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1. On n -dependent groups and fields II

   https://doi.org/10.1017/fms.2021.35  

   Chernikov, Artem; Hempel, Nadja (January 2021, Forum of Mathematics, Sigma)

   null (Ed.)

   Abstract We continue the study of n -dependent groups, fields and related structures, largely motivated by the conjecture that every n -dependent field is dependent. We provide evidence toward this conjecture by showing that every infinite n -dependent valued field of positive characteristic is henselian, obtaining a variant of Shelah’s Henselianity Conjecture in this case and generalizing a recent result of Johnson for dependent fields. Additionally, we prove a result on intersections of type-definable connected components over generic sets of parameters in n -dependent groups, generalizing Shelah’s absoluteness of $$G^{00}$$ in dependent theories and relative absoluteness of $$G^{00}$$ in $$2$$ -dependent theories. In an effort to clarify the scope of this conjecture, we provide new examples of strictly $$2$$ -dependent fields with additional structure, showing that Granger’s examples of non-degenerate bilinear forms over dependent fields are $$2$$ -dependent. Along the way, we obtain some purely model-theoretic results of independent interest: we show that n -dependence is witnessed by formulas with all but one variable singletons; provide a type-counting criterion for $$2$$ -dependence and use it to deduce $$2$$ -dependence for compositions of dependent relations with arbitrary binary functions (the Composition Lemma); and show that an expansion of a geometric theory T by a generic predicate is dependent if and only if it is n -dependent for some n , if and only if the algebraic closure in T is disintegrated. An appendix by Martin Bays provides an explicit isomorphism in the Kaplan-Scanlon-Wagner theorem. 

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2. Subsurface Soil Carbon and Nitrogen Losses Offset Surface Carbon Accumulation in Abandoned Agricultural Fields

   https://doi.org/10.1007/s10021-022-00807-z  

   Yang, Yi; Knops, Johannes M. (November 2022, Ecosystems)

   Abandoned agricultural fields (old fields) are thought to accumulate soil organic matter (SOM) after cultivation cessation. However, most research on old fields soil carbon (C) and nitrogen (N) sequestration has focused on the surface (10 or 30 cm depth) and overlooked their dynamics below 30 cm. This study quantified C and N stock change in both the surface and subsurface with repeated inventories over 13 years. We conducted repeated soil surveys in 8 old fields that form a 64-year chronosequence at Cedar Creek Ecosystem Science Reserve (CCESR), Minnesota in 2001 and 2014. On average, soil C and N accumulated by 16.5 ± 14.5 g C m−2 y−1 and 1.0 ± 1.1 g N m−2 y−1 in the surface (0–20 cm). In contrast, we found soil C and N decreased by 78.9 ± 26.3 g C m−2 y−1 and 12.9 ± 2.42 g N m−2 y−1 in the subsurface (20–100 cm). The C and N losses in the subsurface soil were correlated with low deep root biomass; the majority of roots are located in the top 20 cm of soil. Such root distribution may be attributed to the continuing dominance of nonnative and shallow-rooted C3 grasses and the lack of legumes after field abandonment. This study shows that agriculture has a long legacy effect after abandonment on subsurface soil C and N. Some abandoned agricultural fields can continue to lose C and N because surface C and N accumulation does not offset the ongoing deeper soil C and N losses. 

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3. Determinantal Representations and the Image of the Principal Minor Map

   https://doi.org/10.1093/imrn/rnae038  

   Al_Ahmadieh, Abeer; Vinzant, Cynthia (March 2024, International Mathematics Research Notices)

   Abstract In this paper we explore determinantal representations of multiaffine polynomials and consequences for the image of various spaces of matrices under the principal minor map. We show that a real multiaffine polynomial has a definite Hermitian determinantal representation if and only if all of its so-called Rayleigh differences factor as Hermitian squares and use this characterization to conclude that the image of the space of Hermitian matrices under the principal minor map is cut out by the orbit of finitely many equations and inequalities under the action of $$(\textrm{SL}_{2}(\mathbb{R}))^{n} \rtimes S_{n}$$. We also study such representations over more general fields with quadratic extensions. Factorizations of Rayleigh differences prove an effective tool for capturing subtle behavior of the principal minor map. In contrast to the Hermitian case, we give examples to show for any field $$\mathbb{F}$$, there is no finite set of equations whose orbit under $$(\textrm{SL}_{2}(\mathbb{F}))^{n} \rtimes S_{n}$$ cuts out the image of $$n\times n$$ matrices over $${\mathbb{F}}$$ under the principal minor map for every $$n$$. 

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4. No‐till establishment improves the climate benefit of bioenergy crops on marginal grasslands

   https://doi.org/10.1002/saj2.20082  

   Ruan, Leilei; Robertson, G_Philip (June 2020, Soil Science Society of America Journal)

   Abstract Expanding biofuel production is expected to accelerate the conversion of unmanaged marginal lands to meet biomass feedstock needs. Greenhouse gas production during conversion jeopardizes the ensuing climate benefits, but most research to date has focused only on conversion to annual crops and only following tillage. Here we report the global warming impact of converting USDA Conservation Reserve Program (CRP) grasslands to three types of bioenergy crops using no‐till (NT) vs. conventional tillage (CT). We established replicated NT and CT plots in three CRP fields planted to continuous corn, switchgrass, or restored prairie. For the 2 yr following an initial soybean year in all fields, we found that, on average, NT conversion reduced nitrous oxide (N₂O) emissions by 50% and CO₂emissions by 20% compared with CT conversion. Differences were higher in Year 1 than in Year 2 in the continuous corn field, and in the two perennial systems the differences disappeared after Year 1. In all fields net CO₂emissions (as measured by eddy covariance) were positive for the first 2 yr following CT establishment, but following NT establishment net CO₂emissions were close to zero or negative, indicating net C sequestration. Overall, NT improved the global warming impact of biofuel crop establishment following CRP conversion by over 20‐fold compared with CT (−6.01 Mg CO₂e ha⁻¹ yr⁻¹for NT vs. −0.25 Mg CO₂e ha⁻¹ yr⁻¹for CT, on average). We also found that Intergovernmental Panel on Climate Change estimates of N₂O emissions (as measured by static chambers) greatly underestimated actual emissions for converted fields regardless of tillage. Policies should encourage adoption of NT for converting marginal grasslands to perennial bioenergy crops to reduce C debt and maximize climate benefits. 

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5. On realization of isometries for higher rank quadratic lattices over number fields

   https://doi.org/10.1090/tran/8670  

   Chan, Wai Kiu; Li, Han (July 2022, Transactions of the American Mathematical Society)

   Let F F be a number field, and n ≥ 3 n\geq 3 be an integer. In this paper we give an effective procedure which (1) determines whether two given quadratic lattices on F n F^n are isometric or not, and (2) produces an invertible linear transformation realizing the isometry provided the two given lattices are isometric. A key ingredient in our approach is a search bound for the equivalence of two given quadratic forms over number fields which we prove using methods from algebraic groups, homogeneous dynamics and spectral theory of automorphic forms. 

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