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1. Global meta-analysis shows pervasive phosphorus limitation of aboveground plant production in natural terrestrial ecosystems

   https://doi.org/10.1038/s41467-020-14492-w  

   Hou, Enqing; Luo, Yiqi; Kuang, Yuanwen; Chen, Chengrong; Lu, Xiankai; Jiang, Lifen; Luo, Xianzhen; Wen, Dazhi (January 2020, Nature Communications)

   Abstract Phosphorus (P) limitation of aboveground plant production is usually assumed to occur in tropical regions but rarely elsewhere. Here we report that such P limitation is more widespread and much stronger than previously estimated. In our global meta-analysis, almost half (46.2%) of 652 P-addition field experiments reveal a significant P limitation on aboveground plant production. Globally, P additions increase aboveground plant production by 34.9% in natural terrestrial ecosystems, which is 7.0–15.9% higher than previously suggested. In croplands, by contrast, P additions increase aboveground plant production by only 13.9%, probably because of historical fertilizations. The magnitude of P limitation also differs among climate zones and regions, and is driven by climate, ecosystem properties, and fertilization regimes. In addition to confirming that P limitation is widespread in tropical regions, our study demonstrates that P limitation often occurs in other regions. This suggests that previous studies have underestimated the importance of altered P supply on aboveground plant production in natural terrestrial ecosystems. 

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2. A simple proof of reflexivity and separability of N^{1,p} Sobolev spaces

   https://doi.org/10.54330/afm.127419  

   Alvarado, Ryan; Hajłasz, Piotr; Malý, Lukáš (October 2022, Annales Fennici Mathematici)

   We present an elementary proof of a well-known theorem of Cheeger which states that if a metric-measure space \(X\) supports a \(p\)-Poincaré inequality, then the \(N^{1,p}(X)\) Sobolev space is reflexive and separable whenever \(p\in (1,\infty)\). We also prove separability of the space when \(p=1\). Our proof is based on a straightforward construction of an equivalent norm on \(N^{1,p}(X)\), \(p\in [1,\infty)\), that is uniformly convex when \(p\in (1,\infty)\). Finally, we explicitly construct a functional that is pointwise comparable to the minimal \(p\)-weak upper gradient, when \(p\in (1,\infty)\). 

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3. Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian

   https://doi.org/10.1090/tran/8903  

   Bañuelos, Rodrigo; Mariano, Phanuel; Wang, Jing (August 2023, Transactions of the American Mathematical Society)

   For domains in R d \mathbb {R}^d , d ≥ 2 d\geq 2 , we prove universal upper and lower bounds on the product of the bottom of the spectrum for the Laplacian to the power p > 0 p>0 and the supremum over all starting points of the p p -moments of the exit time of Brownian motion. It is shown that the lower bound is sharp for integer values of p p and that for p ≥ 1 p \geq 1 , the upper bound is asymptotically sharp as d → ∞ d\to \infty . For all p > 0 p>0 , we prove the existence of an extremal domain among the class of domains that are convex and symmetric with respect to all coordinate axes. For this class of domains we conjecture that the cube is extremal. 

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4. MBSE Online Professional Development Learning Modules Data

   https://doi.org/10.4231/3DR2-VY15  

   Douglas, Kerrie; Huang, Wanju; Li, Tiantian; Marcos, Leonardo; Huang, Wanju (January 2025, Purdue University Research Repository)

   <p>The data was downloaded and captured through MBSE online learning modules. Deidentified learners&#39; activities within the modules, such as clickstreams and assignments, were captured in the data/</p> <p>&bull; All files here are student submissions to one or more of the modules in the MBSE program.</p> <p>&bull; All user data has either been removed or redacted from the submission.</p> <p>&bull; &ldquo;Andrew Hurt&rdquo; is not a student and none of these files came from him. He is the person who did the redaction.</p> <p>&bull; The naming structure of the files is as follows: [Module number]-[Module Offering Date]-[Submission Number]-[Part Number of Submission]. Example: M5-040422-S1-Part3. This file is from Module 5, which was offered on April 4, 2022, it is submission 1, and part 3 of submission 1.</p> <p>&bull; Note that submissions within or between modules are not necessarily connected to specific students. So &ldquo;Submission 1&rdquo; from module 5 is not the same user as &ldquo;Submission 1&rdquo; from module 6.</p> <p>&bull; Not all submissions have multiple parts.</p> <p>&bull; No .mdzip files (proprietary MagicDraw software files) have been included in this list.</p> <p>&bull; If a module or folder in the module is missing content from a particular offering, it is because either no one submitted anything or because the file was a .mdzip file and was not downloaded.</p> <p>&nbsp;</p> 

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5. Centers of Sylow subgroups and automorphisms

   https://doi.org/10.1007/s11856-020-2064-2  

   Glauberman, George; Guralnick, Robert; Lynd, Justin; Navarro, Gabriel (September 2020, Israel Journal of Mathematics)

   Suppose that p is an odd prime and G is a finite group having no normal non-trivial p′-subgroup. We show that if a is an automorphism of G of p-power order centralizing a Sylow p-group of G, then a is inner. 

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