Suppose that f (x) E 1[8[x1, ... , xn] and g(x) E 1[8[x1, ... , xn] are two real polynomials of degree d in n variables. If the polynomials f and g are the same up to orthogonal symmetry, a natural question is then what element of the orthogonal group induces the orthogonal symmetry; i.e. to find the element R E O(n) such that f (R inverted perpendicular x) = g(x). One may directly solve this problem by constructing a nonlinear system of equations induced by the relation f (R inverted perpendicular x) = g(x) along with the identities of the orthogonal group. However, this approach becomes quite computationally expensive for larger values of nand d. To give an alternative and significantly more scalable solution to this problem, we introduce the concept of Polynomial-Weighted Principal Component Analys is (PW-PCA). We in particular show how PW-PCA can be effectively computed and how these techniques can be used to obtain a certificate of orthogonal equivalence, that is we find the R E O(n) such that f (R inverted perpendicular x) = g(x). (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Bio-oil obtained from biomass pyrolysis needs further hydrodeoxygenation (HDO) for its suitability in fuel applications. However, catalysts studied to date suffer from coke formation and low yields. In this study, Cu-based catalysts, prepared using the wet impregnation method, were characterized, and their performance in the twostep HDO (mild stabilization followed by severe treatment in a batch reactor) was investigated. HDO in the presence of a Cu/Al2O3 catalyst achieved a maximum 50.5 wt.% treated oil yield and 67.6% carbon conversion compared to Co-Mo/Al2O3 and Co/Al2O3 catalysts. The measured coke formation was less than 3% for the Cubased catalyst, which was attributed to controlled deoxygenation and hydrogenation. The high heating value of the treated bio-oil ranged from 31.4 to 34.6 MJ kg-1. Additionally, gas chromatography-mass spectrometry showed that the treated bio-oils were rich in alkyl phenols and hydrocarbons, with the concentration ranging from 4.6 to 55.3 and 15.9 to 32.0 wt.% of total, respectively. Direct deoxygenation, hydrogenation, and demethoxylation were the significant reactions leading to the formation of hydrocarbons. Based on the findings, Cu-based catalysts can be used for HDO of pyrolysis bio-oil to obtain valuable chemicals and fuels.
Let Cm-P(n) k stand for the space of globally Cm, m >= 1 and locally piecewise n-dimensional polynomials of degree k on n-dimensional simplicial grids. We construct bases of Cm-Pk(3), k >= 23m+1 and Cm-P(4) k , k >= 24m+1 finite elements on 3D tetrahedral and 4D simplicial grids, respectively, and prove the uni-solvency and the Cm continuity of the finite element spaces Cm-P(3) k and Cm-P(4) k .
Saltwater intrusion (SWI) is rapidly transforming coastal agricultural landscapes through rising soil salinity, altered nutrient cycling, and declining crop productivity. On Maryland’s Lower Eastern Shore (USA), we examined how salinization affects nitrogen (N) in soils, porewater, and plants under land management strategies representing common farmer responses to SWI: perennial grass establishment, restoration, and abandonment. Across three saltwater-intruded farms and over three years, soil electrical conductivity (EC1:5) increased two- to fourfold, soil sodium (Na) four- to sixfold, and porewater electrical conductivity (EC) twofold, suggesting these fields are rapidly salinizing. Topsoil (0–10 cm) Na and EC1:5 were strongly correlated (R2 = 0.88), while relationships between topsoil Na and N were significant but modest (R2 = 0.33), suggesting that Na explained only part of the variation in soil N pools. Soil inorganic N (nitrate and ammonium) declined, indicating depletion of available N pools under progressing salinization. However, aboveground biomass N increased substantially under Panicum virgatum (perennial grass establishment) and Spartina patens (restoration), accumulating four times more N than abandoned plots. These results demonstrate that perennial grass systems can maintain productivity and accumulate greater aboveground biomass N, even as fields salinize. In contrast, abandoned fields exhibited lower biomass and reduced standing biomass N pools. Establishing salt-tolerant perennials therefore represents an effective strategy for coastal farms transitioning due to sea-level rise and SWI. These findings provide actionable guidance for easement and conservation programs seeking to support adaptive management of salinizing agricultural lands.
Building on Frenkel’s century-old theoretical foundation for understanding defects, modern computational methods for studying defects in semiconductors and insulators have evolved from the initial interpretive tools to predictive approaches capable of guiding technological applications. In this article, we examine the current state and future directions of computational approaches for studying point defects in semiconductors. Density functional theory (DFT) has become the primary tool for defect calculations, with hybrid functionals proving essential for accurately describing electronic structure and charge localization effects that standard DFT cannot capture. We discuss recent advances in treating excited states and calculating experimentally observable properties from first principles. Current methods can predict thermodynamic properties within 0.1 eV accuracy and luminescence spectra with meV precision through sophisticated electron–phonon coupling treatments. Emerging techniques include quantum-embedding methods and machine learning interatomic potentials that promise to extend current capabilities while reducing computational costs. Future developments in exchange–correlation functionals and beyond-DFT methods offer exciting possibilities for further advancing computational defect physics.
