. Allometric relationships for Quercus gambelii and Robinia neomexicana for biomass estimation following disturbance

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   Krofcheck, Dan J. ; Litvak, Marcy E. ; Hurteau, Matthew D. ( October 2019 , Ecosphere)
5. Counting and Enumerating Optimum Cut Sets for Hypergraph k -Partitioning Problems for Fixed k

   https://doi.org/10.1287/moor.2022.0259  

   Beideman, Calvin ; Chandrasekaran, Karthekeyan ; Wang, Weihang ( December 2023 , Mathematics of Operations Research)

   We consider the problem of enumerating optimal solutions for two hypergraph k-partitioning problems, namely, Hypergraph-k-Cut and Minmax-Hypergraph-k-Partition. The input in hypergraph k-partitioning problems is a hypergraph [Formula: see text] with positive hyperedge costs along with a fixed positive integer k. The goal is to find a partition of V into k nonempty parts [Formula: see text]—known as a k-partition—so as to minimize an objective of interest. (1) If the objective of interest is the maximum cut value of the parts, then the problem is known as Minmax-Hypergraph-k-Partition. A subset of hyperedges is a minmax-k-cut-set if it is the subset of hyperedges crossing an optimum k-partition for Minmax-Hypergraph-k-Partition. (2) If the objective of interest is the total cost of hyperedges crossing the k-partition, then the problem is known as Hypergraph-k-Cut. A subset of hyperedges is a min-k-cut-set if it is the subset of hyperedges crossing an optimum k-partition for Hypergraph-k-Cut. We give the first polynomial bound on the number of minmax-k-cut-sets and a polynomial-time algorithm to enumerate all of them in hypergraphs for every fixed k. Our technique is strong enough to also enable an [Formula: see text]-time deterministic algorithm to enumerate all min-k-cut-sets in hypergraphs, thus improving on the previously known [Formula: see text]-time deterministic algorithm, in which n is the number of vertices and p is the size of the hypergraph. The correctness analysis of our enumeration approach relies on a structural result that is a strong and unifying generalization of known structural results for Hypergraph-k-Cut and Minmax-Hypergraph-k-Partition. We believe that our structural result is likely to be of independent interest in the theory of hypergraphs (and graphs).

   Funding: All authors were supported by NSF AF 1814613 and 1907937.

    

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