Let R be a standard graded polynomial ring over a field k. The paper focuses on homogeneous ideals J subset of R of codimension 2 generated by three forms of the same degree d >= 2 that are almost Cohen-Macaulay, i.e., of homological dimension 2. Based on the structure of the minimal graded free resolution of J and numerical data inspired by the corresponding shifts, one introduces the notion of a level matrix associated with these data. The main result provides a complete characterization of an almost Cohen-Macaulay 3generated ideal J of codimension 2 in terms of the existence of a related level matrix for which J arises as the ideal of its maximal minors that fix a submatrix. One provides algebraic and geometric examples illustrating the results. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a threedimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product B & times; & Ropf;, where B is a lambda-Einstein surface or one of the examples obtained by L. B & eacute;rard Bergery and described in Besse's book [6, Section 9.118]. Moreover, we prove that any asymptotically flat n-dimensional quasi-Einstein manifold with lambda = 0 is necessarily Ricci-flat. (c) 2026 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Rising extreme climate events threaten agricultural production and food security. Climate adaptation strategies that enhance soil health are key to strengthening the stability and resilience of agricultural systems. This study reveals how crop diversification influences soil health functions and yield stability, by combining soil, yield, and climate data from thirteen farmer-led experiments in southern Brazil, a region highly exposed to climate variability. Twelve soil health indicators were integrated into four latent functions via factor analysis (79% of total variance explained) and linked to crop diversification, soil texture, and crop yield through structural equation modeling (~76% of variance explained in crop yield). Crop diversification, particularly combined crop rotation and cover crop mixtures, were positively associated with soil water storage independently of soil texture (β = 0.41). Among the four soil health functions, biochemical regulation of soil processes was the most significantly linked to crop yield (R²m = 0.31). Yield instability was the strongest direct predictor of crop yield (β = −0.61). On average, systems integrating crop rotation with multispecies cover crops achieved yields 1.76 times higher than the state average, and with markedly lower instability (24%) than conventional or single-practice systems (1.08 times the average; 33–39% instability, respectively). These findings identify yield stability as a key component of climate adaptation, and support integrated crop diversification as a promising strategy for regenerative agriculture and climate policy in Brazil.
This paper introduces a novel parallel hybrid algorithm, based on an accelerated shrinking projection method, for solving the Split Monotone Variational Inclusion problems with multiple output sets in Hilbert spaces. Under an appropriate set of conditions, we establish the strong convergence of the proposed algorithm. Its practical viability is further demonstrated through a numerical experiment. The results obtained herein generalize and improve upon several existing findings in the literature.
Background: The METER study (NCT05444972) described real-world treatment patterns and outcomes for myelofibrosis across 14 countries. Given the potential regional variability, the present analysis evaluates the Brazilian cohort within METER to investigate local treatment approaches and patient results. Methods: This subanalysis of the METER study included all patients enrolled in Brazil, based on the same eligibility criteria as in the global study. The primary objective was to describe real-world treatment patterns for myelofibrosis. Main results: Of 50 eligible patients enrolled in Brazil, 37 (74%) presented with primary myelofibrosis. At diagnosis, nine (20.9%) individuals had high-risk and 14 (32.6%) intermediate-2 risk disease, mostly using the Dynamic International Prognostic Scoring System (DIPSS) criteria. Among patients with available data (n = 18), 50% had a high-risk mutation at diagnosis. Hydroxyurea was the most frequent initial therapy (n = 32; 64%), followed by ruxolitinib (n = 12; 24%). A total of 23 patients (46%) had discontinuation or change of initial therapy, with a median overall duration of first-line treatment of 29.9 months (95% confidence interval: 21.5 to not estimable). The median overall survival from index date was 45.5 months (95% confidence interval: 28.5 to not estimable), with 1- and 2-year survival rates of 87.3% and 74.7%, respectively. Conclusion: The treatment patterns in Brazil reflect insufficient access to novel agents. Whether the shorter observed median overall survival compared with the overall METER study is a consequence of insufficient access to treatment or of different biological features warrants further investigation.
